GMAT Practice Test Quantitative (Problem Solving)

Question 1

Jed has more than twice as many strawberries as Dianna, but only half as many as Lisa. If Dianna has ‘a' number of strawberries, how many strawberries do Jed, Dianna, and Lisa have in terms of ‘a'?

Accepted Answer

7a+6

Answer

Let Dianna have 'a' strawberries. If Jed has `2a+2` strawberries, this satisfies the condition of having "more than twice as many" as Dianna (since `2a+2 > 2a`). If Jed has `2a+2` strawberries, then Lisa has twice that amount, which is `2 * (2a+2) = 4a+4` strawberries. The total number of strawberries for Jed, Dianna, and Lisa combined is `a + (2a+2) + (4a+4)`, which simplifies to `7a+6`.

Question 2

Milk should be thinned to a 3:2 ratio of milk to water. The milkman accidentally added water, resulting in 8 liters of milk that is half water and half milk. What must he add to correct the proportions of the mixture?

Accepted Answer

2 liters milk

Answer

The desired milk to water ratio is 3:2. The current mixture is 8 liters, half milk and half water, meaning 4 liters milk and 4 liters water. To achieve a 3:2 ratio with 4 liters of water, we need (3/2) * 4 = 6 liters of milk. Since there are currently 4 liters of milk, the milkman must add 6 - 4 = 2 liters of milk to correct the proportions.

Question 3

A rectangle's width is 2/3 times its length. What is the perimeter of this rectangle if the length is calculated to be 9?

Accepted Answer

30

Answer

The length of the rectangle is given as 9. The width is 2/3 times its length, so the width is (2/3) * 9 = 6. The perimeter of a rectangle is calculated as 2 * (length + width). Therefore, the perimeter is 2 * (9 + 6) = 2 * 15 = 30.

Question 4

A line l passes through the point and is parallel to the y-axis (2,3). What are the gradient (m) and x-intercept?

Accepted Answer

m= ∞ , x= (2,0)

Answer

A line parallel to the y-axis is a vertical line. Vertical lines have an undefined or infinite gradient (m = ∞). Since the line passes through the point (2,3) and is vertical, every point on the line will have an x-coordinate of 2. Therefore, it intersects the x-axis at the point where y=0, which is (2,0).

Question 5

What is the equation of the new parabola formed by shifting y = x2 three units to the positive y-axis?

Accepted Answer

y = x2 + 3

Answer

To shift a parabola vertically on the y-axis, you add or subtract a constant from the entire function. Shifting 'k' units to the positive y-axis means adding 'k' to the original equation. Therefore, shifting y = x² three units up results in the new equation y = x² + 3.