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Is mn < 10?

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Is mn < 10?

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Is mn < 10?

(1) m < 5 and n < 2
(2) 1 < m < 3 and n^2<25

The OA is C.

I think that the right answer should be A. Can any expert clarify this DS question to me?

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Hi Vincen,

We're asked if (M)(N) is less than 10. This is a YES/NO question. We can solve it by TESTing VALUES.

1) M < 5 and N < 2

IF.....
M=4 and N=1 then the product is 4 and the answer to the question is YES.
M= -6 and N= -2 then the product is 12 and the answer to the question is NO.
Fact 1 is INSUFFICIENT

2) 1 < M < 3 and N^2 <25

IF.....
M=2 and N=1 then the product is 2 and the answer to the question is YES.
M= 2.9999 and N=4.9999 then the product is really close to 15 and the answer to the question is NO.
Fact 2 is INSUFFICIENT

Combined, the various inequalities 'limit' us down to:
1 < M < 3
-5 < N < 2
At MOST, the product (M)(N) would get really close to 6 - but no higher. Thus, the answer to the question is ALWAYS YES.
Combined, SUFFICIENT

Final Answer: C

GMAT assassins aren't born, they're made,
Rich

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Contact Rich at Rich.C@empowergmat.com

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GMAT/MBA Expert

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Vincen wrote:
Is mn < 10?

(1) m < 5 and n < 2
(2) 1 < m < 3 and n^2<25

The OA is C.

I think that the right answer should be A. Can any expert clarify this DS question to me?
Target question: Is mn < 10?

Statement 1: m < 5 and n < 2
Let's TEST some values.
There are several values of m and n that satisfy statement 1. Here are two:
Case a: m = 0 and n = 0. In this case mn = (0)(0) = 0. So, the answer to the target question is YES, mn IS less than 10
Case b: m = -5 and n = -5. In this case mn = (-5)(-5) = 25. So, the answer to the target question is NO, mn is NOT less than 10
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: 1 < m < 3 and n² < 25
Let's TEST some values again.
There are several values of m and n that satisfy statement 2. Here are two:
Case a: m = 1 and n = 0. In this case mn = (1)(0) = 0. So, the answer to the target question is YES, mn IS less than 10
Case b: m = 2.9 and n = 4. In this case mn = (2.9)(4) = 11.6. So, the answer to the target question is NO, mn is NOT less than 10
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
IMPORTANT: When we combine the statements, we must adhere to the most RESTRICTIVE case for m and n each
For example, statement 1 tells us that m < 5, and statement 2 tells us that 1 < m < 3
Since both statements are TRUE, we can conclude that 1 < m < 3 since those possible values of m also satisfy the condition that m < 5

Likewise, for the value of n, statement 1 tells us that n < 2, and statement 2 tells us that n² < 25 (which is the SAME as saying -5 < n < 5)
Since both statements are TRUE, we can conclude that -5 < n < 2

So, we know the following about m and n:
1 < m < 3
-5 < n < 2

So, one possible case is that m = 2 and n = 0. In this case mn = (2)(0) = 0. So, the answer to the target question is YES, mn IS less than 10

IMPORTANT: Since we've already shown that mn can be LESS THAN 10 (yielding a YES answer to the target question)
Is it possible for mn to be GREATER THAN or equal to 10 (which would yielding a NO answer to the target question)?

To find out, let's maximize the values of m and n.
So, m COULD equal 2.9999999... and n COULD equal 1.9999999....., in which case mn is LESS THAN 10
This tells us that, if 1 < m < 3 and -5 < n < 2, then it's IMPOSSIBLE for mn to be GREATER THAN or equal to 10

So, the answer to the target question is YES, mn IS less than 10
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C

Cheers,
Brent

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Brent Hanneson – Creator of GMATPrepNow.com
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