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OG2016 DS #93

by k3roro » Sun Jul 19, 2015 10:40 am
In statement number 2, it mentions that N is 4less than to 4 times the unit digit.

Based on the solution, it seems that using the biggest unit digit (9) results in 9*4 = 36 - 4 = 32 < 40. Making this statement sufficient.

However, is this a flawed question? Since if N is 32... then technically the unit digit is 2.. not 9.. which we used to calculate N...
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by theCEO » Sun Jul 19, 2015 10:57 am
Please post the full question if possible.
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by Brent@GMATPrepNow » Sun Jul 19, 2015 11:12 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

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Brent
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by Brent@GMATPrepNow » Sun Jul 19, 2015 11:18 am
k3roro wrote:Since if N is 32... then technically the unit digit is 2.. not 9.. which we used to calculate N...
Based on statement 2, N CANNOT equal 32
I believe you are reading statement 2 incorrectly. It does not say that the TENS digit of N is 4 less than 4 times the units digit.
Statement 2: N is 4 less than 4 times the units digit
N itself is 4 less than 4 times the units digit

In your suggested value of N (32), The units digit = 2
This means N is 4 less than 4 times the units digit
In other words, N = 4(2) - 4 = 3
This makes no sense, since 3 is not a positive two-digit integer. Also, the units digit of 3 is not 2

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by k3roro » Sun Jul 19, 2015 4:35 pm
Brent@GMATPrepNow wrote:
Is the positive two-digit integer N less than 40 ?

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
Hi Brent - thank you for your response. I understand where you are coming from and I was originally arriving at the same conclusion. However - if we go by 9 as the greatest value, as you sated, N would equal (4)(9)-4, which is 32. If N is 32, then the unit digit, which is 2, differs from the unit digit 9 that we had assumed to arrive at N = 32.

I was able to arrive at the same answer as you, but upon further thinking I was getting confused - perhaps I just need to stop. Please let me know.

Thanks!
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by Brent@GMATPrepNow » Sun Jul 19, 2015 4:41 pm
k3roro wrote:
Brent@GMATPrepNow wrote:
Is the positive two-digit integer N less than 40 ?

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
Hi Brent - thank you for your response. I understand where you are coming from and I was originally arriving at the same conclusion. However - if we go by 9 as the greatest value, as you sated, N would equal (4)(9)-4, which is 32. If N is 32, then the unit digit, which is 2, differs from the unit digit 9 that we had assumed to arrive at N = 32.

I was able to arrive at the same answer as you, but upon further thinking I was getting confused - perhaps I just need to stop. Please let me know.

Thanks!
Hi k3roro,

The important thing is that we need not find the actual value of N, since the target question doesn't ask us to do this.
So, we need only recognize that N must be less than 40.
So, statement 2 is sufficient.

If we WERE to start testing different units digits, we would learn that N = 28 and that not other values of N satisfy statement 2.
So, again, statement 2 is sufficient.

Cheers,
Brent
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by k3roro » Sun Jul 19, 2015 4:43 pm
Thank you - loud and clear :)
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by nikhilgmat31 » Wed Jul 22, 2015 12:34 am
statement 1 - unit digit is 6 greater than tens digit.
so possible numbers are 17,28,39 . But 4 & 10 is not possible since it will be a 4 digit number.

17,28,39 is < 40 so SUFFICIENT.

statement 2 = let the number is 10x + y
4y - 4 = 10x + y

3y = 10x + 4
x can't 1,3,4,5,6,7,8 since value of y is not feasible in a 2 digit number.

x = 2 y = 8 number is 28 which is less than 40
so SUFFICIENT.

Answer is D
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