If m # n represents the integer remainder that results when a positive

Question

If m # n represents the integer remainder that results when a positive integer m is divided by a positive integer n, what is the value of positive integer x?

(1) 81 # x = 1
(2) x # 40 = 0

GMATinsight · Answer

Statement 1: 81 # x = 1

i.e. when 81 is divided by x the remainder is 1

i.e. x MUST be the  FACTOR  of 80 and greater than 1

i.e. x may be 2, 4, 5, 10, 20, 40, 80 etc

NOT SUFFICIENT

Statement 2: x # 40 = 0

i.e. when x is divided by 40 the remainder is 0

i.e. x MUST be the  MULTIPLE  of 40

i.e. x may be 40, 80, 120 etc

NOT SUFFICIENT

Combining the two statements:

x must be a FACTOR of 80 and MULTIPLE of 40

i.e. x can be either 40 or 80

Hence,   NOT SUFFICIENT

Answer: Option  E

peachfuzz · Answer

what is the value of positive integer x?

(1) 81 # x = 1
x could be 2, 4, 8, 10, 40, 80, etc.
Insufficient

(2) x # 40 = 0
x could be 40, 80, 120, etc
Insufficient

Combined, x could still be 40 or 80
Insufficient

Answer: E

Bunuel · Answer

MANHATTAN GMAT OFFICIAL SOLUTION:

Let's be sure we understand the function given in the question stem by thinking of some examples:
16 # 5 = 1, since 16 divided by 5 leaves a remainder of 1.
21 # 3 = 0, since 21 divided by 3 leaves a remainder of 0.
17 # 3 = 2, since 17 divided by 3 leaves a remainder of 2.

(1) INSUFFICIENT: If a remainder of 1 is left when 81 is divided by x, then x divides evenly into 80. In other words, x is a factor of 80, but not of 81. The factors of 80 are 1, 2, 4, 5, 8, 10, 16, 20, 40, and 80; of these, only the number 1 is also a factor of 80. Thus, the possible values of x are: 2, 4, 5, 8, 10, 16, 20, 40, and 80.

(2) INSUFFICIENT: If a remainder of 0 is left when 40 is divided by x, then 40 divides evenly into x. We might conclude that x must be 40. However, we must realize that x could be any multiple of 40: 40, 80, 120, 160, etc.

(1) AND (2) INSUFFICIENT: x could be either 40 or 80, according to both statements.

The correct answer is E.

bumpbot · Answer

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If m # n represents the integer remainder that results when a positive

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GMAT Data Sufficiency (DS) Questions

If m # n represents the integer remainder that results when a positive

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