# GRE Practice Test (Quantitative Reasoning Test)

#### Compare the following two figures:

Explanation:

When solving a Quantitative Comparison type of question, the first step is to simplify quantities A and B.

Remember that any operation performed on Quantity A to simplify it, must also be performed on Quantity B.

Simplifying:

(Note that the blank underline represents the unknown equality/inequality sign in each equation/inequality.)

Comparing the simplified quantities:

a3–1 ____ 1

After simplifying and then dividing both quantities by a4, we find that Quantity B is equal to 1.

Trying a negative value for a will result in a negative value for quantity A, which means that B is greater.

Using a positive value bigger than 1 for a, however, will result in a positive value bigger than 1 for quantity A,
which means that A is greater.

These inconsistent results show that, with the information given, we don’t know how A compares to B.

Our conclusion is that the relationship cannot be determined from the information given.

#### Adam has bought a certain number of apples. Jen has bought 5 times the natural product that Adam has bought. In case Jen has bought two and a half dozen apples how many apples does Adam have?

It's a relatively simple question. Jen has five times the number of apples which Adam has. If Jen has 30 apples, Adam has 30/5=6 apples.

#### What would be the circumference of a circle that has been inscribed in a square of area 5?

Area of a square is multiple of any two sides. If the area is 5, each side of the square has to be √5 i.e. √5*√5=5 Now, the radius of the circle would be half of √5 because the circle in inscribed inside the square. So Radius = √5/2 So, Circumference= 2*( π)*√5/2 Circumference= π√5

#### In 30 days, 20 employees built a house. In order to do the job in 15 days, how many workers will be required?

As stated in the question, the work needs to be completed in half the days as compared to the earlier timeline for completion, therefore, the number the workers needs to be doubled.

#### Every day, Master Chef Alan prepares a dish from one of his cookbooks. He has written three books, each with 15 distinct recipes. What are the chances that he would prepare the fourth dish from the third book today?

We note that there are three books and each book contains 15 recipes so there are a total of 45 recipes. The probability that he will cook 4th dish from 3rd book today is 1/45. It's important that you must not get distracted by irrelevant information. All the recipes are different from each other.

#### Dell Laptop prices were dropped by 10% for the general public during a Christmas sale. Employees of Dell, on the other hand, were given a 5% discount. If a laptop's original price was $330 before the Christmas sale, how much would it cost a Dell employee during the Christmas sale?

Original Price = $330 Price after 10% discount= 330 * 0.9 = $297 Price after further 5% discount (for Dell employees) = 297* 0.95 = $282.

#### If B < 0: compare the two quantities:

Explanation: Select and test values for A, B, and C: A=0, B=−2, C=1: Quantity A: A+C=0+1=1 Quantity B: AB+BC=0(−2)+1(−2)=−2 Quantity A > Quantity B. A=−1, B=−2, C=1: Quantity A: A+C=−1+1=0 Quantity B: AB+BC=−1(−2)+1(−2)=0 Quantity A = Quantity B. The answer cannot be determined. A=0, B=−2, C=1: Quantity A: A+C=0+1=1 Quantity B: AB+BC=0(−2)+1(−2)=−2 Quantity A > Quantity B. A=−1, B=−2, C=1: Quantity A: A+C=−1+1=0 Quantity B: AB+BC=−1(−2)+1(−2)=0 Quantity A = Quantity B. The answer cannot be determined.

#### If m=1/2, compare the two quantities.

Substitute the value m=1/2 into each quantity and compare the resulting values: Quantity A: (1/2)−3/4, which becomes 2 3/4 = 8 1/4 ≈ 1.68 Quantity B: 8⋅(1/2)−1/4, which becomes 8⋅2 1/4 ≈ 9.51 Quantity A < Quantity B Note: You’ll notice that we followed PEMDAS (order of operations) and dealt with the exponent first when finding the answer for Quantity A.

#### Which of the following integers fulfills this condition: It may be a multiple of 8 and it is the cube of an indeed number? Demonstrate all such integers. A) 72 (B) 64 (C) 128 (D) 216 (E) 1000 (F) 1728

(A) 72 and (C) 128 are multiples of 8 but are not cubes of any integer. The following satisfy the given condition: (B) 64 is a multiple of 8 (8 x 8) and the cube of 4 (4 x 4 x 4) (D) 216 is a multiple of 8 (8 x 27) and the cube of 6 (6 x 6 x 6) (E) 1000 is a multiple of 8 (8 x 125) and the cube of 10 (10 x 10 x 10) (F) 1728 is a multiple of 8 (8 x 216) and the cube of 12 (12 x 12 x 12)

#### In the diagram above, what is the area of triangle ALC?

First of all, we need to find LC, but for that, we need to find DL. We know that AB= DC = 7. So, LC = DC- DL Now, DL = √(5^2- 3^2 )= 4 (using Pythagoras Theorem) So, LC = 7-4 = 3 Therefore, Area = (1/2)(Base)(Altitude) = (0.5)(3)(3) = 4.5

#### Alan has nearly twice as many chocolates as Alice and half as many as Nadia. If Alice has ‘a’ number of chocolates, then in terms of ‘a’, how many chocolates do Alan, Alice and Nadia have?

We know that Alice has 'a' chocolates. Alan has 2a+2 chocolates from the given statement in the question. Nadia has double the chocolates as Alan has, so she has 4a+4 chocolates. Adding these, we get 4a+4+2a+2+a = 7a +6 .

#### Milk should be thinned using 3 parts milk and 2 parts water. Because the milkman accidentally added water, he now has 8 liters of milk that is half water and half milk. What does he need to add to get the proportions of the mixture right?

We note that the final ratio must be 3:2 for milk and water respectively. Now, according to given scenario in the question, we have eight liters of solution with 4 liters milk and 4 liters water, which makes it 2:2. In order to make it 3:2, we add 2 liters milk. This would make a total of 6 liters milk and 4 liters water i.e. 6:4 which can be simplified to 3:2.

#### A rectangle's width is equal to two-thirds of its length. What is the perimeter of this rectangle if the length is computed to be 9?

As the width of the rectangle is 2/3 times its length which is 9, the width comes out to be 6. Therefore, the perimeter becomes, 6+6+9+9 = 30. (Perimeter of a rectangle is calculated by adding the lengths of each side of that rectangle)

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

As the given line is parallel to the y-axis, and the slope of y-axis is infinite, therefore its slope is also infinite. As the line is defined by x=2, hence its x intercept will also be 2 because all of its points will be of the form (2,y).

#### A one-unit-diameter sphere is enclosed in a cube with one-unit-wide sides. Find the remaining unoccupied volume inside the cube.

We find the volume of the cube by the formula length^3. We then subtract from it the volume of the sphere to find the empty volume. The volume of cube amounts to 1*1*1=1. The volume of the sphere is (4/3)* π *(radius)^3. Putting in the values we get (4/3)* π *(0.5) ^3. This is equal to pi/6. Subtracting the two gives 1- π /6.

#### If A is the longest side of a triangle, then B and C are the other two sides. What connection exists between them?

The largest side is greater than the difference of the smaller sides and less than the sum of the two smaller sides. Therefore, option C is the correct answer.

#### A square PQRS is enclosed in another square ABCD. Discover the proportion of the area of PQRS to the range of ABCD

If we divide the figure in 4 equal parts we see that the shaded area is half the total area. An alternate approach is to find the unshaded area by observing that it is composed of right angled triangles, adding this area and subtracting from total can get the shaded area.

#### If CB=(CF)/4, what is the ratio of the area of triangle ABC to the area of square ADFC?

We find the area using the one fourth length, 0.5*base*height, then divide it by the area of the square (square of side). For length we use an arbitrary variable, but the choice doesn't matter as the ratio is independent of it. Let's suppose that the length of one side is 'x'. Then area of square becomes x2. The area of triangle becomes (1/2)(x)( x/4) = x2/8. So, the ratio becomes (x2/8)/x2 which simplifies to 1/8

#### If the product of two integers x and y, with y being a multiple of three, is less than 82, What is the highest possible value for x?

In order to find the maximum value of x, we need to put the minimum value of y i.e. 3. Now, if we divide 82 by 3, we get 27.33, which means the maximum integer value that x can have must be less than 27.33.

#### Which of the following is greater than ‘b' when a/b = 1/6 and 9a-b = 12? mark all the probable answers.

Please select 2 correct answers

a/b = 1/6 means b= 6a. Putting this in the other equation, we get 9a-6a = 12 -> 3a =12 -> a=4 9(4) – b = 12 -> 36-12 = b -> b= 24 Only options (e,f) are greater than 24.

#### Adam has purchased a set number of apples. Jen has purchased five times the amount of fruit that Adam has. How many apples does Adam have if Jen bought two and a half dozen?

It's a relatively simple question. Jen has five times the number of apples which Adam has. If Jen has 30 apples, Adam has 30/5=6 apples.

#### Which of the following represents the sum of two integers such that their product equals 12? Mark all probable answers.

Please select 3 correct answers

First of all, we note that we can get 12 by multiplying 1 with 12, 2 with 6,and 3 with 4. Similarly, multiplying the negative of these numbers also yields the same results. Therefore, the sums of these numbers could be 13,8, 7, -13, -8, and -7.

#### Alan went to the store to get some household supplies. He purchased a total of four products. The top three items have an average price of $100. What was the cost of the fourth item if the total cost of the four products was less than $105 but more than $95?

Please select 3 correct answers

Lets these four items be W,X,Y,Z. Now, (w+x+y)/3=100 -> w+x+y = 300 Now, 95<(w+x+y+z)/4 380< w+x+y+z <420 And w+x+y is 300 (calculated in the first step). So, the equation becomes, $80 < z < $120.

#### Rectangle A has twice the length and 1/2 the width of rectangle B. Rectangle B features a length of six units and a width of four units. What is the edge of rectangle A?

Two times 6 is 12 and half of 4 is 2, so rectangle A has two 12-unit sides and two 2-unit sides and 12 + 12 + 2 + 2 = 28.

#### There are at least 15 different brands of biscuits available in a supermarket store. In this store, the ratio of different brands of chocolates to biscuits is 3 to 5. Which of the following is the maximum amount of chocolate brands that this retailer might have? Mark all the probable answers.

Please select 2 correct answers

The least number of biscuit brands are 15. Also, the ratio of chocolate brands to biscuit brands is 3: 5. Therefore, 3/5= x/15 x=9 where 'x' is the minimum number of chocolate brands. It is possible that there are more than 15 brands of biscuits and thus, the possibility of more than 9 chocolate brands. However, 19 is not a valid answer because the number of chocolate brands must be divisble by 3 as you cannot have a fraction of a brand sold at a store.

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