GMAT Classic Mock Test - 2 - GMAT MCQ

The copy machine produces 20 copies of the one-page document each minute. Because there are 60 minutes in an hour, the constant rate of 20 copies per minute is equal to 60 x 20 = 1,200 copies per hour. With the machine working at this rate, the amount of time that it takes to produce 4,800 copies of the document is 

4800 copies  / 1200 copies/hours  = 4 hours

x + y = 2 given

y = 2 - x subtract x from both sides 

x² + (2 - x)² = 2 substitute y = 2 - x into x² + y² = 2 

2x² - 4x + 4 = 2 expand and combine like terms 

2x² - 4x + 2 = 0 subtract 2 from both sides

x² - 2x + 1 = 0 divide both sides by 2 

(x - l)(x - 1) = 0 factor

x = 1 set each factor equal to 0 

y = 1 use x = l and y = 2 - x

xy = 1  multiply 1 and 1 

The correct answer is D .

Given that the sum of the first n even numbers is n(n + 1), the sum is equal to 110 when 110 = n(n + 1). To find the value of n in this case, we need to find the two consecutive integers whose product is 110. These integers are 10 and 11; 10 x 11 = 110. The smaller of these numbers is n.

The boat traveled in a straight line from docking station #2 on the west dock to one of the docking stations on the south dock, passing through a single point that is both due east of docking station #4 and due north of docking station #7. Call this point P. Having traveled to P, the boat was both 2d south of its starting point and 2d east of its starting point. Therefore, traveling in a straight line, the boat traveled one unit south for every one unit traveled east. And because at point P the boat was a distance d north of the south dock, the boat must have reached the south dock at a point which is a distance of d east of docking station #7 (which is due south of point P). This point is the position of doctang station #8. The boat therefore arrived at docking station #8.

The correct answer is B

This question is most efficiently answered by distributing the 6 over 87.30 and 0.65, and then combining the terms that contain a factor of 87.30, as follows:
6(87.30 + 0.65) - 5(87.30) = 6 (87.30) + 6 (0.65) - 5 (87.30) = (6 - 5) 87.30 + 6(0.65) = 87.30 + 3.90 = 91.20

The correct answer is D.

The figure shows points A, B, C, and D as well as the given measurements.
Since AC = AB + BC, it
follows that 4 = 3 + BC, and so BC =  1.
Then, since BD =BC+ CD, it follows that 6 = 1 + CD, and so CD= 5.
Alternately, AD = AB + BD = 3 + 6 = 9.
Also, AD = AC + CD,so 9 = 4 + CD and CD = 5. 

The correct answer 1s E.

Given that x = -2,y = 1, and z = 3, it follows by substitution that
x²yz - xyz² = (-2)² (1)(3)- (- 2)(1)(3²)
= (4)(1)(3) - (- 2)(1)(9)
= 12 - (-18)
= 12 + 18
= 30

The correct answer is C.

If the company produces and sells 1,000 radios, its gross profit from the sale of these radios is equal to the total revenue from the sale of these radios minus the total cost.
The total cost is equal to the number of radios produced multiplied by the production cost per radio: 1,000 x $15.00. 
The total revenue is equal to the number of radios sold multiplied by the selling price: 1,000 x $14.00.
The gross profit in this case is therefore 1,000 x $15.00 -1,000 X $14.00 = 1,000 X ($15.00 - $14.00) =1,000 ($1.00) = $1,000.
If 2,000 radios are produced and sold, the total cost is equal to 2,000 x $13.50 and the total revenue is equal to 2,000 x $15.00.
The gross profit in this case is therefore 2,000 x $15.00 -2,000 X $13.50 = 2,000 X ($15.00 -$13.50) = 2,000 x ($1.50)= $ 3,000.
This profit of$ 3,000 is $2,000 greater than the gross profit of $1,000 from producing and selling 1,000 radios.
The correct answer is D.

Find the value of each expression to determme if it is positive.
I. -3 - (-5) = -3 + 5 = 2, which is positive.
II. (-3)(-5) = 15, which is positive.
III. -5 -(-3) = -5 + 3 = -2,
which is not
positive.

The correct answer is D.

Write an equation for the given information and solve for x.

Given:
Point X lies on side BC of rectangle ABCD.
Length of rectangle ABCD is 12 and width is 18.

To find:
Area of triangular region AXD.

Approach and Working

Area of triangle = ½ × Base × Height
= ½ × Length of rectangle × width of rectangle
= ½ ×12 × 8= 48 
Hence, the correct answer is B.

The grocer has 400 pounds of coffee in stock, of which (400)(20%) = 80 pounds is decaffeinated coffee. Therefore, if the grocer buys 100 pounds of coffee, of which (100)(60%) = 60 pounds is decaffeinated coffee, then the percent of the grocer’s stock of coffee that is decaffeinated would be
80 + 60 / 400 + 100 = 140 / 500
= 28/100
= 28%

The Correct answer is A

The 18-wheel truck has 2 wheels on its front axle and 4 wheels on each of its other axles, and so if A represents the number of axles on the truck in addition to the front axle,
then 2 + 4A = 18, from which it follows that AA = 16 and A - 4.
Therefore, the total number of axles on the truck is 1 +A  = 1 + 4 = 5.
Then, using T = 1.50 + 0.5Q(x - 2), where x is the number of axles on the truck and x = 5, it follows that T= 1.50 + 0.50(5 -2) = 1.50 + 1.50 - 3.00.
Therefore, the toll for the truck is $3.00.
The correct answer is B.

Given the expression x² - 10x + 16, a table of values can be created for the corresponding fonction f(x) = x² - 10x + 16 and the graph in the standard (x,y) coordinate plane can be sketched by plotting selected points:

It is clear from both the table of values and the sketch of the graph that as the value of x increases from -4 to 4, the values of x² -10x + 16 decrease.
Therefore, the value of x² -10x +16 is greatest when x = -4.

If x  = -5/8 and y = -1/2 then, 

The correct answer is C

Knowing that statement 1, x + y = 12, is true is not enough to determine the value of x³ + y³.
Also statement 2, x − y = 8, is not enough to determine the values of x3 + y³.
Strategy 5 tells you to consider statements 1 and 2 together.
When you know both x + y = 12 and x − y = 8, you can determine that x = 10 and y = 2.
Thus, the value of x³ + y³ is 1,008.
The answer to the problem is C.

Simply knowing that two angles of the triangle have the same measure does not allow you to find the area of the triangle, so statement 1 is not sufficient.
Using statement 2, knowing that AB = 9, BC = 12, and CA = 15 allows you to determine that triangle ABC is a right triangle.
Since AB² + BC² = 9² + 12² = 15² = CA², triangle ABC is a right triangle.
The legs of the right triangle, AB and BC , can be the base and altitude of the triangle, so the area of triangle ABC is 1/2bh = 1/2 x 9 x 12 = 54.
Thus, statement 2 is sufficient alone. As indicated by strategy 3, you must check statement 2 alone.
Since it is sufficient, the answer is B.

For statement 1, if 1/2(x + y) = w, then x + y = 2w and w + x + y = 3w,
so the average of w, x, and y is 3w ÷ 3 = w and z = w.
Thus, statement 1 is sufficient. Using strategy 2, you need to check statement 2 alone to determine if the answer is A or D.
For statement 2, if w = x = y, then awn+d wx + y = 3w and (w + x + y) ÷ 3 = 3w ÷ 3 = w.
Thus, w is the average = z, so statement 2 is sufficient.
Since each statement is sufficient alone, the answer is D.

D For statement 1, if the perimeter of the square is 28, then 45 = 28 and 5 = 7.
The area of a square is s², so s² = 7² = 49.
Thus, statement 1 is sufficient. Using strategy 2, you need to see if statement 2 alone is sufficient.
The diagonal forms an isosceles right triangle with two of the sides of the square.
If the diagonal is7√2, then s² + s² = (7√2)2 and 2s² = 98. So s² = 49.
Thus, statement 2 is sufficient.
Since each statement alone is sufficient, the answer is D.

As stated in the problem, if the ratio of x : y : z = 1:2:3, then y = 2x and z = 3x.
Thus, x + y + z = 6x. For statement 1,
if x + z = 16, then x + 3x = 16, and x = 4. So x + y + z = 6x = 6(4) = 24.
Thus, statement 1 is sufficient. From strategy 2, you know to check each statement.
Statement 2 does not provide any additional information.
Since the ratio is 1 : 2 : 3, you can already conclude that x < y < z.
Thus, statement 2 is not sufficient alone.
Since only statement 1 yielded a result for the question, A is the correct answer for this question.

Evaluate Statement (1) ALONE
Statement 1: Cindy, the wife of Bill's only brother Chris does not have any siblings.
We know that Cindy has no siblings and she is the wife of Bill's only brother Chris. So, this statement has helped us establish the relation between Cindy and Bill. However, this statement does not provide any information about Betty and is hence not sufficient to answer the question.

Statement 1 ALONE is NOT sufficient.
Eliminate choices A and D. Choices narrow down to B, C, or E.

Evaluate Statement (2) ALONE
Statement 2: Betty is Cindy's brother in law's wife.
We know that Betty is Cindy's brother in law's wife. This statement establishes a relation between Cindy and Betty. This does not answer the question of how Bill is related to either Cindy or Betty.

Statement 2 ALONE is not sufficient. Eliminate choice B.

Evaluate the statements together
Statement 1: Cindy, the wife of Bill's only brother Chris does not have any siblings.
Statement 2: Betty is Cindy's brother in law's wife.
We combine the two statements, we know that Bill and Cindy are related to each other through Chris, who is the only brother of Bill and that Cindy is Betty's brother in law's wife.
Cindy does not have any siblings and hence her brother in law has to necessarily be her husband's sibling. As Chris is the only brother of Bill, Cindy's brother in law has to be Bill and Betty is his wife.

Statements TOGETHER are sufficient.

Choice C is the answer.

Evaluate Statement (1) ALONE: y³ is an integer
We know that y³ is an integer.
However, that does not necessarily mean that y is an integer.
Let us say, y³ = 2, then y is not an integer.
However, if y³ = 8, then y = 2 and is an integer.

Statement 1 ALONE is NOT sufficient.
Eliminate choices A and D. Choices narrow down to B, C, or E.

Evaluate Statement (2) ALONE: 3y is an integer
We know that 3y is an integer.
Let us say 3y = 2, then y is not an integer.
However, if 3y = 3, then y will be an integer.

Statement 2 ALONE is NOT sufficient.
Eliminate choice B. Choices narrow down to C or E.

Evaluate Statements (1) & (2) Together: y³ is an integer and 3y is an integer
Only for integer values of y, will both y3 and 3y be integers simultaneously.
Why? If 3y is an integer and y is not an integer, y3 will not be an integer.

Statements TOGETHER are sufficient. Choice C is the answer.

Evaluate Statement 1 ALONE
Statement 1: The sales booked by the salesman in the month of November 2003 minus salesman's commission was $245,000

From statement 1, we know the value of sales after the salesman's commission is subtracted.
From the question stem, we know his commission is 3% of the sales booked. Then value of sales after subtracting his commission is 100 − 3 = 97% of the sales booked.
Putting the two together, we can deduce that 97% of sales booked = $245,000. So we can find out the sales booked.
Statement 1 ALONE is SUFFICIENT.
Eliminate choices B, C, and E.
Answers narrow down to choices (A) or (D).

Evaluate Statement 2 ALONE
Statement 2: The selling price of the sales booked by the salesman in the month of November 2003 was 125 percent of the original purchase price of $225,000.

From statement 2, we know that the original purchase of the products is $225,000.
We can compute the sales booked as 125% of 225,000 = 1.25 × 225,000.
Statement 2 ALONE is SUFFICIENT.
Each statement is INDEPENDENTLY sufficient.

Choice D is the correct answer.

Evaluate Statement (1) ALONE: x is divisible by 6
Approach: Look for a counter example

Example: x = 6. It is divisible by 6. However, it is NOT divisible by 12.
Counter Example: x = 12. It is divisible by 6. It is divisible by 12 as well.
Knowing that x is divisible by 6 is not enough to answer the question.

If x is divisible by 6, we can infer that it is divisible by 3 and 2. But we cannot deduce whether it is also divisible by 22 - which is essential to deduce that x is divisible by 12.

Statement 1 ALONE is NOT sufficient.
Eliminate choices A and D. Choices narrow down to B, C, or E.

Evaluate Statement (2) ALONE: x is divisible by 8
If x is divisible by 8, then x will definitely be divisible by 4.
However, from statement (2) alone we do not know if x is divisible by 3.
Alternative Approach: Look for a counter example

Example: x = 8. It is divisible by 8. However, it is NOT divisible by 12.
Counter Example: x = 24. It is divisible by 8. It is divisible by 12 as well.
Knowing that x is divisible by 8 is not enough to answer the question.

Statement 2 ALONE is NOT sufficient.
Eliminate choice B. Choices narrow down to C or E.

Evaluate Statements (1) & (2) Together: x is divisible by 6 & x is divisible by 8
From statement 1, if x is divisible by 6, it is definitely divisible by 3.
From statement 2, if x is divisible by 8, it is definitely divisible by 4.
So, by combining the two statements, we can conclude that x is divisible by 3 and by 4.
Or that x is divisible by 12.

Statement TOGETHER are sufficient. Choice C is the answer.

Evaluate Statement (1) ALONE: (a + b)² < (a - b)²

Expanding both sides of the inequality, we get a² + b² + 2ab < a² + b² - 2ab
Simplifying we get, 4ab < 0 or ab < 0.
So, we can conclude that ab is not positive. We have got a definite NO as the answer.

Statement 1 ALONE is sufficient.
Eliminate choices B, C and E. Choices narrow down to A or D.

Evaluate Statement (2) ALONE: a = b

This is actually the statement that could trick you.
a = b.
So, either both a and b or positive or both a and b are negative. In either case ab is positive.
We will certainly be "tempted" to decide that statement 2 is also sufficient.

The catch is that, both a and b could be 0. In that case ab = 0, which is not positive.
If 'a' and 'b' are either both positive or both negative, the answer is yes. If both are 0, the answer is no.
As we are not able to conclude whether ab is positive with statement 2, it is not sufficient.

Statement 2 ALONE is NOT sufficient.
Eliminate choice D.

Statement 1 ALONE is sufficient but statement 2 is not sufficient. Choice A is the answer.

Evaluate Statement (1) ALONE:
(-1)^(Y+2) = -1

Property: (-1)^{ODD NUMBER} = -1

Therefore, Y + 2 is an odd number.
Hence, Y has to be an odd number.
So, when Y is divided by 2, the remainder is 1.
The answer to the question is a definite YES.

Statement 1 ALONE is sufficient.
Eliminate choices B, C and E. Choices narrow down to A or D.

Evaluate Statement (2) ALONE: Y is prime.

Possibility 1: Y could be '2' which is an even number.
So, if Y is 2, when Y is divided by 2, the remainder is '0'.

Possibility 2: Any prime number other than 2
All prime numbers other than 2 are odd numbers.
So, if Y is one of the other prime numbers, when Y is divided by 2, the remainder is '1'.
We donot have enough data in the question stem or statement 2 to conclude whether Y is 2 or one of the other prime numbers.
As we are not able to conclude whether Y is an even number using statement 2, it is not sufficient.

Statement 2 ALONE is NOT sufficient.
Eliminate choice D.

Statement 1 ALONE is sufficient, but statement 2 is not sufficient. Choice A is the answer.

Evaluate Statement (1) ALONE: (P + 2) and (P - 2) are prime.

Inference: (P - 2), P and (P + 2) are 3 consecutive odd integers.
Why?
Because (P - 2) and (P + 2) are prime, both numbers have to be odd.
(P - 2), P, and (P + 2) are three numbers in an arithmetic progression with a common difference of 2.
So, the 3 numbers have to be 3 consecutive odd or consecutive even integers. If (P - 2) and (P + 2) are odd, then these 3 numbers have to be 3 consecutive odd integers.

One out of 3 consecutive odd integers, (P - 2), P, and (P + 2) will definitely be a multiple of '3'.
If (P + 2) and (P - 2) are prime, then P has to be a multiple of '3', which is not prime.

The only exception is if the 3 consecutive odd numbers are 3, 5, and 7. However, we are dealing with two digit positive integers. So that possibility is ruled out.

Statement 1 ALONE is sufficient.
Eliminate choices B, C, and E. Choices narrow down to A or D.

Evaluate Statement (2) ALONE: (P - 4) and (P + 4) are prime.

This is a brilliant statement.
1. The remainder when (P - 4) and (P - 1) are divided by 3 will be the same.
2. Similarly, the remainder when (P + 4) and (P + 1) are divided by 3 will be the same.
If (P - 4) and (P + 4) are prime, both (P - 4) and (P + 4) will leave a remainder when divided by 3.

Therefore, (P - 1) and (P + 1) will also leave a remainder when divided by 3. i.e., they are not divisible by 3.
(P - 1), P, (P + 1) are 3 consecutive positive integers.
One out of 3 consecutive integers, (P - 1), P, and (P + 1) will definitely be a multiple of '3'.
If (P - 1) and (P + 1) are not divisible by 3, then P has to be a multiple of '3'.
P cannot be 3 because P is a 2-digit number. So, that possiblity is ruled out.
Any 2-digit number that is a multiple of 3 cannot be prime.
Therefore, P is not prime.

Statement 2 ALONE is also sufficient.
Eliminate choice A.

Each statement is INDEPENDENTLY sufficient. Choice D is the answer.

Evaluating Statement (1) ALONE: m > a

If a = b = c = d, the average m will be the same as a.
Since m > a, all the elements in the set cannot be the same, and therefore, s > 0.

Statement 1 ALONE is sufficient.
Eliminate choices B, C and E. Choices narrow down to A or D.

Evaluating Statement (2) ALONE: a + b + c + d = 0

Approach: Look for a counter example

Example: When a = b = c = d = 0, s = 0
Counter Example: When a = -4, b = 0, c = 0, and d = 4, s > 0

Statement 2 ALONE is NOT sufficient.
Eliminate choice D.

Statement 1 ALONE is sufficient. Choice A is the answer.

Evaluate Statement (1) ALONE
Statement 1: x > 0

We know that x is a positive number.

Interval 1: If 0 < x < 1, then x³ < x².
For example, (0.5)³ = 0.125, which is lesser than (0.5)² = 0.25
The answer to the question is NO.

Interval 2: If x > 1, then x³ > x²
For example, 2³ = 8 which is greater than 2² = 4
The answer to the question is YES.
We do NOT have a DEFINITE answer using statement 1.

Statement 1 ALONE is NOT sufficient.
Eliminate choices A and D. Choices narrow down to B, C, or E.

Evaluate Statement (2) ALONE
Statement 2: x < 1

Interval 1: For positive values of x, i.e., 0 < x < 1, we know x³ < x².
The answer to the question is NO.

Interval 2:For negative values of x, x³ will be a negative number and x² will be a positive number.
Hence, x³ < x²
The answer to the question is NO.

Lastly, what is the answer if x = 0?
When x = 0, x³ = x².
The answer to the question is NO.

Hence, if we know that x < 1, we can conclude that x³ is NOT GREATER THAN x².
We have a DEFINITE answer, even if it is NO.

Statement 2 ALONE is sufficient. Eliminate choices C and E.

Choice B is the answer.

Evaluate Statement (1) ALONE: (y - 3)(x - 4) = 0

If product of the two terms (y - 3) and (x - 4) is 0, then at least one of the two terms equals 0.
(y - 3) = 0 or (x - 4) = 0 or both (y - 3) and (x - 4) equal 0.
i.e., either y = 3 or x = 4 or that both y = 3 and x = 4.
If x = 4, y could take any value. The value of 'y' could be 3 or it could be some other value and the product will still be a 0.
Example: x = 4 and y = 5. The equation holds good. y ≠ 3.
Counter example: x = 4 and y = 3. The equation holds good. y = 3
We CANNOT determine whether 'y' is 3 from this statement.

Statement 1 ALONE is NOT sufficient.
Eliminate choices A and D. Choices narrow down to B, C or E.

Evaluate Statement (2) ALONE: (x - 4) = 0

The statement provides no information about y.

Statement 2 ALONE is NOT sufficient.
Eliminate choice B. Choices narrow down to C or E.

Evaluate Statements (1) & (2) Together: (y - 3)(x - 4) = 0 & (x - 4) = 0

When x = 4, (y - 3)(x - 4) will be 0 irrespective of the value that y takes.
Can 'y' be 3? Yes 'y' can be 3.
Is y = 3? Not necessary.It can take values other than 3 and the data in the two statements will still hold good.

Eliminate choice C.

Statements TOGETHER are NOT sufficient. Choice E is the answer.