Free practice questions/GMAT Focus Edition

GMAT Focus Edition — Two-Part Analysis

6 free practice questions with full explanations.

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Question 1

Two numbers, x and y, satisfy the equations x + y = 18 and x - y = 4. Select the value of x and the value of y that satisfy both equations.

A) x = 11, y = 7
B) x = 7, y = 11
C) x = 10, y = 8
D) x = 12, y = 6

Show answer & explanation

Correct answer: A) x = 11, y = 7

Adding the equations: 2x = 22, so x = 11. Substituting: 11 + y = 18, so y = 7. This satisfies both x+y=18 (11+7=18) and x-y=4 (11-7=4).

Question 2

A company sells two products, A and B. Product A costs $15 to produce and sells for $25. Product B costs $20 to produce and sells for $35. Last month, the company sold a combined total of 100 units of A and B and earned a combined total profit of $1,350. Select the number of units of Product A sold and the number of units of Product B sold.

A) A = 50, B = 50
B) A = 40, B = 60
C) A = 60, B = 40
D) A = 30, B = 70

Show answer & explanation

Correct answer: D) A = 30, B = 70

Profit per unit: A = 25-15 = $10, B = 35-20 = $15. Let a+b=100 and 10a+15b=1350. From a=100-b: 10(100-b)+15b=1350, so 1000-10b+15b=1350, 1000+5b=1350, 5b=350, b=70, a=30.

Question 3

A rectangular garden has a perimeter of 60 feet. The length is 6 feet more than the width. Select the length and the width of the garden.

A) Length = 15, Width = 15
B) Length = 18, Width = 12
C) Length = 20, Width = 10
D) Length = 21, Width = 9

Show answer & explanation

Correct answer: B) Length = 18, Width = 12

Perimeter = 2(length+width) = 60, so length+width=30. With length = width+6: (width+6)+width=30, 2(width)=24, width=12, length=18.

Question 4

An investor splits $20,000 between two accounts: one earning 4% annual interest and another earning 7% annual interest. After one year, the investor earned a total of $1,190 in interest. Select the amount invested at 4% and the amount invested at 7%.

A) $7,000 at 4%, $13,000 at 7%
B) $6,000 at 4%, $14,000 at 7%
C) $8,000 at 4%, $12,000 at 7%
D) $10,000 at 4%, $10,000 at 7%

Show answer & explanation

Correct answer: A) $7,000 at 4%, $13,000 at 7%

Let x = amount at 4%, (20000-x) = amount at 7%. 0.04x + 0.07(20000-x) = 1190. 0.04x + 1400 - 0.07x = 1190. -0.03x = -210. x = 7000. So $7,000 was invested at 4% and $13,000 at 7%. Check: 0.04(7000) + 0.07(13000) = 280 + 910 = 1190.

Question 5

Two runners start at the same point and run in opposite directions. Runner 1 runs at a constant speed, and Runner 2 runs 2 mph faster than Runner 1. After 3 hours, they are 42 miles apart. Select the speed of Runner 1 and the speed of Runner 2.

A) Runner 1 = 6 mph, Runner 2 = 8 mph
B) Runner 1 = 7 mph, Runner 2 = 9 mph
C) Runner 1 = 8 mph, Runner 2 = 10 mph
D) Runner 1 = 9 mph, Runner 2 = 11 mph

Show answer & explanation

Correct answer: A) Runner 1 = 6 mph, Runner 2 = 8 mph

Let r = Runner 1's speed. Combined speed = r + (r+2) = 2r+2. Distance apart after 3 hours = 3(2r+2) = 42. 6r+6=42. 6r=36. r=6. Runner 1 = 6 mph, Runner 2 = 8 mph.

Question 6

A store marks up the wholesale price of an item by a certain percentage to set the retail price. An item with a wholesale price of $40 is later put on sale at 20% off the retail price, resulting in a sale price of $48. Select the markup percentage used to set the original retail price and the original retail price.

A) Markup = 40%, Retail = $56
B) Markup = 50%, Retail = $60
C) Markup = 60%, Retail = $64
D) Markup = 75%, Retail = $70

Show answer & explanation

Correct answer: B) Markup = 50%, Retail = $60

Sale price = Retail x 0.80 = 48, so Retail = 48/0.80 = $60. Markup = (60-40)/40 = 20/40 = 50%.

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