Question 1: If x4 = 2y2 and 4y = 8, what is the value of x4 + 2y?
(a) 8
(b) 10
(c) 12
(d) 14
(e) 16
Solution: 4y = 8 means y = 2.
x4 = 2y2
x4 = 2·22
x4 = 8
x4 + 2y = 8 + 4
x4 + 2y = 12
Question 2: The numbers drawn by a state lottery are 2, 3, a, b, 6, 7. What is the number a, if:
(1) The average of all numbers is 5.
(2) a < b
(a) Statement (1) ALONE is sufficient, but statement (2) is not sufficient.
(b) Statement (2) ALONE is sufficient, but statement (1) is not sufficient.
(c) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
(d) EACH statement ALONE is sufficient.
(e) Statements (1) and (2) TOGETHER are NOT sufficient.
Answer:
Statement (1) is not sufficient because the equation (2 + 3 + a + b + 6 + 7)/6 = 5 has 2 unknowns.
Statement (2) is not sufficient because the inequality a < b can't determine a.
Statements (1) and (2) together are also not sufficient.
The correct answer is (e).
Question 3: What is the circumference of circle O from the figure below if the length of the sides of the ABCD square is 5 inches?
(a) 10·¶ inches
(b) 15/¶ inches
(c) 1/¶ inches
(d) 8·¶ inches
(e) 10 inches
Answer: Angle BOA is 60o and OA = OB, so triangle BOA is equilateral, and the radius of the circle is equal to the side of the square ABCD.
The circumference of the circle is 2·¶5 = 10·¶.
Question 4: A number is increased 50% and the resulting number is decreased 50%. The final number is what percentage of the original number?
(a) 50%
(b) 80%
(c) 100%
(d) 75%
(e) 105%
Answer: If the original number is x, after it is increased 50% the resulting number is 1.5x.
1.5x is decreased 50% so the final number is .5·1.5x = .75·x or 75% of x.
Question 5: $100,000 are shared between John, Michael and Ed. How much did Michael receive?
(1) John received 3 times more than Ed.
(2) Ed received 4 times more than Michael.
(a) Statement (1) ALONE is sufficient, but statement (2) is not sufficient.
(b) Statement (2) ALONE is sufficient, but statement (1) is not sufficient.
(c) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
(d) EACH statement ALONE is sufficient.
(e) Statements (1) and (2) TOGETHER are NOT sufficient.
Answer:
If x, y and z are the sums that John, Michael and Ed received, we know that x + y + z = $100,000.
Statement (1):
x = 3z.
x + y + z = $100,000.
We have a system with 2 equations and 2 unknowns that can’t be solved.
Statement (2):
z = 4y.
x + y + z = $100,000.
We have a system with 2 equations and 2 unknowns that can’t be solved.
Statement (1) and (2) together:
x = 3z.
z = 4y.
x + y + z = $100,000.
We have a system with 3 equations and 3 unknowns that can be solved. The correct answer is (c).
Question 6: Does 2m – 3n = 0?
(1) m ≠ n
(2) 6m = 9n
(a) Statement (1) ALONE is sufficient, but statement (2) is not sufficient.
(b) Statement (2) ALONE is sufficient, but statement (1) is not sufficient.
(c) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
(d) EACH statement ALONE is sufficient.
(e) Statements (1) and (2) TOGETHER are NOT sufficient.
Answer:
Statement (1): m ≠ n does not answer the question. 2m could be equal to 3n for some (m, n) pairs or could be different for other (m, n) pairs.
Statement (2): 6m = 9n could be rewritten as 2m = 3n, so 2m – 3n = 0.
Statement (2) alone is sufficient.
Question 7: If the lengths of two of the edges of a triangle are 5 inches and 8 inches, which of the following can be the length of the third edge?
(a) 2 inches
(b) 3 inches
(c) 6 inches
(d) 13 inches
(e) 17 inches
Answer: If a, b, and c are the lengths of the edges of the triangle, a = 5 and b = 8, the length of edge c should satisfy the following two inequalities:
1. c < a + b
c < 13 inches and answers (d) and (e) cannot be true.
2. c > b – a
c > 3 inches and answers (a) and (b) cannot be true.
Question #8: Is x < 0?
(1) -2x > 0
(2) x3 < 0
(a) Statement (1) ALONE is sufficient, but statement (2) is not sufficient.
(b) Statement (2) ALONE is sufficient, but statement (1) is not sufficient.
(c) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
(d) EACH statement ALONE is sufficient.
(e) Statements (1) and (2) TOGETHER are NOT sufficient.
Answer:
Statement (1): -2x > 0
2x < 0
x < 0 and statement (1) is sufficient.
Statement (2): x3 < 0
x2·x < 0
x2 > 0 so x < 0 and statement (2) is sufficient.
The correct answer is (d).
Question 9: If half of the money in a mutual fund was invested in stocks, one fifth in bonds and the remaining $300,000 in cash, what was the total amount of the mutual fund?
(a) $1,800,000
(b) $2,200,000
(c) $2,600,000
(d) $1,000,000
(e) $4,000,000
Answer:
If the total amount in the mutual fund is x,
(1/2)x + (1/5)x + $300,000 = x
(3/10)x = $300,000
x = $1,000,000
Question 10: In the figure below, what is the value of angle a?
(1) Angle b is 120o
(2) The triangle created by the 3 lines is equilateral.
(a) Statement (1) ALONE is sufficient, but statement (2) is not sufficient.
(b) Statement (2) ALONE is sufficient, but statement (1) is not sufficient.
(c) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
(d) EACH statement ALONE is sufficient.
(e) Statements (1) and (2) TOGETHER are NOT sufficient.
Answer:
Statement (1): Angle b is 120o.
AngleBCA = 60o
AngleCAB = 60o
AngleCBA = 180o – 60o – 60o.
Statement (2): If the triangle is equilateral, all of its angles are 60o. Angle a is 180o – 60o = 120o.
Each statement alone is sufficient.
GMAT problems #1
GMAT problems #2
GMAT problems #3
GMAT problems #4