Quantitative and verbal sub-tests 35
Data sufficiency questions
This second type of question in the quantitative sub-test is also based on the same regular mathematics as the problem-solving questions. But that is where the similarity between these two sorts of questions ends. Your task in these questions is quite different. Each question comprises a mathematics question and two statements that refer to the question. You must decide whether the question can be answered with the information given in the statements. There are five possible answers and you must indicate which is correct. You must decide whether the question can be answered using the first statement alone, the second statement alone, both statements together (but neither separately), either statement alone, or if the problem cannot be solved. If you are new to this style of question, then you will need to undertake some practice before you fully understand the challenge.
Below, you will find 57 practice data sufficiency questions. As with all the questions in this chapter, do not impose a time limit on yourself, but use them to become fully conversant with the task and continue building your speed, accuracy and confidence in the mathematics on which the questions are based.
Example question
1.Can you find the diameter of a circle?
(1)A straight line through the circle is twice its radius
(2)The circumference can be found with the formula d
A. |
1 alone, not 2 alone |
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B. |
2 alone, not 1 alone |
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Answer E |
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C. |
1 and 2 together (need both) |
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D.1 alone or 2 alone
E.1 and 2 together are not sufficient
Explanation: We cannot establish the length of the diameter of the circle with either statement so cannot calculate its circumference.
2.Is y negative?
(1)y2 – y – 2 = 0
(2)2y < 0
A. |
1 alone, not 2 alone |
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B. |
2 alone, not 1 alone |
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C. |
1 and 2 together (need both) |
Answer |
D.1 alone or 2 alone
E.1 and 2 together are not sufficient
36 How to pass the GMAT®
3.
A
a
Is angle A the largest and side a the longest?
(1)The sum of the length of the other two sides is greater than the length of a
(2)A is the largest angle
A. |
1 alone, not 2 alone |
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B. |
2 alone, not 1 alone |
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C. |
1 and 2 together (need both) |
Answer |
D.1 alone or 2 alone
E.1 and 2 together are not sufficient
4.Is x negative?
(1)xy < 1
(2)y is positive
A. |
1 alone, not 2 alone |
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B. |
2 alone, not 1 alone |
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C. |
1 and 2 together (need both) |
Answer |
D.1 alone or 2 alone
E.1 and 2 together are not sufficient
5.Can a polygon be divided into three triangles?
(1)It is a pentagon
(2)It has five sides
A. |
1 alone, not 2 alone |
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B. |
2 alone, not 1 alone |
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C. |
1 and 2 together (need both) |
Answer |
D.1 alone or 2 alone
E.1 and 2 together are not sufficient
6.Is x positive?
(1)x3 < 0
(2)x5 < 0
A. |
1 alone, not 2 alone |
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B. |
2 alone, not 1 alone |
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C. |
1 and 2 together (need both) |
Answer |
D.1 alone or 2 alone
E.1 and 2 together are not sufficient
Quantitative and verbal sub-tests 37
7.How many sides does a regular polygon have?
(1)The total sum of all the interior and exterior angles = 1,800°
(2)The sum of its exterior angles = 360°
A. |
1 alone, not 2 alone |
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B. |
2 alone, not 1 alone |
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C. |
1 and 2 together (need both) |
Answer |
D.1 alone or 2 alone
E.1 and 2 together are not sufficient
8.Is x negative?
(1)xy = 3
(2)x2 = y
A. |
1 alone, not 2 alone |
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B. |
2 alone, not 1 alone |
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C. |
1 and 2 together (need both) |
Answer |
D.1 alone or 2 alone
E.1 and 2 together are not sufficient
9.Are two triangles similar?
(1)Corresponding sides are in the same ratio
(2)Two pairs of angles are similar
A. |
1 alone, not 2 alone |
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B. |
2 alone, not 1 alone |
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C. |
1 and 2 together (need both) |
Answer |
D.1 alone or 2 alone
E.1 and 2 together are not sufficient
10.Is n divisible by 8 with no remainder?
(1)n + 8 is divisible by 8 with integer result
(2)n + 16 is divisible by 8 with integer result
A. |
1 alone, not 2 alone |
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B. |
2 alone, not 1 alone |
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C. |
1 and 2 together (need both) |
Answer |
D.1 alone or 2 alone
E.1 and 2 together are not sufficient
38 How to pass the GMAT® |
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11. Two shapes are congruent (identical) |
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(1) |
The angles in one shape are equal to the corresponding angles of the other |
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(2) |
All pairs of corresponding sides are the same size |
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A. |
1 alone, not 2 alone |
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B. |
2 alone, not 1 alone |
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C. |
1 and 2 together (need both) |
Answer |
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D.1 alone or 2 alone
E.1 and 2 together are not sufficient
12.Is n divisible by 3 with no remainder?
(1)n – 3 is divisible by 3 with integer result
(2)n – 21 is divisible by 3 with integer result
A. |
1 alone, not 2 alone |
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B. |
2 alone, not 1 alone |
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C. |
1 and 2 together (need both) |
Answer |
D.1 alone or 2 alone
E.1 and 2 together are not sufficient
13.How many sides does a regular polygon have?
(1)The sum of its exterior angles = 360°
(2)The total sum of all the interior and exterior angles = 1,800°
A. |
1 alone, not 2 alone |
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B. |
2 alone, not 1 alone |
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C. |
1 and 2 together (need both) |
Answer |
D.1 alone or 2 alone
E.1 and 2 together are not sufficient
14.Is n divisible by 8 with remainder 6?
(1)n/2 is divisible by 4 with remainder 3
(2)n is divisible by 2 with integer result
A. |
1 alone, not 2 alone |
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B. |
2 alone, not 1 alone |
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C. |
1 and 2 together (need both) |
Answer |
D.1 alone or 2 alone
E.1 and 2 together are not sufficient
Quantitative and verbal sub-tests 39
15.Is a triangle right-angled?
(1)A line drawn from the vertical angle to meet the base divides it at the mid-point
(2)The length of the sides are a multiple of 5, 12, 13
A. |
1 alone, not 2 alone |
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B. |
2 alone, not 1 alone |
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C. |
1 and 2 together (need both) |
Answer |
D.1 alone or 2 alone
E.1 and 2 together are not sufficient
16.Is n divisible by 3 with remainder 2?
(1)n – m is divisible by 3 with no remainder
(2)m is divisible by 2 with integer result
A. |
1 alone, not 2 alone |
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B. |
2 alone, not 1 alone |
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C. |
1 and 2 together (need both) |
Answer |
D.1 alone or 2 alone
E.1 and 2 together are not sufficient
17.What is the surface area of the cone?
L
(1)L = 7 cm and the base is 6 cm wide
(2)The cone has a height of 4 cm and the base a radius of 3 cm
A. |
1 alone, not 2 alone |
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B. |
2 alone, not 1 alone |
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C. |
1 and 2 together (need both) |
Answer |
D.1 alone or 2 alone
E.1 and 2 together are not sufficient
40 How to pass the GMAT®
18.Is the shape is a parallelogram?
(1)The diagonals bisect each other
(2)It has four sides
A. |
1 alone, not 2 alone |
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B. |
2 alone, not 1 alone |
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C. |
1 and 2 together (need both) |
Answer |
D.1 alone or 2 alone
E.1 and 2 together are not sufficient
19.Which of these two is the greater, x or y?
(1)x = 2a
(2)y = 5a
A.1 alone, not 2 alone
B.2 alone, not 1 alone
C. |
1 and 2 together (need both) |
Answer |
D. |
1 alone or 2 alone |
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E. 1 and 2 together are not sufficient
20.A bar of soap costs 60 cents, how much would a similar bar cost?
(1)The similar bar has dimensions 4/5 of the original
(2)The original weighs 6oz
A. |
1 alone, not 2 alone |
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B. |
2 alone, not 1 alone |
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C. |
1 and 2 together (need both) |
Answer |
D.1 alone or 2 alone
E.1 and 2 together are not sufficient
21.Which of these two is the greater, x or y?
(1)x is divisible by 4 with integer solution
(2)y is divisible by 4 with remainder 1
A. |
1 alone, not 2 alone |
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B. |
2 alone, not 1 alone |
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C. |
1 and 2 together (need both) |
Answer |
D.1 alone or 2 alone
E.1 and 2 together are not sufficient
Quantitative and verbal sub-tests 41
22.Is the shape a kite?
(1)The diagonals are perpendicular
(2)Two pairs of sides are equal
A. |
1 alone, not 2 alone |
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B. |
2 alone, not 1 alone |
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C. |
1 and 2 together (need both) |
Answer |
D.1 alone or 2 alone
E.1 and 2 together are not sufficient
23.Which of these two is the greater, x or y?
(1)x – y < 0
(2)x + y > 0
A. |
1 alone, not 2 alone |
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B. |
2 alone, not 1 alone |
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C. |
1 and 2 together (need both) |
Answer |
D.1 alone or 2 alone
E.1 and 2 together are not sufficient
24.Is the quadrilateral a square?
(1)All angles equal 90°
(2)The diagonals divide the shape into 4 identical triangles
A. |
1 alone, not 2 alone |
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B. |
2 alone, not 1 alone |
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C. |
1 and 2 together (need both) |
Answer |
D.1 alone or 2 alone
E.1 and 2 together are not sufficient
25.Which of these two is the greater, x or y?
(1)x/3 > y
(2)x3 > y3
A. |
1 alone, not 2 alone |
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B. |
2 alone, not 1 alone |
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C. |
1 and 2 together (need both) |
Answer |
D.1 alone or 2 alone
E.1 and 2 together are not sufficient
42 How to pass the GMAT®
26.If a ball bearing is dropped into a beaker of water 3 cm deep, by how much does the water rise?
(1)The radius of the ball bearing is 7 mm
(2)The radius of the beaker is 5 cm
A. |
1 alone, not 2 alone |
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B. |
2 alone, not 1 alone |
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C. |
1 and 2 together (need both) |
Answer |
D.1 alone or 2 alone
E.1 and 2 together are not sufficient
27.Which of these two is the greater, x or y?
(1)1/x > 1/y
(2)Both are negative
A. |
1 alone, not 2 alone |
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B. |
2 alone, not 1 alone |
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C. |
1 and 2 together (need both) |
Answer |
D.1 alone or 2 alone
E.1 and 2 together are not sufficient
28.How far up the wall does the ladder reach?
(1)The ladder is on horizontal ground and the wall is vertical
(2)The angle between the ladder and the ground is 80°
A.1 alone, not 2 alone
B.2 alone, not 1 alone
C. |
1 and 2 together (need both) |
Answer |
D. |
1 alone or 2 alone |
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E. 1 and 2 together are not sufficient
29.A sequence of numbers a1, a2, a3 etc. is generated using the following algorithm: an+1 = (an)2. Does the number 9 appear in the sequence if:
(1)a1 = 3
(2)a3 = 81
A. |
1 alone, not 2 alone |
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B. |
2 alone, not 1 alone |
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C. |
1 and 2 together (need both) |
Answer |
D.1 alone or 2 alone
E.1 and 2 together are not sufficient
Quantitative and verbal sub-tests 43
30.How big is each angle in the pentagon?
(1)One angle is 100°
(2)Four angles are equal
A.1 alone, not 2 alone
B.2 alone, not 1 alone
C. |
1 and 2 together (need both) |
Answer |
D. |
1 alone or 2 alone |
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E. 1 and 2 together are not sufficient
31.A sequence of numbers a1, a2, a3 etc. is generated using the following algorithm: an+1 = (an)2. Does the number 36 appear in the sequence if:
(1)a2 = 6
(2)1,296 appears in the sequence
A. |
1 alone, not 2 alone |
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B. |
2 alone, not 1 alone |
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C. |
1 and 2 together (need both) |
Answer |
D.1 alone or 2 alone
E.1 and 2 together are not sufficient
32.What is the size of the non-shaded area?
(1)The square has sides 10 cm long
(2)The semicircle has a radius of 5 cm
A. |
1 alone, not 2 alone |
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B. |
2 alone, not 1 alone |
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C. |
1 and 2 together (need both) |
Answer |
D.1 alone or 2 alone
E.1 and 2 together are not sufficient
44 How to pass the GMAT®
33.A sequence of numbers a1, a2, a3 etc. is generated using the following algorithm: an+1 = an/2. Does the number 2 appear in the sequence if:
(1)a1 is not 0
(2)There are no numbers in the sequence between 17 and 31 inclusive
A.1 alone, not 2 alone
B.2 alone, not 1 alone
C. |
1 and 2 together (need both) |
Answer |
D. |
1 alone or 2 alone |
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E. 1 and 2 together are not sufficient
34.A disc revolves at 75 revolutions a minute. What is the speed at which a point on the disc is rotating?
(1)The disc has a circumference of 12 in
(2)The point on the disc is 2 in from the center
A. |
1 alone, not 2 alone |
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B. |
2 alone, not 1 alone |
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C. |
1 and 2 together (need both) |
Answer |
D.1 alone or 2 alone
E.1 and 2 together are not sufficient
35.A sequence of numbers a1, a2, a3 etc. is generated using the following algorithm:
an+1 = an + m. Does the number 2 not appear in the sequence if:
(1)m = –2
(2)a16 is a positive even number
A. |
1 alone, not 2 alone |
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B. |
2 alone, not 1 alone |
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C. |
1 and 2 together (need both) |
Answer |
D.1 alone or 2 alone
E.1 and 2 together are not sufficient
36.Are the shapes similar?
(1)All pairs of corresponding sides are in the same ratio
(2)The shape is not a triangle
A. |
1 alone, not 2 alone |
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B. |
2 alone, not 1 alone |
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C. |
1 and 2 together (need both) |
Answer |
D.1 alone or 2 alone
E.1 and 2 together are not sufficient
Quantitative and verbal sub-tests 45
37.Is x2 > y2?
(1)x > y
(2)x/y >0
A. |
1 alone, not 2 alone |
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B. |
2 alone, not 1 alone |
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C. |
1 and 2 together (need both) |
Answer |
D.1 alone or 2 alone
E.1 and 2 together are not sufficient
38.Is x3 > y3?
(1)x > y
(2)x/y >0
A. |
1 alone, not 2 alone |
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B. |
2 alone, not 1 alone |
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C. |
1 and 2 together (need both) |
Answer |
D.1 alone or 2 alone
E.1 and 2 together are not sufficient
39.How high is the building with a shadow 19 m long?
(1)We look up on the internet the angle of the sun for that time and place
(2)At the same time, a gatepost of known height casts a shadow 1.5 m long
A. |
1 alone, not 2 alone |
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B. |
2 alone, not 1 alone |
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C. |
1 and 2 together (need both) |
Answer |
D.1 alone or 2 alone
E.1 and 2 together are not sufficient
40.Is x2 > y?
(1)0 < x < 1
(2)x > y
A. |
1 alone, not 2 alone |
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B. |
2 alone, not 1 alone |
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C. |
1 and 2 together (need both) |
Answer |
D.1 alone or 2 alone
E.1 and 2 together are not sufficient
46 How to pass the GMAT® |
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41. How high is the kite from the ground? |
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(1) |
It is on a string 70 ft long |
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(2) |
The person holding the string calculated that the angle of elevation is 70° |
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A. |
1 alone, not 2 alone |
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B. |
2 alone, not 1 alone |
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C. |
1 and 2 together (need both) |
Answer |
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D.1 alone or 2 alone
E.1 and 2 together are not sufficient
42.Is 1/x2 + 1/y2 > 0?
(1)y < x
(2)x and y 0
A. |
1 alone, not 2 alone |
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B. |
2 alone, not 1 alone |
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C. |
1 and 2 together (need both) |
Answer |
D.1 alone or 2 alone
E.1 and 2 together are not sufficient
43.Is x/8 > y/12?
(1)3x > 2y
(2)x < y
A. |
1 alone, not 2 alone |
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B. |
2 alone, not 1 alone |
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C. |
1 and 2 together (need both) |
Answer |
D.1 alone or 2 alone
E.1 and 2 together are not sufficient
44.Is x/8 > y/12?
(1)y = 0
(2)x > 1
A. |
1 alone, not 2 alone |
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B. |
2 alone, not 1 alone |
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C. |
1 and 2 together (need both) |
Answer |
D.1 alone or 2 alone
E.1 and 2 together are not sufficient
Quantitative and verbal sub-tests 47
45.Is 1/x > 1/y?
(1)(1/x) – (1/y) > 0
(2)(y – x)/(xy) > 0
A. |
1 alone, not 2 alone |
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B. |
2 alone, not 1 alone |
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C. |
1 and 2 together (need both) |
Answer |
D.1 alone or 2 alone
E.1 and 2 together are not sufficient
46.Is y > 3x + 2?
(1)y > 4x
(2)x > 2
A. |
1 alone, not 2 alone |
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B. |
2 alone, not 1 alone |
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C. |
1 and 2 together (need both) |
Answer |
D.1 alone or 2 alone
E.1 and 2 together are not sufficient
47.What is the value of xy?
(1)x + y = 6
(2)2x + y = 10
A. |
1 alone, not 2 alone |
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B. |
2 alone, not 1 alone |
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C. |
1 and 2 together (need both) |
Answer |
D.1 alone or 2 alone
E.1 and 2 together are not sufficient
48.What is the value of xy?
(1)1/x = 12
(2)2/y = 10
A. |
1 alone, not 2 alone |
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B. |
2 alone, not 1 alone |
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C. |
1 and 2 together (need both) |
Answer |
D.1 alone or 2 alone
E.1 and 2 together are not sufficient
48 How to pass the GMAT®
49.What is the value of xy?
(1)x2y2 = 16
(2)y2 = 6
A. |
1 alone, not 2 alone |
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B. |
2 alone, not 1 alone |
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C. |
1 and 2 together (need both) |
Answer |
D.1 alone or 2 alone
E.1 and 2 together are not sufficient
50.What is the value of xy?
(1)x3y3 = 8
(2)5x + 10y = 25
A. |
1 alone, not 2 alone |
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B. |
2 alone, not 1 alone |
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C. |
1 and 2 together (need both) |
Answer |
D.1 alone or 2 alone
E.1 and 2 together are not sufficient
51.What is the value of xy?
(1)(x + y)2 = 8
(2)(x – y)2 = 6
A. |
1 alone, not 2 alone |
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B. |
2 alone, not 1 alone |
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C. |
1 and 2 together (need both) |
Answer |
D.1 alone or 2 alone
E.1 and 2 together are not sufficient
52.What is the value of x?
(1)x/y = 4
(2)xy = 4
A. |
1 alone, not 2 alone |
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B. |
2 alone, not 1 alone |
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C. |
1 and 2 together (need both) |
Answer |
D.1 alone or 2 alone
E.1 and 2 together are not sufficient
Quantitative and verbal sub-tests 49
53.What is the value of x?
(1)x2 = 4
(2)xy = 4
A. |
1 alone, not 2 alone |
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B. |
2 alone, not 1 alone |
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C. |
1 and 2 together (need both) |
Answer |
D.1 alone or 2 alone
E.1 and 2 together are not sufficient
54.What is the value of x?
(1)1/x + x/y = 5/12
(2)3x/xy – 2x/y = 1/y
A. |
1 alone, not 2 alone |
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B. |
2 alone, not 1 alone |
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C. |
1 and 2 together (need both) |
Answer |
D.1 alone or 2 alone
E.1 and 2 together are not sufficient
55.What is the value of x?
(1)x3 – 3x2 + 3x = 1
(2)(x – 1)2 = 0
A. |
1 alone, not 2 alone |
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B. |
2 alone, not 1 alone |
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C. |
1 and 2 together (need both) |
Answer |
D.1 alone or 2 alone
E.1 and 2 together are not sufficient
56.Is x positive or negative?
(1)x3 + 8 = 0
(2)x2 – 4 = 0
A. |
1 alone, not 2 alone |
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B. |
2 alone, not 1 alone |
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C. |
1 and 2 together (need both) |
Answer |
D.1 alone or 2 alone
E.1 and 2 together are not sufficient
50 How to pass the GMAT®
57.Is x positive or negative?
(1)x2 > y2
(2)y > 0
A. |
1 alone, not 2 alone |
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B. |
2 alone, not 1 alone |
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C. |
1 and 2 together (need both) |
Answer |
D.1 alone or 2 alone
E.1 and 2 together are not sufficient