# GMAT Quant | Data Sufficiency

#### 32 GMAT Sample Questions | DS Lessons, Theory, Practice & Strategy

About 40% of the questions that appear in the GMAT quant section are data sufficiency questions. You will be provided with a question and two statements. You have to determine whether the information given in the statements is sufficient to answer the question asked. The embedded video is your starting point for everything GMAT DS. The video covers the basics of GMAT DS.

A good first step to start learning basic concepts in data sufficiency and build a strategy to solve GMAT DS questions is to watch the embedded video.

### Watch this GMAT Data Sufficiency Basics | Getting Started with DS video (37 minutes)

This data sufficiency problem consists of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements, plus your knowledge of mathematics and everyday facts (such as the number of days in a leap year or the meaning of the word counterclockwise), you must indicate whether -

1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
3. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
5. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

#### Numbers

All numbers used are real numbers.

#### Figures

A figure accompanying a data sufficiency question will conform to the information given in the question but will not necessarily conform to the additional information given in statements (1) and (2)

Lines shown as straight can be assumed to be straight and lines that appear jagged can also be assumed to be straight

You may assume that the positions of points, angles, regions, etc. exist in the order shown and that angle measures are greater than zero.

All figures lie in a plane unless otherwise indicated.

#### Note

In data sufficiency problems that ask for the value of a quantity, the data given in the statement are sufficient only when it is possible to determine exactly one numerical value for the quantity.

1. What is the value of X, if X and Y are two distinct integers and their product is 30?

1. X is an odd integer
2. X > Y
Approach to solve this GMAT Number Properties Data Sufficiency Question

List down all possibile integer values of X and Y such that their product is 30. Use the information in the two statements to determine whether you can compute a unique value of X. A 650 level GMAT data sufficiency question in number systems.

2. What is the standard deviation (SD) of the four numbers p, q, r, s?

1. The sum of p, q, r and s is 24
2. The sum of the squares of p, q, r and s is 224
Approach to solve this GMAT Statistics and Averages Data Sufficiency Question

Step 1: The given question is a "What is" question. The answer is a value. Data is sufficient if we get a unique value for the standard deviation of the 4 numbers.
Step 2: Evaluate statement 1 alone. Will the sum of the 4 numbers help find the SD? If not, will it help in determining the average of the 4 numbers?
Step 3: Evaluate statement 2 alone. Sum of squares alone is of not much use.
Step 4: Combine the statements. Revisit formula (alternative method) to find SD and determine whether we have a unique value for the SD of the 4 numbers.

3. How is Bill related to Betty?

1. Cindy, the wife of Bill's only brother Chris does not have any siblings.
2. Betty is Cindy's brother in law's wife.

4. Is y an integer?

1. y3 is an integer
2. 3y is an integer

5. If a salesman received a commission of 3% of the sales that he has booked in a month, what was the sales booked by the salesman in the month of November 2003?

1. The sales booked by the salesman in the month of November 2003 minus salesman's commission was $245,000 2. The selling price of the sales booked by the salesman in the month of November 2003 were 125 percent of the original purchase price of$225,000.
Approach to solve this GMAT Percentages DS Question

Question Stem: Commission earned = 3% of sales.
Statement 1: Sales booked - 3% sales booked = 245,000. Solving this equation will give a unique value. Statement 1 alone sufficient.
Statement 2: Selling price of sales booked = 125% of 225,000. Solving this equation will give a unique answer. Statement 2 alone is also sufficient.

6. Is the positive integer m divisible by 12?

1. m is divisible by 6
2. m is divisible by 8
Approach to solve this GMAT Number Properties DS Question

A number that is divisible by 6 should be divisible by both 3 and 2. Use the information in the statements to determine whether 'm' is divisible by both 3 and 2. A 600 to 650 level GMAT practice question in number systems.

7. Is ab positive?

1. (a + b)2 < (a - b)2
2. a = b
Hint to solve this GMAT Number Properties DS Question

The product of two numbers is positive either if both the numbers are positive or if both the numbers are negative. Solve the expression in statement 1 to determine whether you get a unique answer to the question. Consider all possible values that 'a' and 'b' can take when determining whether statement 2 is sufficient. Watch out for values that one might tend to overlook. A 650 level GMAT sample question in number properties data sufficiency.

8. When Y is divided by 2, is the remainder 1?

1. (-1) (Y+2) = -1
2. Y is prime.
Method to solve this GMAT Number Properties Data Sufficiency Question

If Y is an odd number, you will get a remainder of 1 when 2 divides Y. If Y is an even number, the remainder will be 0 when 2 divides Y. (-1) raised to an odd power is negative. (-1) raised to an even power is positive. Use this property about positive and negative numbers while evaluating statement 1. Do not miss out the obvious when evaluating statement 2. A 600 level GMAT data sufficiency question in number properties.

9. Is the two digit positive integer P a prime number?

1. (P + 2) and (P - 2) are prime.
2. (P - 4) and (P + 4) are prime.

10. If m, s are the average and standard deviation of integers a, b, c, and d, is s > 0?

1. m > a
2. a + b + c + d = 0
Method to solve this GMAT Averages DS Question

Step 1: Decoding the Question: Standard deviation is a non-negative number. So, it can either be zero or positive. So, the question boils down to figuring out whether 's' is zero or is it positive.
Step 2: Evaluate statement 1 alone to determine whether 's' is zero or positive
Step 3: Evaluate statement 2 alone to determine whether 's' is zero or positive
Step 4: If the statements are independently not sufficient, combine the statements to determine whether answer is C or E

11. Is x3 > x2 ?

1. x > 0
2. x < 1
Approach to solve this GMAT Number Properties Data Sufficiency Question

This GMAT sample question is a number properties DS question. The data is sufficient if we can answer the question with a definite yes or definite no.

When evaluating different powers of 'x', the break points are -1, 0, and 1. So, as a standard approach, check what the answer is when x < -1, -1 < x < 0, 0 < x < 1, x > 1 if you see a question that compares two different powers of an unknown. Also evaluate the answer at the break points - i.e., when x = -1, x = 0 and x = 1. A 650 to 700 level GMAT data sufficiency question.

12. Is y = 3?

1. (y - 3)(x - 4) = 0
2. (x - 4) = 0
Approach to solve this GMAT Number Properties Data Sufficiency Question

A GMAT data sufficiency question about solution to system of equations. Check whether you get a definite yes or no to the question asked using the information in the statements. If you get a definite answer, data is sufficient. If using the statements, you do not get a definite answer, the data is not sufficient. A 600 to 650 level GMAT data sufficiency sample question in system of equations.

13. Is $$frac{x}{y}$ a terminating decimal? 1. x is a multiple of 2 2. y is a multiple of 3 Approach to solve this GMAT Number Properties DS Question This GMAT question is a number systems data sufficiency question. A value of a fraction will be a terminating decimal if the denominator contains a prime factor other than 2 or 5. Look for a counter example for each of the statements. If you are able to find a counter example, the data is not sufficient. A 650 to 700 level GMAT sample question in number systems. 14. Is the positive integer X divisible by 21? 1. When X is divided by 14, the remainder is 4 2. When X is divided by 15, the remainder is 5 Hint to solve this GMAT DS Question in Number Properties This GMAT practice question is a data sufficiency practice question in tests of divisibility in number systems. The test of divisibility by 21 is that the number should be divisible by both 3 and 7. If it fails for either one, the number is not divisible by 21. With the information in the two statements whether you are able to determine this information. A 650 to 700 level GMAT sample question in number systems. 15. A set S contains the following elements: {7, 11, 15, 19, 23, x}. What is the value of x? 1. The elements are in arithmetic progression. 2. x is prime. Approach to solve this GMAT Data Sufficiency Question in Number Properties Note: Do not assume 'x' to be a number greater than 23 because it is written to the right of 23 in the set. If you could glean that information from the question stem or the statements, only then can you consider x to be greater than 23. Using the information in the statements, list down possible values for 'x'. If you are able to narrow it to a single value, the data is sufficient. A 600 to 650 level GMAT DS question in number systems and arithmetic progression. 16. Is xy < 0? 1. 5|x| + |y| = 0 2. |x| + 5|y| = 0 Approach to solve this GMAT DS Question in Number Properties This GMAT practice question is an algebra and number properties data sufficiency question. |x| or |y| cannot be negative. So, if the sum of the absolute values of two numbers is 0, it is possible only when both the numbers are 0. A 600 level GMAT question in absolute values and number systems. 17. Is triangle ABC obtuse angled? 1. a2 + b2 > c2. 2. The center of the circle circumscribing the triangle does not lie inside the triangle. 18. Is triangle ABC with sides a, b and c acute angled? 1. Triangle with sides a2, b2, c2 has an area of 140 sq cms. 2. Median AD to side BC is equal to altitude AE to side BC. 19. When a positive integer 'x' is divided by a divisor 'd', the remainder is 24. What is d? 1. When 2x is divided by d, the remainder is 23. 2. When 3x is divided by d, the remainder is 22. Approach to solve this GMAT Number Properties Data Sufficiency Question This GMAT sample question is a number properties DS question testing concepts in remainders. Use the following rules about remainders to solve the DS question. Rule 1: Remainder of the sum of two numbers is the same as the sum of the remainders of the two numbers. Rule 2: Remainder obtained when dividing a number by a divisor 'd' is lesser than the divisor. Using the information given in the two statements, evaluate whether you could find a unique value for the divisor. A 700 level GMAT data sufficiency question in number properties. 20. How many of the numbers x, y, and z are positive if each of these numbers is less than 10? 1. x + y + z = 20 2. x + y = 14 Approach to solve this GMAT Number Properties Data Sufficiency Question The key data is that each of x, y, and z is less than 10. Use this information along with the data given in the statements to determine how many of these 3 numbers are positive. A 600 to 650 level GMAT question in number systems. 21. Is a < b? 1. ab < ba 2. ${$frac{a}{b}}$ > 1 Approach to solve this GMAT Inequalities Data Sufficiency Question Step 1: Make a note of when is the answer to the question 'yes' and when is the answer 'no'. Step 2: Evaluate statement 1 alone. Approach - find a counter example. If you can find a counter example, statement 1 is not suficient. Step 3: Evaluate statement 2 alone. Approach - find a counter example. If you can find a counter example, statement 1 is not suficient. Step 4: If the statements are independently not sufficient, combine the statements and determine sufficiency. 22. Is | a | > | b |? 1. \\frac{1}{$a-b$}) > $$frac{1}{$b-a$})
2. a + b < 0
Approach to solve this GMAT 650 Inequalities Data Sufficiency Question

Step 1: Make a note of when is the answer to the question 'yes' and when is the answer 'no'.
Step 2: Evaluate statement 1 alone. Understand the implication of statement 1 and check whether we can get a conclusive answer using statement 1. Approach - counter example.
Step 3: Evaluate statement 2 alone. Approach counter example.
Step 4: If the statements are independently not sufficient, combine them and determine the answer. For the given statements, should there be a need to combine the statements, counter example will be an ideal approach.

23. What is the 6th term of the Arithmetic sequence?

1. The sum of the 6th to the 12th term of the sequence is 77.
2. The sum of the 2nd to the 10th term of the sequence is 108.
Approach to solve this GMAT Progressions Data Sufficiency Question

Express the information in the first statement in terms of the first term and common difference of the AP. Determine whether it will help compute the value of the 6th term of the arithmetic sequence. Repeat the process for the second term. If the statements individually do not give a conclusive answer, combine the statements, solve for the first term and the common difference and arrive at the answer to the DS question. A 600 to 650 level GMAT DS question in arithmetic sequences.

24. Is a3 > a2

1. $$frac{1}{a}$ > a 2. a5 > a3 Approach to solve this GMAT Inequalities Data Sufficiency Question Question Stem: Make a note of when is the answer to the question 'yes' and when is the answer 'no'. Statement 1: Evaluate Statement 1 Alone: Identify the interval in which the statement will hold good if 'a' is positive and evaluate whether we get a conclusive answer to the question. Also, evaluate the range of values in which the statement will hold good if 'a' is negative. Determine whether for negative values of 'a' we get the same definitive answer to the question. Statement 2: Evaluate Statement 2 Alone: For positive values of 'a' when will a5 > a3? In that interval, what is answer to the question. For negative values of 'a' when will a5 > a3? For those values of 'a' what is the answer to the question. Do we have a conclusive answer? 25. Line L is perpendicular to line K whose equation is 3y = 4x + 12; Lines L and K intersect at$p, q).

1. x intercept of Line L is less than that of Line K
2. y intercept of Line L is less than that of Line K
Approach to solve this GMAT Coordinate Geometry Data Sufficiency Question

Concept: Line K is a positive sloping line. Line L, therefore, is a negative sloping line.
Step 1: Compute x-intercept of line K and draw line L to satisfy information given in statement 1. Deduce possible points of intersection and determine whether we get a unique answer to the question.
Step 2: Compute y-intercept of line K and draw line L to satisfy information given in statement 2. Deduce possible points of intersection and determine whether we get a unique answer to the question.
Step 3: If we do not get a conclusive answer using either statement independently, combine the information in the two statements and determine sufficiency.

26. Is | a | > a?

1. a2 < a
2. $$frac{a}{2}$ > $\frac{2}{a}$ Approach to solve this GMAT Inequalities Data Sufficiency Question Step 1: Rephrase the question? For what values of 'a' will | a | > a? Will be easier to find an answer to this question. Step 2: Make a note of when is the answer to the question 'yes' and when is the answer 'no'. Step 3: Evaluate Statement 1 Alone. It is clear that a2 is non-negative. Find the solution set for the inequality, a2 < a. Determine whether we get a definite answer to the rephrased question. Step 4: Evaluate Statement 2 Alone. Find the solution set for the expression given in statemnet 2 for the possibility that 'a' is positive. Compute the range of values of 'a' that satisfy the inequality in statement 2 when 'a' is negative. Check whether we have a conclusive answer to the question for both positive and negative values of 'a'. 27. Does the line x + y = 6 intersect or touch the circle C with radius 5 units? 1. Center of the circle lies in the third quadrant. 2. Point$-4, -4) does not lie inside the circle.
Approach to solve this GMAT Coordinate Geometry Data Sufficiency Question

Step 1 - Question Stem: The line is a negative sloping line with intercepts (6, 0), (0, 6). It passes through II, IV, and I quadrants.
Step 2: Evaluate statement 1 by looking for a counter example. If the shortest distance between the center of the circle and the line is less than or equal to the radius, the line will touch or intersect with the circle. If a counter example exists, statement 1 is not sufficient. Else it is sufficient.
Step 3: Look for a counter example with two different points that could be centers of the circle satisfying statement 2. If we are able to find a counter example, statement 2 will not be sufficient.
Step 4: If we do not get a conclusive answer using either statement independently, combine the information in the two statements and determine sufficiency.

28. Is 'a' positive?

1. a - b > 0
2. 2a - b > 0
Approach to solve this GMAT Inequalities Data Sufficiency Question

Step 1: Make a note of when is the answer to the question 'yes' and when is the answer 'no'.
Step 2: Evaluate Statement 1 Alone. Approach: Counter example.
Step 3: Evaluate Statement 2 Alone. Approach: Counter example.
Step 4: Evaluate statements together if required. Approach: Counter example.

29. If x and y are positive integers, is y odd?

1. x is odd.
2. xy is odd.
Approach to solve this GMAT Number Properties Data Sufficiency Question

This GMAT sample question is a number systems DS question. The product of two integers is odd only when both the numbers are odd. Use this property to evaluate whether 'y' is odd. A sub 600 level GMAT practice question in data sufficiency.

30. Is 'b' the median of 3 numbers a, b, and c?

1. $$frac{b}{a}$ = $\frac{c}{b}$ 2. ab < 0 Approach to solve this GMAT Averages Data Sufficiency Question Step 1: The given question is an "IS" question. The answer should be yes or no. Data is sufficient when we get a definite yes or definite no. Step 2: Evaluate statement 1 alone. We know the numbers are in GP. Check whether 'b' is the median of the 3 numbers. Points to check are - will 'b' be the median if the common ratio is negative. Step 3: Evaluate statement 2 alone. Look for a counter example. Step 4: Combine the statements if you did not get a conclusive answer using either statements alone. 31. Is the slope of the line that passes through the point$p, q) positive?

1. p, q > 0
2. The x-intercept of the line is k, such that k > p.
Approach to solve this GMAT Coordinate Geometry Data Sufficiency Question

Step 1: Evaluate Statement 1 Alone: We know point (p, q) is a I quadrant point. Can we deduce the slope of the line with this information?
Step 2: Evaluate Statement 2 Alone: The x-intercept of line k is greater the x-coordinate of the point. Try to describe two lines one with positive slope and the other with a negative slope satisfying this condition. If it is possible statement 2 alone is not sufficient.
Step 3: If we do not get a conclusive answer using either statement independently, combine the information in the two statements and determine sufficiency.

32. Is an > bn?

1. a > b
2. ab < 0
Approach to solve this GMAT Inequalities Data Sufficiency Question

Step 1: Make a note of when is the answer to the question 'yes' and when is the answer 'no'.
Step 2: Evaluate Statement 1 Alone. Approach: Counter example. Hint - check with positive and negative values for 'b'.
Step 3: Evaluate Statement 2 Alone. Approach: Counter example. Hint - swap values of 'a' and 'b'.
Step 4: Evaluate the statements together by reasoning out the two conditions.

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