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OG 13 DS Q75

by travelteer » Sun Jun 15, 2014 9:52 am
Q. Is the positive two-digit integer N less than 40 ?

1. The units digit of N is 6 more than the tens digit.
2. N is less than 4 times the unit digit.

I responded it as C. Logic being,
Statement 1 yields: 17, 28, 39 (though all are less than 40 I thought multiple answers will be insufficient.)
Statement 2 yields: Since N is two digit number I got 20, 28, 32. Again more than one solution.

Suffice to say I thought C gives me one answer that is 28 which is also less than 40.

However the correct answer seems is D. Can someone please advise where I could be going wrong?

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by Brent@GMATPrepNow » Sun Jun 15, 2014 10:17 am
Is the positive two-digit integer N less than 40 ?

(1) The units digit of N is 6 more than the tens digit
(2) N is 4 less than 4 times the units digit
Target question: Is N less than 40

Given: N is a positive two-digit integer

Statement 1: The units digit of N is 6 more than the tens digit
This statement is, essentially, restricting the value of the tens digit.
If the units digit is 6 more than the tens digit, then the tens digit cannot be very big.
For example, the tens digit cannot be 8, because the units digit would have to be 14, which is impossible.
Likewise, the tens digit cannot be 4, because the units digit would have to be 10, which is also impossible.
So, the greatest possible value of the tens digit of N is 3.
As such, N must be less than 40
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: N is 4 less than 4 times the units digit.
Well, 9 is the greatest possible value of any integer, and if the units digit were 9, then N would equal (4)(9) - 4, which is less than 40
So, no matter what value the units digit has, the resulting number (N), must be less than 40
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = D

Cheers,
Brent
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by Brent@GMATPrepNow » Sun Jun 15, 2014 10:24 am
travelteer wrote: Statement 1 yields: 17, 28, 39 (though all are less than 40 I thought multiple answers will be insufficient.)
Statement 2 yields: Since N is two digit number I got 20, 28, 32. Again more than one solution.
This is where it's very important to remind yourself of what the target question is.
The question is NOT, "What is the value of N"?
The target question is: "Is N less than 40?"

IF the question were, "What is the value of N?", your assessment would be correct, because N can have many different values.
HOWEVER, since the question wants us to determine whether or not N is less than 40, each statement (alone) provides sufficient information.
For example, for statement 1, you suggest that N can have many values (17, 28, 39). This is true. However, for EACH value, the answer to the target question remains the same.
If N = 17, N is less than 40.
If N = 28, N is less than 40.
If N = 39, N is less than 40.
etc.
Since EVERY possible value of N yields the SAME answer to the target question, statement 1 is sufficient.

The same applies to statement 2.

Cheers,
Brent
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by Brent@GMATPrepNow » Sun Jun 15, 2014 10:26 am
If you're interested, we have a free set of videos that cover everything you need to know about Data Sufficiency questions on the GMAT: https://www.gmatprepnow.com/module/gmat-data-sufficiency

Cheers,
Brent
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by travelteer » Sun Jun 15, 2014 11:23 am
Hi Brent,

Thank you so much for your detailed response - I see what you mean. I did end up misunderstanding the question. Thanks for helping me get back on track. I am also following your 60 day Guide, so I did come across the free videos on DS - very informative, again.

Looking forward to your continued support.

Best,
Travelteer.
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