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# If the product of the digits of the two-digit positive integer n is 2,

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Math Expert
Joined: 02 Sep 2009
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If the product of the digits of the two-digit positive integer n is 2,  [#permalink]

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19 Nov 2017, 09:19
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Difficulty:

15% (low)

Question Stats:

84% (00:49) correct 16% (01:18) wrong based on 49 sessions

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If the product of the digits of the two-digit positive integer n is 2, what is the value of n ?

(1) n is odd.

(2) n is greater than 20.

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If the product of the digits of the two-digit positive integer n is 2,  [#permalink]

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Updated on: 19 Nov 2017, 09:30
Bunuel wrote:
If the product of the digits of the two-digit positive integer n is 2, what is the value of n ?

(1) n is odd.

(2) n is greater than 20.

as the product of digits of n is 2, so n could be 12 or 21

Statement 1: n is odd. so n=21. sufficient

Statement 2: n>20 so n=21. Sufficient

Option D

Originally posted by niks18 on 19 Nov 2017, 09:24.
Last edited by niks18 on 19 Nov 2017, 09:30, edited 1 time in total.
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Re: If the product of the digits of the two-digit positive integer n is 2,  [#permalink]

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19 Nov 2017, 09:27
From statement 1
If N is odd . Then N has to be 21 (2x1=2)
Sufficient
From statement 2
if N> 20
still N = 21 (2X1=2)
hence D
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Re: If the product of the digits of the two-digit positive integer n is 2,  [#permalink]

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19 Nov 2017, 09:29
niks18 wrote:
Bunuel wrote:
If the product of the digits of the two-digit positive integer n is 2, what is the value of n ?

(1) n is odd.

(2) n is greater than 20.

as the product of digits of n is 2, so n could be 12 or 21

Statement 1: n is odd. so n=21. sufficient

Statement 2: n>20 so n=21. Sufficient

Option B

you mean D. There must be a typo
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Re: If the product of the digits of the two-digit positive integer n is 2,  [#permalink]

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19 Nov 2017, 09:30
Bunuel wrote:
If the product of the digits of the two-digit positive integer n is 2, what is the value of n ?

(1) n is odd.

(2) n is greater than 20.

Hi Bunuel

Just a thought, if the question had not mentioned n to be a positive integer, then we could have had 4 scenarios for n= -21, -12, 12 & 21 and the question would have been a bit tricky. Do you have similar kind of question?
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Re: If the product of the digits of the two-digit positive integer n is 2,  [#permalink]

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19 Nov 2017, 09:31
Raksat wrote:
niks18 wrote:
Bunuel wrote:
If the product of the digits of the two-digit positive integer n is 2, what is the value of n ?

(1) n is odd.

(2) n is greater than 20.

as the product of digits of n is 2, so n could be 12 or 21

Statement 1: n is odd. so n=21. sufficient

Statement 2: n>20 so n=21. Sufficient

Option B

you mean D. There must be a typo

Yup. thanks for highlighting
Intern
Joined: 12 Nov 2017
Posts: 5
Re: If the product of the digits of the two-digit positive integer n is 2,  [#permalink]

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19 Nov 2017, 16:34
I guess the answer is C.

n can be 12 or 21

(1) n is odd - n can be even or odd, insufficient
(2) n > 20 - n can be < 20 or > 20, insufficient

(1) + (2) = n is odd + n > 20 = 21, sufficient
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Re: If the product of the digits of the two-digit positive integer n is 2,  [#permalink]

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19 Nov 2017, 17:21
1
vrkr wrote:
I guess the answer is C.

n can be 12 or 21

(1) n is odd - n can be even or odd, insufficient
(2) n > 20 - n can be < 20 or > 20, insufficient

(1) + (2) = n is odd + n > 20 = 21, sufficient

I'd recommend reviewing the steps of Data Sufficiency, using something like this: https://www.manhattanprep.com/gmat/blog ... ncy-works/. You've ended up approaching this one a little backwards. You aren't trying to test the statements to see whether they're true or not. You start by assuming that the statement you're working with is true. Then, based on that, you try to answer the question.

When we work with statement 1, we start out by saying 'I know that n is odd.' n is definitely odd; the statement always tells the true. Now, you're wondering whether knowing that n is odd is enough information to narrow down the possible answers to just one right answer. In this case, it is. Since there were only two possible answers in the first place, 12 and 21, and statement (1) eliminates one of those two possible answers, it's sufficient.
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Joined: 12 Nov 2017
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Re: If the product of the digits of the two-digit positive integer n is 2,  [#permalink]

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19 Nov 2017, 17:48
Got it! Thanks ccooley. Appreciate your detailed clarification.
Re: If the product of the digits of the two-digit positive integer n is 2, &nbs [#permalink] 19 Nov 2017, 17:48
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