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Math Expert V
Joined: 02 Sep 2009
Posts: 56251
If m # n represents the integer remainder that results when a positive  [#permalink]

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Difficulty:   45% (medium)

Question Stats: 66% (01:42) correct 34% (01:35) wrong based on 316 sessions

### HideShow timer Statistics 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

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Re: If m # n represents the integer remainder that results when a positive  [#permalink]

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Bunuel wrote:
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

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

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Re: If m # n represents the integer remainder that results when a positive  [#permalink]

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1
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

Math Expert V
Joined: 02 Sep 2009
Posts: 56251
Re: If m # n represents the integer remainder that results when a positive  [#permalink]

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2
Bunuel wrote:
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

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.

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Re: If m # n represents the integer remainder that results when a positive  [#permalink]

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_________________ Re: If m # n represents the integer remainder that results when a positive   [#permalink] 23 Mar 2018, 05:41
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