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Positive two-digit integer

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Positive two-digit integer

by greenwich » Mon Jun 24, 2013 2:20 pm
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

Source: OG13

For (1), if the units digit of N is 6 more than the tens digit, should it be u=10t+6 instead of u=t+6?
OE from OG13 states u=t+6.
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by srcc25anu » Mon Jun 24, 2013 3:29 pm
St1: Only cases where Units digit is 6 more than ten's digit can be when N is 39, 28 or 17 (each of them is less than 40)
hence sufficient

St2: N is 4 less than 4 times the units digit.
If Units digit = 1,2 or 3, N will be 0, 4 and 8 respectively which are not 2 digit integers. (Exclude from analysis)
If Units digit = 4, N = 12 (NO)
If Units digit = 5, N = 16 (NO)
If Units digit = 6, N = 20 (NO)
If Units digit = 7, N = 24 (NO)
If Units digit = 8, N = 28 (KEEP)
If Units digit = 9, N = 32 (NO)
Only one value satifies and 28 < 40
Hence sufficient

IMO Ans = D
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by Brent@GMATPrepNow » Tue Jun 25, 2013 6:20 am
greenwich wrote: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.
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 digit, 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
Brent Hanneson - Creator of GMATPrepNow.com
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