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Is mn < m/n ? (1) mn is a positive integer (2) n is a negative number

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Bunuel
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Is mn < m/n ? (1) mn is a positive integer (2) n is a negative number [#permalink] Is mn < m/n ? (1) mn is a positive integer (2) n is a negative number   13 Apr 2022, 07:00
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E

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35% (medium)

Question Stats:

71% (01:49) correct 29% (01:24) wrong based on 66 sessions
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Is mn < m/n ?

(1) mn is a positive integer.
(2) n is a negative number.
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E
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BrentGMATPrepNow
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Re: Is mn < m/n ? (1) mn is a positive integer (2) n is a negative number [#permalink] Is mn < m/n ? (1) mn is a positive integer (2) n is a negative number   13 Apr 2022, 09:30
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Bunuel wrote:
Is mn < m/n ?

(1) mn is a positive integer.
(2) n is a negative number.


Target question: Is mn < m/n ?

When I scan the two statements, they both feel insufficient, AND I’m pretty sure I can identify some cases with conflicting answers to the target question. So, I’m going to head straight to……

Statements 1 and 2 combined
Statement 1 tells us that mn is a positive integer.
Statement 2 tells us that n is a negative number.
There are several values of m and n that satisfy BOTH statements. Here are two:
Case a: m = -2 and n = -1/2. So, mn = (-2)(-1/2) = 1 and m/n = (-2)/(-1/2) = 4. In this case, the answer to the target question is YES, mn is less than m/n
Case b: m = -1/2 and n = -2. So, mn = (-1/2)(-2) = 1 and m/n = (-1/2)/(-2) = 1/4. In this case, the answer to the target question is NO, mn is NOT less than m/n
Since we can’t answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

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Brent
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Is mn < m/n ? (1) mn is a positive integer (2) n is a negative number [#permalink] Is mn < m/n ? (1) mn is a positive integer (2) n is a negative number   13 Apr 2022, 15:15
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BrentGMATPrepNow wrote:
Bunuel wrote:
Is mn < m/n ?

(1) mn is a positive integer.
(2) n is a negative number.


Target question: Is mn < m/n ?

When I scan the two statements, they both feel insufficient, AND I’m pretty sure I can identify some cases with conflicting answers to the target question. So, I’m going to head straight to……



From statement 1, we can infer that both m and n are not equal to zero

Problem statement:
Is mn < m/n ?
Dividing both sides by m, we get
Is n^2 < 0 ?
n can be positive or negative however n^2 will always be positive

So Is n^2 < 0 ? is a definite No

Isn't statement 1 sufficient using the above approach?

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BrentGMATPrepNow
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Re: Is mn < m/n ? (1) mn is a positive integer (2) n is a negative number [#permalink] Is mn < m/n ? (1) mn is a positive integer (2) n is a negative number   13 Apr 2022, 16:18
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logan2022 wrote:
From statement 1, we can infer that both m and n are not equal to zero

Problem statement:
Is mn < m/n ?
Dividing both sides by m, we get
Is n^2 < 0 ?
n can be positive or negative however n^2 will always be positive

So Is n^2 < 0 ? is a definite No

Isn't statement 1 sufficient using the above approach?

Posted from my mobile device


Be careful, dividing both sides of an inequality by m can have unintended consequences if we don't know whether m is positive or negative.

If m is negative, then once we divide both sides by m, we must reverse the direction of the inequality symbol.
If m is positive, then once we divide both sides by m, the direction of the inequality symbol remains the same.

More here:
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Re: Is mn < m/n ? (1) mn is a positive integer (2) n is a negative number [#permalink] Is mn < m/n ? (1) mn is a positive integer (2) n is a negative number   03 Jan 2024, 03:47
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Re: Is mn < m/n ? (1) mn is a positive integer (2) n is a negative number [#permalink]
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