Dost thou seek the answer to yesterday’s Challenge Problem?  As promised, find it below!

Question
If p, x, and y are positive integers, y is odd, and p = x2 + y2, is x divisible by 4?

(1) When p is divided by 8, the remainder is 5.

(2) x – y = 3

(A) Statement (1) ALONE is sufficient to answer the question, but statement (2) alone is not.
(B) Statement (2) ALONE is sufficient to answer the question, but statement (1) alone is not.
(C) Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient.
(D) EACH statement ALONE is sufficient to answer the question.
(E) Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the . . . → Continue Reading

Welcome to this week’s edition of Workbook Wednesdays, featuring the type of problem one would see if scoring above a 700 on the GMAT. As always, thanks to ManhattanGMAT for providing this week’s challenge problem! Be sure to check back tomorrow for the answer!

Question
If p, x, and y are positive integers, y is odd, and p = x2 + y2, is x divisible by 4?

(1) When p is divided by 8, the remainder is 5.

(2) x – y = 3

(A) Statement (1) ALONE is sufficient to answer the question, but statement (2) alone is not.
(B) Statement (2) ALONE is sufficient to answer the question, but statement (1) alone is not.
(C) Statements (1) and (2) TAKEN TOGETHER are sufficient . . . → Continue Reading

Check out the answer to yesterday’s Challenge Problem!

Question
If n is a positive integer and x does not equal zero, is x^n > x^(n+1)?

1) x < 1

2) n is even.

(A) Statement (1) ALONE is sufficient to answer the question, but statement (2) alone is not.
(B) Statement (2) ALONE is sufficient to answer the question, but statement (1) alone is not.
(C) Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient.
(D) EACH statement ALONE is sufficient to answer the question.
(E) Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question.

Solution
The answer to the question depends on the values of both x and n. Specifically, we care about the value of . . . → Continue Reading

Welcome to this week’s edition of Workbook Wednesdays! If you’re ready to sharpen your quantitative skills, check out the Challenge Problem below, courtesy of our friends at ManhattanGMAT.

Question
If n is a positive integer and x does not equal zero, is x^n > x^(n+1)?

1) x < 1

2) n is even.

(A) Statement (1) ALONE is sufficient to answer the question, but statement (2) alone is not.
(B) Statement (2) ALONE is sufficient to answer the question, but statement (1) alone is not.
(C) Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient.
(D) EACH statement ALONE is sufficient to answer the question.
(E) Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer . . . → Continue Reading

Check below to see what was paid at the pump in yesterday’s GMAT question!

Question
A certain military vehicle can run on pure Fuel X, pure Fuel Y, or any mixture of X and Y. Fuel X costs $3 per gallon; the vehicle can go 20 miles on a gallon of Fuel X. In contrast, Fuel Y costs $5 per gallon, but the vehicle can go 40 miles on a gallon of Fuel Y. What is the cost per gallon of the fuel mixture currently in the vehicle’s tank?

1) Using fuel currently in its tank, the vehicle burned 8 gallons to cover 200 miles.

2) The vehicle can cover 7 and 1/7 miles for every dollar of fuel currently in its tank.

(A) . . . → Continue Reading

Welcome to this week’s edition of Workbook Wednesdays, featuring the type of problem one would see if scoring above a 700 on the GMAT. As always, thanks to ManhattanGMAT for providing this week’s challenge problem!  Be sure to check back tomorrow for the answer!

A certain military vehicle can run on pure Fuel X, pure Fuel Y, or any mixture of X and Y. Fuel X costs $3 per gallon; the vehicle can go 20 miles on a gallon of Fuel X. In contrast, Fuel Y costs $5 per gallon, but the vehicle can go 40 miles on a gallon of Fuel Y. What is the cost per gallon of the fuel mixture currently in the vehicle’s tank?

1) Using fuel . . . → Continue Reading

The results from yesterday’s GMAT question are in!  See below for a detailed answer:

Question
A medical test for a certain liver enzyme can be given in the morning, in the afternoon, or in the evening; moreover, the result of the test can be low, average, or high. At least three-quarters of low and medium readings are not given in the evening. Sixty percent of exams are given in the morning or in the afternoon, and 20% of exams result in a high reading. What percent of exams given in the evening result in low or medium readings?

(A) 20%
(B) 30%
(C) 40%
(D) 50%
(E) 60%

Answer
The key to this problem is to realize that you can collapse certain categories together. The distinction between low and . . . → Continue Reading

Get ready for your quantitative check-up! As always, we’d like to thank ManhattanGMAT for providing this week’s Challenge Question and – more importantly – tomorrow’s answer!

Question
A medical test for a certain liver enzyme can be given in the morning, in the afternoon, or in the evening; moreover, the result of the test can be low, average, or high. At least three-quarters of low and medium readings are not given in the evening. Sixty percent of exams are given in the morning or in the afternoon, and 20% of exams result in a high reading. What percent of exams given in the evening result in low or medium readings?

(A) 20%
(B) 30%
(C) 40%
(D) . . . → Continue Reading

Check out the answer to yesterday’s Challenge Problem below!

Question
Line k lies in a coordinate plane. Is the slope of line k positive?

(1) Line k and the graph of the function f(x) = x^2 – bx, where b is positive, intersect on the x-axis.

(2) Line k and the graph of the function g(x) = –x^2 – c, where c is positive, intersect on the y-axis.

(A) Statement (1) ALONE is sufficient to answer the question, but statement (2) alone is not.
(B) Statement (2) ALONE is sufficient to answer the question, but statement (1) alone is not.
(C) Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient.
(D) EACH statement ALONE is sufficient to answer the question.
(E) . . . → Continue Reading

Welcome to this week’s edition of Workbook Wednesdays, courtesy of our friends at ManhattanGMAT! Get ready to wrap your brain around an advanced quantitative problem – the kind you would see if you are scoring a 700 or higher on the GMAT – then be sure to check back tomorrow for the answer.

Question
Line k lies in a coordinate plane. Is the slope of line k positive?

(1) Line k and the graph of the function f(x) = x^2 – bx, where b is positive, intersect on the x-axis.

(2) Line k and the graph of the function g(x) = –x^2 – c, where c is positive, intersect on the y-axis.

(A) Statement (1) ALONE is sufficient to answer the question, but statement . . . → Continue Reading

Find the answer to yesterday’s Challenge Problem below!

Question
If n is a positive integer, what is n?

(1) 3^n – 1 has three prime factors, not necessarily distinct.
(2) n^2 = 2^n.

(A) Statement (1) ALONE is sufficient to answer the question, but statement (2) alone is not.
(B) Statement (2) ALONE is sufficient to answer the question, but statement (1) alone is not.
(C) Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient.
(D) EACH statement ALONE is sufficient to answer the question.
(E) Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question.

Answer
The given information simply guarantees that n is a positive integer.

Statement (1) indicates that 3^n – 1 has three prime factors, not necessarily . . . → Continue Reading

Welcome to this week’s edition of Workbook Wednesdays! As always, we’d like to thank our friends at ManhattanGMAT for providing this week’s Challenge Problem. Check back tomorrow for an in-depth look at the answer!

Question
If n is a positive integer, what is n?

(1) 3^n – 1 has three prime factors, not necessarily distinct.
(2) n^2 = 2^n.

(A) Statement (1) ALONE is sufficient to answer the question, but statement (2) alone is not.
(B) Statement (2) ALONE is sufficient to answer the question, but statement (1) alone is not.
(C) Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient.
(D) EACH statement ALONE is sufficient to answer the question.
(E) Statements (1) and (2) TAKEN . . . → Continue Reading

Here is the answer to Wednesday’s Challenge Question from Manhattan GMAT. Check back next week for another Workbook Wednesday question!

Question

If a, b, and c are integers, and the product abc is even, is b even?
(1) (ab)/c is an even integer.
(2) (ac)/b is an odd integer.

(A) Statement (1) ALONE is sufficient to answer the question, but statement (2) alone is not.
(B) Statement (2) ALONE is sufficient to answer the question, but statement (1) alone is not.
(C) Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient.
(D) EACH statement ALONE is sufficient to answer the question.
(E) Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question.

Answer

The given information simply guarantees that at . . . → Continue Reading

Welcome to this week’s edition of Workbook Wednesdays, courtesy of our friends at ManhattanGMAT!  Just like last week, this problem mimics the most advanced quantitative problems on the exam, the type of problem you will see if you are scoring around 700 or higher.  Check back tomorrow for the answer!

If a, b, and c are integers, and the product abc is even, is b even?

(1) (ab)/c is an even integer.
(2) (ac)/b is an odd integer.

(A) Statement (1) ALONE is sufficient to answer the question, but statement (2) alone is not.
(B) Statement (2) ALONE is sufficient to answer the question, but statement (1) alone is not.
(C) Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, but NEITHER . . . → Continue Reading

As promised, here is the answer to yesterday’s Challenge Problem!

Question
The function f(x) is defined as f(x) = 1 – 1/(1-x) for all x not equal to 1. The sequence A(n) for all integers n > 1 is defined as A(n) = f(A(n-1)).

What values of A(1) create a sequence such that A(n) = A(n-2) for all n > 2?

(I) x < 0
(II) x = 0
(III) 0 < x < 1
(IV) x > 1

(A) I only
(B) II only
(C) II and III only
(D) II, III, and IV only
(E) I, II, III, and IV

Answer
The definition of the sequence means that you apply the function f to A(1) to get A(2); then you apply the function again to A(2) to get A(3), and so on.

Now, you . . . → Continue Reading

Welcome to this week’s edition of Workbook Wednesdays, brought to you by our friends at ManhattanGMAT. Check back tomorrow for an in-depth look at the answer!

Question
The function f(x) is defined as f(x) = 1 – 1/(1-x) for all x not equal to 1. The sequence A(n) for all integers n > 1 is defined as A(n) = f(A(n-1)).

What values of A(1) create a sequence such that A(n) = A(n-2) for all n > 2?

(I) x < 0
(II) x = 0
(III) 0 < x < 1
(IV) x > 1

(A) I only
(B) II only
(C) II and III only
(D) II, III, and IV only
(E) I, II, III, . . . → Continue Reading

Pencil’s up! Here is the answer to yesterday’s Challenge Question.

Question
If x and n are positive integers, is n = 1?

(1) The sum of n consecutive integers, starting at x, is divisible by xn.
(2) The product of n consecutive integers, starting at x, is divisible by x^n.

(A) Statement (1) ALONE is sufficient to answer the question, but statement (2) alone is not.
(B) Statement (2) ALONE is sufficient to answer the question, but statement (1) alone is not.
(C) Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient.
(D) EACH statement ALONE is sufficient to answer the question.
(E) Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question.

Answer
The problem asks a “Yes or . . . → Continue Reading

Welcome to the another installment of Workbook Wednesdays. Thanks again to Manhattan GMAT for supplying today’s question and (more importantly) tomorrow’s answer! Just like last week, this problem mimics the most advanced quantitative problems on the exam, the type of problem you will see if you are scoring around 700 or higher.

Question
If x and n are positive integers, is n = 1?

(1) The sum of n consecutive integers, starting at x, is divisible by xn.
(2) The product of n consecutive integers, starting at x, is divisible by x^n.

(A) Statement (1) ALONE is sufficient to answer the question, but statement (2) alone is not.
(B) Statement (2) ALONE is sufficient to answer the question, but statement (1) alone is not.
(C) Statements . . . → Continue Reading

As promised, here is the answer to yesterday’s Manhattan GMAT Challenge Question!

The key to this problem is to make the common term in both ratios equal. We should set up a table to display both ratios:

Cat

Can

Kay

4

7

5

9

Now, we can double any of the ratios. In fact, we can multiply any row by any positive-integer factor (x2, x3, x10, etc.). We are constrained to positive-integer factors, though, because the actual number of any boat must be a positive integer.

The number of canoes in each row should be the same, so that we can merge the ratios. The least common multiple of 7 and 5 is 35, so we multiply the top row by 5 and the bottom . . . → Continue Reading

Welcome back to another edition of Workbook Wednesdays, brought to you by our friends at Manhattan GMAT. Take a look at the problem below, and be sure to check back in with us tomorrow for an explanation of the answer!

Question:

On Lake Coheeries, there are only three kinds of boats: catamarans, canoes, and kayaks. The ratio of catamarans to canoes is 4:7, and the ratio of canoes to kayaks is 5:9. Which of the following could be the total number of boats on the lake?

A) 575
B) 580
C) 585
D) . . . → Continue Reading

Below is the answer to yesterday’s GMAT Challenge Question!

Question
A restaurant pays a seafood distributor d dollars for 6 pounds of Maine lobster. Each pound can make v vats of lobster bisque, and each vat makes b bowls of lobster bisque. If the cost of the lobster per bowl is an integer, and if v and b are different prime integers, then which of the following is the smallest possible value of d?

(A) 15
(B) 24
(C) 36
(D) 54
(E) 90

Answer
Let’s start by finding the cost of the lobster, per bowl, in terms of the variables given (d, v, and b).

(d dollars/6 pounds) x (1 pound/v vats) x (1 vat/b bowls) = (d/6vb).

The problem states that this value, the cost of the lobster per bowl, . . . → Continue Reading