Data sufficiency (DS) checks students ability to answer a question with the information provided in the question. Therefore, these questions require maximum clarity of fundamentals. The techniques introduced in this session provide you the guideline to approach DS questions of two-statement type, most effectively.
The Data Sufficiency Format:
A data sufficiency (DS) question consists of three parts. The actual question is called the question stem.
e.g. Is P > 1?
That’s all you will be given. Sometimes the question is literally a question, like the preceding example. Sometimes the ‘question’ is actually a statement, telling you to do something. e.g.
Mr Prasad drives at 80 mph in 5 hr. Find the distance that Mr Prasad drives. or like this: Find the rate at which oil flows into a container.
The second part of the DS question is statement 1. It may be like this:
1. P+ Q > 1
or
1. Mr Prasad drives thrice as far as his brother, but at half his speed.
or
1. The container has a capacity of 18 Tons
The third part of the question is statement 2. It may be like this:
2. p + q > 1
or
2. Mr Prabhu starts 300 miles east of the point at which his sister started.
or
2. The container is 2/5th full by evening.
You need to decide whether the data (the information) is sufficient to answer the question and hence the title, Data Sufficiency. No answer choices are given at the end of the DS questions. Instead, instructions are given at the beginning of the section as illustrated below.
Question Format:
Direction: Each of the following problems consist of a question followed by two statements, I and II. You must determine whether the information given by the statements is sufficient to answer the question asked. In addition to the information provided in the statements, you should rely on your knowledge of mathematics and ordinary facts (such as the number of seconds in a minute).
(a) if the question can be answered by using one of the statements alone, but cannot be answered using the other statement alone.
(b) if the question can be answered by using either statement alone.
(c) if the question can be answered by using both statements together, but cannot be answered using either statement alone.
(d) if the question cannot be answered even by using both statements together.
The four answer choices in detail:
The following problems illustrate the meanings of the four answer categories.
1. Choice (a)
In a problem, the answer choice is (a) if statement I ALONE is sufficient to answer the question asked, but statement II alone is not sufficient to answer the question asked
Example:
Is Raja older than Ramu?I. Sita is 4 years younger than Raja and 2 years younger than Ramu.
II. The average age Raja and Ramu is 21 years.
Statement I is by itself sufficient to answer the question asked. If Sita is 4 years younger, then Raja is 2 years younger than Ramu, then Raja must be 2 years older than Ramu. Statement II, however, is not by itself sufficient to answer the question. From the statement about the average of their ages in years, you cannot draw any conclusion about their respective ages. Since statement I alone is sufficient, but statement II is not, the correct answer choice is (a).
2. Choice (b)
In a problem, the answer choice is (B) if statement I ALONE is sufficient to answer the question asked, but statement I alone is not sufficient to answer the question asked
Example:
If x, y and z are consecutive integers, is y even?
I. x < y < z
II. xz is odd integer.
Statement I is not sufficient to answer the question asked. Although statement I describes the order of the integers, it provides no information about which elements of the sequence are even and which are odd. Statement II, however, is by itself sufficient to determine whether y is even or not. If xz is odd, then both x and z must be odd integers. In the series of 3 consecutive integers, at least one of the integers must be even. Therefore, y must be even. Since statement II alone is sufficient to answer the question asked, but statement I alone is not, the correct answer choice is (a).
3. Choice (c)
In any problem the answer choice is (c) if each statement alone is not sufficient to answer the question but the two statements taken together answer the question.
Example:
How many students are enrolled in Sastri's Quant class?
I. If 3 more students sign up for the class and no one drops out, more than 35 students will have enrolled in the class.
II. If 4 students drop out of the class and no more sign-up, fewer than 30 students will have enrolled in the class.
Statement I alone is not sufficient to answer the question asked, but I does imply that at least 33 students are enrolled in the class. Statement II alone is not sufficient to answer the question asked, but II does imply that no more than 33 students are enrolled in the class. Although neither statement alone is sufficient to answer the question, the two statements taken together are sufficient to answer the question that the number of students enrolled in the class is 33. Since neither statement alone is sufficient to answer the question but both together are sufficient, the correct answer choice is (c).
4. Choice (d)
In any problem the answer choice is (d) if the two statements are not capable of answering the question asked, either alone or when taken together.
Example:
Is x < y?I. – 0.26 < x < 0.4
II. 0.11 < y < 0.38
Statement I alone is not sufficient to answer the question asked. Although statement I defines a range for u, the statement provides no information about v. Similarly, statement II alone is not sufficient to answer the question asked. Statement II defines a range for v but provides no information about u. Since the two statements, even when taken together, do not provide enough information to answer the question asked, the correct answer choice is (d).
Flow chart for solving DS questions:
Knowing the Traps:
Data sufficiency questions have many tricks and traps. Here are some examples on how easily you can fall for the traps.
Key point to remember:
1. A unique answer: The data statements (alone or together) should be able to provide you with a unique answer to the question asked. Only then they will be considered as valid.
Example:
What is the value of x?I.x2 = 16
II. x > –10
From statement I we can see that x = +4 or x = –4. Now you may be tempted to consider this as a valid answer, as we have determined the value of x. But since this is not a unique answer, such an answer is not valid. So statement II alone is not sufficient to answer the question. Statement II does not give a definite answer either as both +4 and –4 are less than 10. Hence, the correct answer choice to this question is (d), as neither of the statements (either alone or taken together) helps us get a unique value of x.
Key point to remember:
2. A statement that merely states a mathematics formula is not sufficient to answer the question.
Sometimes a statement gives you a mathematics rule, which does not actually help you to acquire relevant data to answer the question
Example:
Angles a and b are alternate interior angles. What is the measure of angle a? (1) a + b = 180
You already know that a + b = 180 because of the basic geometry rule that the sum of alternate interior angles is 180. When a statement repeats a mathematical formula, it does not give you any new information and thus is not sufficient to answer the question.
What is the area of the trapezoid ABCD? (1) The area of the trapezoid is12×(Base1+Base2)×Height
Again statement I just gives a mathematical formula. While you may be delighted with the information because you personally do not have a clue what the formula for the area of a trapezoid is statement I alone does not give you anything you can use to answer the question, in terms of the values of the bases and the height.
Key point to remember:
3. A statement that only repeats information given in the question stem is not sufficient to answer the question. Sometimes you are given information in a statement that you already know from the question stem.
Example:
When a glass is half full, it contains 5 L of water. What is the weight of the glass when it is full?
(i) The capacity of the glass is 10 L.
It is obvious that if the half-full glass is 5 L, naturally the full glass is 10 L.
No new information is given.
Did you notice the trap built into this question? The question stem asked for the weight of the glass, not the capacity. If you thought you had to find the capacity, you probably thought statement I did the jo(b) Always keep in mind carefully what you are being asked.
Key point to remember:
4. Treat each statement separately, do not transfer information from one statement to the other.
A problem may give you something useful in statement I ... and then give you a variation of that same information in statement II. Many people choose (c), thinking that statement I and II both are required to answer the question.
Example:
What is probability of drawing a red ball, if a bag contains red, blue and green balls.
I. Total balls in the bag are 30
II. The balls are in the ratio 1:2:3
Here you may think that Statement I is not sufficient to answer as no details about the balls were presnet. After reading Statement II you may fee that, now i can calculate the number of balls of each colour so Statement I and II are required. But to calculate probability we just need the ratio's of the balls. So only statement II is enough. Choice (b).
Key point to remember:
5. Choice (c) means that both statements must be used. This is one of the favourite traps. Do not choose (c) just because one statement is helpful.
In order to choose (c) you must absolutely, positively need both the statements.
Example:
What is the perimeter of a rectangle with area 100?
I. The ratio of the length to the width is 4 : 1.
II. The sum of the interior angles of the rectangle is 360.
If you chose (c), you fell for the trap. The correct answer is (a) because statement I alone is sufficient to answer the question. To find a perimeter, you add the lengths of the sides. You already have information that the area is 100. The area of a rectangle is equal to the product of length and breadth. You do not have to come up with the actual number, just determine whether the data is sufficient to do so. Statement II gives you the sum of the interior angles. First decide whether that alone is sufficient information to answer the question. It is not. How about using both statements together? Statement II is nice to know, but it certainly is not necessary to know. (Besides, you already know that the interior angles of a rectangle sum up to 360°.) Do not fall for the trap of choosing (c) just because both statements are true. You choose (c) only when one statement alone is not sufficient and it takes the combined information of both statements to get you to the right answer.
Key point to remember:
6. Do not forget to try both statements I and II together.
Students in a big rush often eliminate choice (a) because statement I does not work. Then they eliminate choice (b) because statement II does not work. They immediately head to choice (d), thinking that there is no way to answer the question. They forget that there is one more possibility: maybe combining the two pieces of information will do the job.
Example:
(A) Is u > v?
I.u2=v2
II. u, v > 0
Look at statement I alone. You may be tempted to say that if the squares of 2 numbers are identical, those 2 numbers are identical. Wrong, one of those numbers could be positive while the other could be negative. Say that u = –2 and v = 2. Then u2 = v2, but u is not equal to v (and you do not know whether u > v because u could be negative and v positive, or v could be negative and u positive). Statement I alone is not sufficient to answer the question. Eliminate choice (A).
Look at statement II alone. Certainly, knowing that u and v are greater than zero does not tell you which is greater, u or v. Eliminate choice (B). At this point many students make the mistake of choosing (D), saying there is not enough information to answer the question. Wrong again. Combine the two statements. If both u and v are greater than zero, then they must be the same numbers for their squares to be equal. In other words, they would no longer be 2 and –2; they would be 2 and 2 (or any other number). Both statements together are necessary to answer the question. Choose (c). You might argue that the answer must be (d) because the answer to the question ‘Is u > v?’ is ‘No, u is not greater than v’. Keep in mind that the answer to the question can be yes or no, as long as an answer is possible.
If you have a few minutes left at the end of a data sufficiency section, go back and double-check all those questions you answered with (d). You may be able to gain a few points by extracting yourself from the trap you had fallen into earlier.
(B) Is K a prime number?
I. K > 10
II. K divided by 2 has a remainder 0.
Statement I alone is not sufficient. Some numbers greater than 10 are prime, like 11. Some numbers greater than 10 are composite, like 12. Eliminate choice (A).
Statement II alone is not sufficient. When a number divided by 2 has no remainder, that number is even. You may be thinking that there are no even prime numbers and statement II alone is sufficient. But there is one even prime number, i.e. 2. Therefore, statement II alone is not sufficient because the answer could be yes or no. Eliminate choice (B).
At this point most students get lazy and choose (d). Put the two statements together. You know from statement II that the number must be even. You know from statement I that the number must be greater than 10. Because the only even prime number is 2, any even number greater than 2 must be composite, not prime. The answer to the question is ‘no’, c is not prime. Because you can answer the question based on both statements. The answer is (c).
Key point to remember:
7. If you can answer the question stem ‘no’, you have sufficient data to answer the problem.
All you need to know about a problem is whether the data is sufficient to answer the question or solve the problem. If the answer to the question is yes or if the answer is no, you have enough data.
Example:
(A) Is r even?
I. r + s is odd.
II. s is even.
The answer is (c). Statement I alone is not sufficient to answer the question. Knowing that r + s is odd will not tell you whether r is even. If s is even, then r is odd, because an even number and an odd number sum up to an odd number. If s is odd, then r is even, for the same reason. Put the two statements together. If s is even, and r + s is odd, then r must be odd. The answer to the question is no, but there is an answer to the problem. The answer to the question ‘Is r even?’ is ‘No, r is not even’. But because you can give an answer, even though that answer is negative, you do have enough data to answer the problem.
(B) Is Babu older than Raghu?
I. The ratio of Raghu’s age to Babu’s age is 7 : 4.
II. In 6 years Raghu will be half as old as he is now.
Statement I alone is sufficient to answer the question. If the ratio of the their ages is 7 : 4, then Raghu, the 7 part, is older than Babu, the 4 part. It makes no difference that the answer to the question is no; you are able to solve the problem. A ‘no’ is as good as a ‘yes’. Statement II alone is not sufficient. You can use it to find out how old Raghu is now, but you have no information about his age relative to Babu’s age.
Did you choose (c)? If so, you thought you actually had to find the exact ages of the two. True, you would need the information in statement II to get the age of Raghu, then the information in statement I to find the age of Babu. But you do not have to find the exact ages. You are not asked the ages; only whether Raghu is older than Babun. Just answer the question and proceed in stead of trying to add more to it.
Key point to remember:
9. As soon as you know the data is sufficient to answer the question, stop.
Do not work out these DS problems right through till the end. You should not care what the final answer is. The name of the game here is not problem-solving, in which you — logically enough — actually solve the problem. The section is called data sufficiency. You need only a simple yes or no: to say whether the data is sufficient or not. You do not have to actually solve the problem.
(A) What is the volume of a right circular cylinder? I. The area of the base of the figure is 196.
II. The height of the figure is 16.
Be smart enough not to actually work out the volume. The volume of a cylinder is the product of the area of the base and its height. You know the area of the base from statement I and the height from statement II. You do not want to multiply 196 times 16, do you? You know that statement I alone is not sufficient, and statement II alone is not sufficient. But both statements together give you required answer.
(B) How old is Subhash? I. In 16 more years Subhash will be twice as old as he is today.
II. Four years ago Subhash was times of his present age.
Once again you could go ahead and solve for Subhash’s age, but you do not have to and should not take the time to do so. Statement I alone is sufficient. Set up the equation x + 16 = 2x, where x stands for Subhash’s current age. On solving, we get x = 16. While it does not take long to set up the equation and prove the answer, why do so if you do not have to? Every second counts, and besides, you might set up the wrong equation, get a weird answer, and get frustrated. You waste even more time ‘trying to get it right’.
The same is true for statement II. You can set up the equation x – 4 = x. On solving, x = 16. As soon as you know you could solve the problem, you are through. The correct answer to this example is (b) because either statement I alone or statement II alone is sufficient.
Thats all for now. In the next lesson we study some more examples!
The Data Sufficiency Format:
A data sufficiency (DS) question consists of three parts. The actual question is called the question stem.
e.g. Is P > 1?
That’s all you will be given. Sometimes the question is literally a question, like the preceding example. Sometimes the ‘question’ is actually a statement, telling you to do something. e.g.
Mr Prasad drives at 80 mph in 5 hr. Find the distance that Mr Prasad drives. or like this: Find the rate at which oil flows into a container.
The second part of the DS question is statement 1. It may be like this:
1. P+ Q > 1
or
1. Mr Prasad drives thrice as far as his brother, but at half his speed.
or
1. The container has a capacity of 18 Tons
The third part of the question is statement 2. It may be like this:
2. p + q > 1
or
2. Mr Prabhu starts 300 miles east of the point at which his sister started.
or
2. The container is 2/5th full by evening.
You need to decide whether the data (the information) is sufficient to answer the question and hence the title, Data Sufficiency. No answer choices are given at the end of the DS questions. Instead, instructions are given at the beginning of the section as illustrated below.
Question Format:
Direction: Each of the following problems consist of a question followed by two statements, I and II. You must determine whether the information given by the statements is sufficient to answer the question asked. In addition to the information provided in the statements, you should rely on your knowledge of mathematics and ordinary facts (such as the number of seconds in a minute).
(a) if the question can be answered by using one of the statements alone, but cannot be answered using the other statement alone.
(b) if the question can be answered by using either statement alone.
(c) if the question can be answered by using both statements together, but cannot be answered using either statement alone.
(d) if the question cannot be answered even by using both statements together.
The four answer choices in detail:
The following problems illustrate the meanings of the four answer categories.
1. Choice (a)
In a problem, the answer choice is (a) if statement I ALONE is sufficient to answer the question asked, but statement II alone is not sufficient to answer the question asked
Example:
Is Raja older than Ramu?I. Sita is 4 years younger than Raja and 2 years younger than Ramu.
II. The average age Raja and Ramu is 21 years.
Statement I is by itself sufficient to answer the question asked. If Sita is 4 years younger, then Raja is 2 years younger than Ramu, then Raja must be 2 years older than Ramu. Statement II, however, is not by itself sufficient to answer the question. From the statement about the average of their ages in years, you cannot draw any conclusion about their respective ages. Since statement I alone is sufficient, but statement II is not, the correct answer choice is (a).
2. Choice (b)
In a problem, the answer choice is (B) if statement I ALONE is sufficient to answer the question asked, but statement I alone is not sufficient to answer the question asked
Example:
If x, y and z are consecutive integers, is y even?
I. x < y < z
II. xz is odd integer.
Statement I is not sufficient to answer the question asked. Although statement I describes the order of the integers, it provides no information about which elements of the sequence are even and which are odd. Statement II, however, is by itself sufficient to determine whether y is even or not. If xz is odd, then both x and z must be odd integers. In the series of 3 consecutive integers, at least one of the integers must be even. Therefore, y must be even. Since statement II alone is sufficient to answer the question asked, but statement I alone is not, the correct answer choice is (a).
3. Choice (c)
In any problem the answer choice is (c) if each statement alone is not sufficient to answer the question but the two statements taken together answer the question.
Example:
How many students are enrolled in Sastri's Quant class?
I. If 3 more students sign up for the class and no one drops out, more than 35 students will have enrolled in the class.
II. If 4 students drop out of the class and no more sign-up, fewer than 30 students will have enrolled in the class.
Statement I alone is not sufficient to answer the question asked, but I does imply that at least 33 students are enrolled in the class. Statement II alone is not sufficient to answer the question asked, but II does imply that no more than 33 students are enrolled in the class. Although neither statement alone is sufficient to answer the question, the two statements taken together are sufficient to answer the question that the number of students enrolled in the class is 33. Since neither statement alone is sufficient to answer the question but both together are sufficient, the correct answer choice is (c).
4. Choice (d)
In any problem the answer choice is (d) if the two statements are not capable of answering the question asked, either alone or when taken together.
Example:
Is x < y?I. – 0.26 < x < 0.4
II. 0.11 < y < 0.38
Statement I alone is not sufficient to answer the question asked. Although statement I defines a range for u, the statement provides no information about v. Similarly, statement II alone is not sufficient to answer the question asked. Statement II defines a range for v but provides no information about u. Since the two statements, even when taken together, do not provide enough information to answer the question asked, the correct answer choice is (d).
Flow chart for solving DS questions:
Data sufficiency questions have many tricks and traps. Here are some examples on how easily you can fall for the traps.
Key point to remember:
1. A unique answer: The data statements (alone or together) should be able to provide you with a unique answer to the question asked. Only then they will be considered as valid.
Example:
What is the value of x?I.
II. x > –10
From statement I we can see that x = +4 or x = –4. Now you may be tempted to consider this as a valid answer, as we have determined the value of x. But since this is not a unique answer, such an answer is not valid. So statement II alone is not sufficient to answer the question. Statement II does not give a definite answer either as both +4 and –4 are less than 10. Hence, the correct answer choice to this question is (d), as neither of the statements (either alone or taken together) helps us get a unique value of x.
Key point to remember:
2. A statement that merely states a mathematics formula is not sufficient to answer the question.
Sometimes a statement gives you a mathematics rule, which does not actually help you to acquire relevant data to answer the question
Example:
Angles a and b are alternate interior angles. What is the measure of angle a? (1) a + b = 180
You already know that a + b = 180 because of the basic geometry rule that the sum of alternate interior angles is 180. When a statement repeats a mathematical formula, it does not give you any new information and thus is not sufficient to answer the question.
What is the area of the trapezoid ABCD? (1) The area of the trapezoid is
Again statement I just gives a mathematical formula. While you may be delighted with the information because you personally do not have a clue what the formula for the area of a trapezoid is statement I alone does not give you anything you can use to answer the question, in terms of the values of the bases and the height.
Key point to remember:
3. A statement that only repeats information given in the question stem is not sufficient to answer the question. Sometimes you are given information in a statement that you already know from the question stem.
Example:
When a glass is half full, it contains 5 L of water. What is the weight of the glass when it is full?
(i) The capacity of the glass is 10 L.
It is obvious that if the half-full glass is 5 L, naturally the full glass is 10 L.
No new information is given.
Did you notice the trap built into this question? The question stem asked for the weight of the glass, not the capacity. If you thought you had to find the capacity, you probably thought statement I did the jo(b) Always keep in mind carefully what you are being asked.
Key point to remember:
4. Treat each statement separately, do not transfer information from one statement to the other.
A problem may give you something useful in statement I ... and then give you a variation of that same information in statement II. Many people choose (c), thinking that statement I and II both are required to answer the question.
Example:
What is probability of drawing a red ball, if a bag contains red, blue and green balls.
I. Total balls in the bag are 30
II. The balls are in the ratio 1:2:3
Here you may think that Statement I is not sufficient to answer as no details about the balls were presnet. After reading Statement II you may fee that, now i can calculate the number of balls of each colour so Statement I and II are required. But to calculate probability we just need the ratio's of the balls. So only statement II is enough. Choice (b).
Key point to remember:
5. Choice (c) means that both statements must be used. This is one of the favourite traps. Do not choose (c) just because one statement is helpful.
In order to choose (c) you must absolutely, positively need both the statements.
Example:
What is the perimeter of a rectangle with area 100?
I. The ratio of the length to the width is 4 : 1.
II. The sum of the interior angles of the rectangle is 360.
If you chose (c), you fell for the trap. The correct answer is (a) because statement I alone is sufficient to answer the question. To find a perimeter, you add the lengths of the sides. You already have information that the area is 100. The area of a rectangle is equal to the product of length and breadth. You do not have to come up with the actual number, just determine whether the data is sufficient to do so. Statement II gives you the sum of the interior angles. First decide whether that alone is sufficient information to answer the question. It is not. How about using both statements together? Statement II is nice to know, but it certainly is not necessary to know. (Besides, you already know that the interior angles of a rectangle sum up to 360°.) Do not fall for the trap of choosing (c) just because both statements are true. You choose (c) only when one statement alone is not sufficient and it takes the combined information of both statements to get you to the right answer.
Key point to remember:
6. Do not forget to try both statements I and II together.
Students in a big rush often eliminate choice (a) because statement I does not work. Then they eliminate choice (b) because statement II does not work. They immediately head to choice (d), thinking that there is no way to answer the question. They forget that there is one more possibility: maybe combining the two pieces of information will do the job.
Example:
(A) Is u > v?
I.
II. u, v > 0
Look at statement I alone. You may be tempted to say that if the squares of 2 numbers are identical, those 2 numbers are identical. Wrong, one of those numbers could be positive while the other could be negative. Say that u = –2 and v = 2. Then u2 = v2, but u is not equal to v (and you do not know whether u > v because u could be negative and v positive, or v could be negative and u positive). Statement I alone is not sufficient to answer the question. Eliminate choice (A).
Look at statement II alone. Certainly, knowing that u and v are greater than zero does not tell you which is greater, u or v. Eliminate choice (B). At this point many students make the mistake of choosing (D), saying there is not enough information to answer the question. Wrong again. Combine the two statements. If both u and v are greater than zero, then they must be the same numbers for their squares to be equal. In other words, they would no longer be 2 and –2; they would be 2 and 2 (or any other number). Both statements together are necessary to answer the question. Choose (c). You might argue that the answer must be (d) because the answer to the question ‘Is u > v?’ is ‘No, u is not greater than v’. Keep in mind that the answer to the question can be yes or no, as long as an answer is possible.
If you have a few minutes left at the end of a data sufficiency section, go back and double-check all those questions you answered with (d). You may be able to gain a few points by extracting yourself from the trap you had fallen into earlier.
(B) Is K a prime number?
I. K > 10
II. K divided by 2 has a remainder 0.
Statement I alone is not sufficient. Some numbers greater than 10 are prime, like 11. Some numbers greater than 10 are composite, like 12. Eliminate choice (A).
Statement II alone is not sufficient. When a number divided by 2 has no remainder, that number is even. You may be thinking that there are no even prime numbers and statement II alone is sufficient. But there is one even prime number, i.e. 2. Therefore, statement II alone is not sufficient because the answer could be yes or no. Eliminate choice (B).
At this point most students get lazy and choose (d). Put the two statements together. You know from statement II that the number must be even. You know from statement I that the number must be greater than 10. Because the only even prime number is 2, any even number greater than 2 must be composite, not prime. The answer to the question is ‘no’, c is not prime. Because you can answer the question based on both statements. The answer is (c).
Key point to remember:
7. If you can answer the question stem ‘no’, you have sufficient data to answer the problem.
All you need to know about a problem is whether the data is sufficient to answer the question or solve the problem. If the answer to the question is yes or if the answer is no, you have enough data.
Example:
(A) Is r even?
I. r + s is odd.
II. s is even.
The answer is (c). Statement I alone is not sufficient to answer the question. Knowing that r + s is odd will not tell you whether r is even. If s is even, then r is odd, because an even number and an odd number sum up to an odd number. If s is odd, then r is even, for the same reason. Put the two statements together. If s is even, and r + s is odd, then r must be odd. The answer to the question is no, but there is an answer to the problem. The answer to the question ‘Is r even?’ is ‘No, r is not even’. But because you can give an answer, even though that answer is negative, you do have enough data to answer the problem.
(B) Is Babu older than Raghu?
I. The ratio of Raghu’s age to Babu’s age is 7 : 4.
II. In 6 years Raghu will be half as old as he is now.
Statement I alone is sufficient to answer the question. If the ratio of the their ages is 7 : 4, then Raghu, the 7 part, is older than Babu, the 4 part. It makes no difference that the answer to the question is no; you are able to solve the problem. A ‘no’ is as good as a ‘yes’. Statement II alone is not sufficient. You can use it to find out how old Raghu is now, but you have no information about his age relative to Babu’s age.
Did you choose (c)? If so, you thought you actually had to find the exact ages of the two. True, you would need the information in statement II to get the age of Raghu, then the information in statement I to find the age of Babu. But you do not have to find the exact ages. You are not asked the ages; only whether Raghu is older than Babun. Just answer the question and proceed in stead of trying to add more to it.
Key point to remember:
9. As soon as you know the data is sufficient to answer the question, stop.
Do not work out these DS problems right through till the end. You should not care what the final answer is. The name of the game here is not problem-solving, in which you — logically enough — actually solve the problem. The section is called data sufficiency. You need only a simple yes or no: to say whether the data is sufficient or not. You do not have to actually solve the problem.
(A) What is the volume of a right circular cylinder? I. The area of the base of the figure is 196.
II. The height of the figure is 16.
Be smart enough not to actually work out the volume. The volume of a cylinder is the product of the area of the base and its height. You know the area of the base from statement I and the height from statement II. You do not want to multiply 196 times 16, do you? You know that statement I alone is not sufficient, and statement II alone is not sufficient. But both statements together give you required answer.
(B) How old is Subhash? I. In 16 more years Subhash will be twice as old as he is today.
II. Four years ago Subhash was times of his present age.
Once again you could go ahead and solve for Subhash’s age, but you do not have to and should not take the time to do so. Statement I alone is sufficient. Set up the equation x + 16 = 2x, where x stands for Subhash’s current age. On solving, we get x = 16. While it does not take long to set up the equation and prove the answer, why do so if you do not have to? Every second counts, and besides, you might set up the wrong equation, get a weird answer, and get frustrated. You waste even more time ‘trying to get it right’.
The same is true for statement II. You can set up the equation x – 4 = x. On solving, x = 16. As soon as you know you could solve the problem, you are through. The correct answer to this example is (b) because either statement I alone or statement II alone is sufficient.
Thats all for now. In the next lesson we study some more examples!
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