GMAT Classic Mock Test - 10 - GMAT MCQ

The correct response is (C). To solve algebraically, start by taking the square root of .00000256. We know the square root of 256 = 16. We can write 0.00000256 in scientific notation as 256 x 10^-8. So:

To double-check, you can backsolve:
04 x .04 = .0016, and .0016 x .0016 = .00000256.
If you chose (A), you miscalculated by one decimal point. Check your work by backsolving: .004 x .004 = .000016. And .000016 x .000016 = .000000000256 (four extra zeros).
If you chose (B), you need to take the square root twice. Zeros aside, the square root of 256 = 16, and the square root of 16 = 4.
If you chose (D), you miscalculated the zeros and you forgot to take the square root twice. If you backsolved to check your work you’d see that .16 x .16 = .0256. That result squared will not give us .00000256.
If you chose (E), you missed the correct choice by one decimal point. If you backsolved to check your work, you’d see that .4 x .4 = .16, and .16 x .16 = .0256, which is much larger than our original number from the question stem.

The correct response is (C). The denominator of any fraction is undefined when it equals 0, so x cannot be 4 in this expression.
However, the question asks what cannot be a value for 1 / 4 – x. 1 divided by any number cannot equal zero.

If you chose (A), it is possible for 1 / 4 – x = -4 if x = 17/4.

If you chose (B), it is possible for 1 / 4 – x = 4/17 if x = -1/4.

If you chose (D), remember the question is asking what the expression can equal, not the possible values for x. This is a “trap” answer choice!

If you chose (E), it’s possible for 1 / 4 – x = 17/4 if x = 64/17.

The correct response is (E). 5/7 = .7142…. Already there are more than four unique digits, which is more than any other number in the answer choices. Remember for each value there are only ten possible digits for each placeholder in a number: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. The word “unique” means different from the other digits.

If you chose (A), 1/6 = .166666. There are only two unique digits in this number: 1 and 6.

If you chose (B), 1/4 = .25. There are only two unique digits in this number: 2 and 5.

If you chose (C), 1/3 = .333333. There is only 1 digit in this number: 3.

If you chose (D), 3/4 = .75. There are only two unique digits in this number: 7 and 5.

To begin, we can translate “ y less than x” as “x – y.” Next, notice how the quotient is 3 x 108. Since “3” is the first part of this number written in scientific notation, let’s start by adjusting the scientific notation of the dividend and divisor (numerator and denominator) so we can achieve that 3.

.0027 / .09 might not equal 3, but 27/9 does, so we’ll have to adjust the exponent of each 10 as we move the decimal. 0.0027 x 10x = 27 x 10x - 4. When we move the decimal to the right, we must shrink the exponent of the 10 power. 0.09 x 10y = 9 x 10y - 2. Now we can rewrite the equation as 27 x 10x - 4 / 9 x 10y - 2 = 3 x 108. Separating out the powers of 10 we arrive at: 10x - 4 / 10y - 2 = 108. If you remember from the exponent rules, when we divide exponents with the same base, we subtract the exponents.
Thus, (x – 4) – (y -2) = 8.
x – 4 – y + 2 = 8
x – y – 2 = 8
x – y = 10

Even though we can’t solve for x and y independently, we found what the question was asking us to find, “x – y.” (B) is correct.

The correct response is (E). This is a great question to choose values for x and y. Let’s say x = 2. “Twice the value of x” would be 4. Now let’s say y = 5. “Three more than y” would be 8. The question is now asking: what percent of 8 is 4? We know that 4 is 50% of 8.

When we plug in our values into the answer choices, the correct response will also yield 50%: (200x/(y + 3) = 200(2) / (5) + 3 = 400/8 = 50. 

The least common multiple is the smallest number that is a multiple of all the numbers in the group.  Let's list some multiples of the two numbers and find the smallest number in common to both.

multiples of 45: 45, 90, 135, 180, 225, 270, ...

multiples of 60: 60, 120, 180, 240, 300, 360, ...

The smallest number in common is 180.

Let T represent the total amount Jill spent, excluding taxes. Jill. paid a 4% tax on the clothing she bought, which accounted for 50% of the total amount she spent, and so the tax she paid on the clothing was (0.04)(0.5T).Jill paid an 8% tax on the other items she bought, which accounted for 30% of the total amount she spent, and so the tax she paid on the other items was (0.08)(0.3T). Therefore, the total amount of tax Jill. paid was (0.04)(0.5T) + (0.08)(0.3T) = 0.02T+ 0.024T= 0.044T. The tax as a percent of the total amount Jill spent, excluding taxes, was

The integers that satisfy 2 < x ≤ 4 are 3 and 4, The integers that satisfy 0 ≤ x ≤ 3 are 0,1,2, and 3. The only integer that satisfies both 2 < x ≤ 4 and 0 ≤ x ≤ 3 is 3, and so there is only one integer that satisfies both 2 < x ≤ 4 and 0 ≤ x ≤, 3.
The correct answer is E.

An increase from $8 to $9 represents an increase of

Given w₂d₁ = w₂d₂, w₁ = 50, w₂ = 30, and d1 = d₂ - 4, it follows that 50(d₂ - 4) = 30d₂, and so
50(d₂ - 4)=30d₂ given
50d₂ - 200 = 30d₂ distributive principle
20d₂ = 200 add 200 - 30d₂ to both sides
d₂ = 10    divide both sides by 20

The correct answer is D. 

Let G be the number of rooms in Hotel G and let Hbe the number of rooms in Hotel H. Expressed in symbols, the given information is the following system of equations 

Solving the second equation for H gives H= 425 - G. Then, substituting 425 - G for H in the first equation gives
G = 2(425 - G) - 10
G = 850 - 2G - 10
G = 840 - 2G
3G = 840
G = 280

If each fraction is written in decimal form, the sum to be found is

The correct answer is E.

lets get the eq into simplest orm..
2^r)(4^s) = 16..
(2^r)(2^2s) = 24..
or r + 2s=4..
since r and s are positive integers, only r as 2 and s as 1 satisfy the Equation..
so 2r + s = 2 x 2 + 1 = 5..

The total to be refunded is equal to the total contributed minus the amount paid, or 3x - y. If 3x - y is divided into three equal amounts, then each amount will

Solving the second equation fory gives
y = 1 - 4x. Then, substituting 1 - 4x from y in the first equation gives
2x + 2(1 - 4x) = -4
2x + 2 - 8x = -4
-6x + 2 = -4
-6x = -6
x = 1

The correct answer is: (B)

First note that Sally must buy at least one pound of each of the fruits, which would result in a sum fixed cost of $10.

(1) If Sally spent less than $5 on orange slices, then she spent must have spent more on one of the other two fruits, but it is unclear which; NOT sufficient

(2) If Sally spent more than $18 then she must spend more than $8 on the two-variable pounds of fruit, which could only be accomplished by buying two more pounds of cut watermelon; Sufficient

The correct answer is B; statement 2 alone is sufficient.

Given the length of one side of a triangle, it is known that the sum of the lengths of the other two sides is greater than that given length. The length of either of the other two sides, however can be any positive number.
(1) Only the length of one side, is given, and that is not enough to determine the length of YZ; NOT sufficient.
(2)  Again, only the length of one side, XZ, is given and that is not enough to determine the length of YZ; NOT sufficient.
Even by using the triangle inequality stated above, only a range of values for YZ can be determined from (1) and (2). If the length of side YZ is represented byk, then it is known both that 3 + 5 > k and that 3 + k > 5,ork> 2. Combining these inequalities to determine the length of k yields only that 8 > k > 2.
The correct answer is E.
Both statements together are still not sufficient.

The correct answer is: (D).

Remember that if there is a constant difference in terms that the average for the sequence = median of the sequence.

The formula for average is sum divided by the number of terms, so in this case the total number of cans = median × number of rows.

And the total number of cans = x + (x + 2) + (x + 4) … up to the total number of rows.

Therefore, two equations are already theoretically known, and only one additional equation is needed to solve for all of the values involved.

(1) If 100 is the total number of cans, then it would be possible to count from 1 + 3 + 5 + 7… to determine the total number of rows, and thereby the median, without completing the process; SUFFICIENT.

(1)If the range in cans per row is 18, then it would be possible to determine that the number of cans in the last row is 19 and from there the median, without completing the process; SUFFICIENT

The correct answer is D; each statement alone is sufficient.

(1) 2 is in K → according to (i) -2 is n K → according to (ii) -2 x 2 = -4 is in K → according to (i) -(-4) = 4 is in K and so on.
Thus we know that 2, -2, -4, 4, 8, -8, 16, -16, ... are in K, so basically powers of 2 and their negative pairs. Is 12 in K? We don't know. Not sufficient.
(2) 3 is in K → according to (i) -3 is n K → according to (ii) -3 x 3=-9 is in K → according to (i) -(-9) = 9 is in K and so on.
Thus we know that 3, -3, -9, 9, 27, -27, 81, -81, ... are in K, so basically powers of 3 and their negative pairs. Is 12 in K? We don't know. Not sufficient.

(1) + (2) From (1) 4 is in K and from (2) 3 is in K,
hence according to (ii) 4 x 3 = 12 must also be in K. Sufficient.

A  includes all multiples of 2; B includes all multiples of 3. A∪B comprises all multiples of either 2 or 3.
Knowing n is a perfect square is neither necessary nor helpful, as, for example, 9 ∈ B⊆ A ∪ B, but 25 ∉ A ∪ B (as 25 is neither a multiple of 2 nor a multiple of 3).
If you know that n is a multiple of 99, then it must also be a multiple of any number that divides 99 evenly, one such number is 3. This means n∈ B ⊆ A ∪ B

Let r be the number ofthe remaining games played, all. of which the team won.
Since the team won (50%)(20) = 10 of the first 20 games and the r remaining games, the total number of games the team won is 10 + r.
Also, the total number of games the team played is 20 + r. Determine thevalue of r.
(1) Given that the total number of games played is 25, it follows that 20 + r = 25, or r = 5;
SUFFICIENT.
(2) It is given that the total number of games won is (60%)(20 + r), which can be expanded as 12 + 0.6r.
Since it is also known that the number of games won is 10 + r, it follows that 12 + 0.6r =10 + r.
Solving this equation gives 12 - 10 = r - 0.6r, or 2 = 0.4r, or r = 5;
SUFFICIENT.

Assume both statements are true.
Consider these two cases:
Case1: A = {1, 2, 3, 4, 5} and B = {5,6}
Case 2: A = {1, 2, 3, 4, 5, 6} and B = {5, 6, 7}
In both situations, A has three more elements than B and A includes exactly four elements not in B (1, 2, 3 and 4). However, the number of elements in the union differ in each case - in the first case, A∪B = {1, 2, 3, 4, 5, 6}, and in the second case, A∪B = {1, 2, 3, 4, 5, 6, 7}. 
The two statements together do not yield an answer to the question.

We need to determine if m^n is an integer, given that m and n are nonzero integers. Notice that m^n is an integer if n is positive OR if n is negative and m is either 1 or -1.
Statement One Alone:
If n = 2 and m = 4, then mⁿ = 4² = 16 is an integer. However, if n = -2 and m = 4, then m^n = 4^(-2) = 1/16 is not an integer. Statement one alone is not sufficient.
Statement Two Alone:
If n = 2 and m = 4, then mⁿ = 4² = 16 is an integer. However, if n = -2 and m = 4, then m^n = 4^(-2) = 1/16 is not an integer. Statement two alone is not sufficient.
Statements One and Two Together:
With the two statements, n^m is a positive integer. We can use the same examples for statement one and statement two to see that both statements together are not sufficient.

Explanation:

A includes all multiples of 2; B includes all multiples of 3. A∪B comprises all multiples of either 2 or 3.

Knowing n is a perfect square is neither necessary nor helpful, as, for example, 9∈B⊆A∪B, but 25∉A∪B (as 25 is neither a multiple of 2 nor a multiple of 3).

If you know that n is a multiple of 99, then it must also be a multiple of any number that divides 99 evenly, one such number is 3. This means n∈B⊆A∪B

If n is the least of three different integers greater than 1, what is the value of n
(1) The product of the three integers is 90.
Prime factorization of 90 = 2 x 32 x 52 x 32 x 5. n could be take multiple values. INSUFFICIENT.
(2) One of the integers is twice one of the other two integers.
Clearly insufficient.
(1&2) We know the prime factorization of 90 = 2 x 32 x 590 = 2 x 32 x 5 and one of the integers is twice one of the other two integers. The only possibility is 3 x 5 x 63 x 5 x 6. SUFFICIENT.

The question is equivalent to asking whether Jerry is an element of set M.

The sets T and M are disjoint - they have no elements in common. From Statement 1 alone, Jerry is an element of T, so he cannot be an element of M. He is not a Mason.

From Statement 2 alone, Jerry is an element of E. Since there are elements not in E that are and are not elements of M, it cannot be determined whether Jerry is an element of M - a Mason.

If x is the number of books Michael had before he acquired the 10 additional books, then x is a multiple of 10. After Michael acquired the 10 additional books, he had x + 10 books and x + 10 is a multiple of 12.
(1) If x < 96, where xis a multiple of 10, then x = 10, 20, 30, 40, 50, 60, 70, 80, or 90 and x + 10 = 20,30,40,50, 60,70, 80,90, or 100.
Since x + 10 is a multiple of 12, then
x + 10 = 60 and x = 50; SUFFICIENT
(2) If x > 24, where x is a multiple of 10, then x must be one of the numbers 30, 40, 50, 60, 70, 80, 90,100,110,... , and x + 10 must be one of the numbers 40, 50, 60, 70, 80, 90, 00,110,120,
Since there is more than one multiple of 12 among these numbers (for example, 60 and 120), the value of x + 10, and therefore the value of x, cannot be determined; NOT sufficient.
The correct answer is A; statement 1 alone is sufficient.

The question asks for the number of students in the set F′∩C′, where F and C are the sets of students who took French and Creative Writing, respectively.
From Statement 1 alone, a Venn diagram representing this situation can be filled in as follows:

It is known that x + y + z + 10 = 98; subsequently, x + y + z = 88. But no other information is given, so x, the desired quantity, cannot be calculated.

From Statement 2 alone, a Venn diagram representing this situation can be filled in as follows:

Again, no further information can be computed.

Now assume that both statements are true. Then it follows from Statement 1 that w=10, and it follows from Statement 2 that the desired quantity is 

56 + w = 56 + 10 = 66.

We are told about 30 businesses of which 21 reported a net profit and 15 had investments in foreign markets.Refer the venn diagram below:

As the total number of businesses is 30 we can write a + b + c + d = 30
Also, 21 firms reported a net profit, that would give us a + b =21. Also, it would give us c + d = 9
Similarly, 15 firms had investments in foreign markets, that would give us b + c = 15. Also it would give us a + d = 15.
We need to find the number of businesses that did not report a net profit nor invest in foreign market i.e. d. Let's see if the statements provide us the information to find a definite value of d

Statement-I
St-I tells us that 12 businesses reported net profit and had investments in foreign markets i.e. b = 12. This would give us the value of a = 9.
We know that a + d = 15 i.e. d = 6.
Hence st-I is sufficient to answer the question.

Statement-II
St-II tells us that 24 businesses reported a net profit or invested in foreign markets or both i.e. a + b + c = 24

Since a + b + c + d = 30 we can find the value of d = 6

Hence st-II is sufficient to answer the question.

Answer is option D

uppose we only know that 200 ml of the 40% solution is used. Then we can call x the amount of 25% solution used, and the total amount made is  200+x. The solution equation becomes, 

200(0.40)  + x(0.25) = (200 + x)(0.35)

80 + 0.25x = 70 + 0.35x

10 = 0.10x

x = 10 ÷ 0.10=100

So 100 ml of the 25% solution is used.

Similarly, if we only know that 100 ml of the 25% solution is used, then we can call y the amount of 40% solution used, and the total amount made is  100+y . The solution equation becomes, 

y(0.40) + 100(0.25) = (100 + y)(0.35)

0.40y + 25 = 35 + 0.35y

0.05y = 10

y =1 0 ÷ 0.05

y = 200

So 200 ml of the 10% solution is used.

Either way, we get that

100 + 200 = 300

and 300 ml of solution is created.

The answer is that either statement is sufficient to answer the question.