Quant Drill — 12 PS Questions + Simple Explanations

GMAT Math Practice Quiz

12 Questions • 24 Minutes

Question 1/12

24:00

Question 1

How many integers n are there such that 1 < 5n + 5 < 25?

(A) Five

(B) Four

(C) Three

(D) Two

(E) One

Correct Answer: B (Four)

Step-by-Step Explanation:
1. Start with: 1 < 5n + 5 < 25
2. Subtract 5 from all parts: 1 - 5 < 5n < 25 - 5
3. Simplify: -4 < 5n < 20
4. Divide by 5: -0.8 < n < 4
5. Integer values: 0, 1, 2, 3
6. Check boundaries:
- n = 0: 5(0) + 5 = 5, 1 < 5 < 25 ✓
- n = 3: 5(3) + 5 = 20, 1 < 20 < 25 ✓
- n = 4: 5(4) + 5 = 25, not < 25 ✗

Therefore, there are 4 integer values.

Strategy: Solve compound inequalities by performing the same operation on all three parts. Remember to test boundary values.

Based on: Inequality problem similar to GMAT question types

Question 2

If y is an integer, then the least possible value of |23 - 5y| is

(A) 1

(B) 2

(C) 3

(D) 4

(E) 5

Correct Answer: B (2)

Step-by-Step Explanation:
1. We want to minimize |23 - 5y| where y is an integer
2. This means we want 5y to be as close as possible to 23
3. Try nearby multiples of 5:
- y = 4: 5y = 20, |23 - 20| = 3
- y = 5: 5y = 25, |23 - 25| = 2
- y = 6: 5y = 30, |23 - 30| = 7
4. The minimum value is 2 when y = 5

Therefore, the least possible value is 2.

Strategy: For expressions like |a - by|, find the multiple of b closest to a.

Based on: Absolute value minimization problem similar to GMAT question types

Question 3

√80 + √125 =

(A) 9√5

(B) 20√5

(C) 41√5

(D) √205

(E) 100

Correct Answer: A (9√5)

Step-by-Step Explanation:
1. Simplify each radical:
√80 = √(16 × 5) = √16 × √5 = 4√5
√125 = √(25 × 5) = √25 × √5 = 5√5
2. Add: 4√5 + 5√5 = 9√5

Therefore, √80 + √125 = 9√5.

Strategy: Simplify radicals by factoring out perfect squares, then combine like terms.

Based on: Radical simplification problem similar to GMAT question types

Question 4

The average of 10, 30, and 50 is 5 more than the average of 20, 40, and what number?

(A) 15

(B) 25

(C) 35

(D) 45

(E) 55

Correct Answer: A (15)

Step-by-Step Explanation:
1. Average of 10, 30, 50 = (10 + 30 + 50)/3 = 90/3 = 30
2. This is 5 more than the other average, so other average = 30 - 5 = 25
3. Let the missing number be x
4. Average of 20, 40, x = (20 + 40 + x)/3 = 25
5. Multiply both sides by 3: 60 + x = 75
6. Solve: x = 75 - 60 = 15

Therefore, the missing number is 15.

Strategy: Calculate the known average first, then work backwards using the average formula.

Based on: Average comparison problem similar to GMAT question types

Question 5

In the equation y = kx + 3, if y = 17 when x = 2, what is the value of y when x = 4?

(A) 34

(B) 31

(C) 14

(D) 11

(E) 7

Correct Answer: B (31)

Step-by-Step Explanation:
1. Use given point to find k: when x = 2, y = 17
2. Substitute: 17 = k(2) + 3
3. Solve for k: 17 - 3 = 2k → 14 = 2k → k = 7
4. Now equation is: y = 7x + 3
5. Find y when x = 4: y = 7(4) + 3 = 28 + 3 = 31

Therefore, when x = 4, y = 31.

Strategy: Use given point to find the constant, then substitute the new value.

Based on: Linear equation problem similar to GMAT question types

Question 6

Jar P has x red and y green marbles totaling 80. Jar Q has y red and z green marbles totaling 120. Jar R has x red and z green marbles totaling 160. How many green marbles are in Jar R?

(A) 70

(B) 80

(C) 90

(D) 100

(E) 110

Correct Answer: D (100)

Step-by-Step Explanation:
1. From the information:
x + y = 80
y + z = 120
x + z = 160
2. Add all three equations: (x+y) + (y+z) + (x+z) = 80 + 120 + 160
3. Simplify: 2x + 2y + 2z = 360
4. Divide by 2: x + y + z = 180
5. We want z (green marbles in Jar R)
6. From x + y + z = 180 and x + y = 80, subtract: z = 180 - 80 = 100

Therefore, there are 100 green marbles in Jar R.

Strategy: Set up equations from the given information and look for ways to combine them to find the desired variable.

Based on: System of equations problem similar to GMAT question types

Question 7

Four staff members worked in the ratio 2:3:5:6. If one person worked 30 hours, which of the following CANNOT be the total number of hours worked by all four?

(A) 80

(B) 96

(C) 160

(D) 192

(E) 240

Correct Answer: D (192)

Step-by-Step Explanation:
1. Ratio 2:3:5:6, total ratio units = 2+3+5+6 = 16
2. Total hours must be multiple of 16
3. The 30 hours must correspond to one of the ratio parts
4. Check which totals give 30 hours for one person:
- If 2 parts = 30, then 1 part = 15, total = 15×16 = 240
- If 3 parts = 30, then 1 part = 10, total = 10×16 = 160
- If 5 parts = 30, then 1 part = 6, total = 6×16 = 96
- If 6 parts = 30, then 1 part = 5, total = 5×16 = 80
5. 192 is not in this list

Therefore, 192 cannot be the total hours.

Strategy: For ratio problems, check that totals are multiples of the sum of ratio parts, and that individual values match the given information.

Based on: Ratio analysis problem similar to GMAT question types

Question 8

A company had 15% more employees in December than in January. If there were 460 employees in December, how many were there in January?

(A) 391

(B) 400

(C) 410

(D) 423

(E) 445

Correct Answer: B (400)

Step-by-Step Explanation:
1. December = January + 15% of January = 1.15 × January
2. December = 460
3. So 1.15 × January = 460
4. January = 460 ÷ 1.15
5. Calculate: 460 ÷ 1.15 = 460 ÷ (115/100) = 460 × (100/115)
6. Simplify: = (460 × 100)/115 = (460 ÷ 115) × 100 = 4 × 100 = 400

Therefore, there were 400 employees in January.

Strategy: For percent increase problems, use: New = Original × (1 + percent/100)

Based on: Percentage calculation problem similar to GMAT question types

Question 9

A glass was filled with 10 ounces of water. If 0.01 ounce evaporated each day for 20 days, what percent of the original amount evaporated during this period?

(A) 0.002%

(B) 0.02%

(C) 0.2%

(D) 2%

(E) 20%

Correct Answer: D (2%)

Step-by-Step Explanation:
1. Total evaporation = 0.01 oz/day × 20 days = 0.2 oz
2. Original amount = 10 oz
3. Percent evaporated = (0.2 ÷ 10) × 100%
4. Calculate: 0.2 ÷ 10 = 0.02, × 100% = 2%

Therefore, 2% of the original amount evaporated.

Strategy: Calculate total amount, then use: Percent = (Part/Whole) × 100%

Based on: Percentage application problem similar to GMAT question types

Question 10

A glucose solution contains 15 grams of glucose per 100 cubic centimeters. If 45 cubic centimeters are poured into an empty container, how many grams of glucose are in the container?

(A) 3.00

(B) 5.00

(C) 5.50

(D) 6.50

(E) 6.75

Correct Answer: E (6.75)

Step-by-Step Explanation:
1. Concentration: 15g per 100cc
2. For 45cc, set up proportion: 15g/100cc = xg/45cc
3. Cross-multiply: 15 × 45 = 100 × x
4. Calculate: 675 = 100x
5. Solve: x = 675 ÷ 100 = 6.75

Therefore, there are 6.75 grams of glucose.

Strategy: Set up and solve proportions using cross-multiplication.

Based on: Proportion calculation problem similar to GMAT question types

Question 11

On day 1, orangeade was made by mixing equal amounts of juice and water. On day 2, it was made with the same amount of juice but twice the amount of water. Both days had the same total revenue. If day 1 price was $0.60 per glass, what was day 2 price per glass?

(A) $0.15

(B) $0.20

(C) $0.30

(D) $0.40

(E) $0.45

Correct Answer: D ($0.40)

Step-by-Step Explanation:
1. Day 1: equal juice and water → 1 unit juice + 1 unit water = 2 units orangeade
2. Day 2: same juice, twice water → 1 unit juice + 2 units water = 3 units orangeade
3. Revenue same both days: Price₁ × Quantity₁ = Price₂ × Quantity₂
4. Quantity ratio: Day 1 has 2 units, Day 2 has 3 units
5. So: 0.60 × 2 = Price₂ × 3
6. Calculate: 1.20 = 3 × Price₂
7. Price₂ = 1.20 ÷ 3 = 0.40

Therefore, day 2 price was $0.40 per glass.

Strategy: Compare the total volumes produced each day, then use the revenue equation.

Based on: Mixture and pricing problem similar to GMAT question types

Question 12

What is the slope of the line with equation 3x + 7y = 9?

(A) -7/3

(B) -3/7

(C) 3/7

(D) 3

(E) 7

Correct Answer: B (-3/7)

Step-by-Step Explanation:
1. Convert to slope-intercept form (y = mx + b)
2. Start with: 3x + 7y = 9
3. Subtract 3x: 7y = -3x + 9
4. Divide by 7: y = (-3/7)x + 9/7
5. Slope is the coefficient of x: -3/7

Therefore, the slope is -3/7.

Strategy: Convert linear equation to slope-intercept form y = mx + b, where m is the slope.

Based on: Coordinate geometry problem similar to GMAT question types

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Time: 0:00

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