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Veritas Prep 10 Year Anniversary Promo Question #9

One quant and one verbal question will be posted each day starting on Monday Sept 17th at 10 AM PST/1 PM EST and the first person to correctly answer the question and show how they arrived at the answer will win a free Veritas Prep GMAT course ($1,650 value). Winners will be selected and notified by a GMAT Club moderator. For more questions and details please check here: veritas-prep-10-year-anniversary-giveaway-138806.html

To participate, please make sure you provide the correct answer (A,B,C,D,E) and explanation that clearly shows how you arrived at it. Winners will be announced the following day at 10 AM Pacific/1 PM Eastern Time.

If n = 14,444, which of the following operations will not yield a number that is divisible by 11?

A) n - 1 B) n + 10 C) n - 100 D) n + 100,000 E) n - 100,000

This question can be made significantly easier by first previewing the answer choices. Choices A and B are 11 apart, and choice C is 99 away from choice A on the number line. Therefore, those choices are all separated by multiples of 11, and if one of them is divisible by 11, then so are the others. Choice D may be better viewed by simply looking at the number. D comes out to 114444, which is 110000 (a multiple of 11) plus 4400 (another multiple of 11) plus 44 (another multiple of 11). Choice E is the answer that doesn’t fit. It’s 99,999 away from choice A, for example – not separated by a multiple of 11 (99000 + 990 + 9, not a multiple of 11).

Note that this question can be solved by simply checking out each answer choice and dividing by 11, as well. But a keen understanding of the number line and factors/multiples may make this question quicker for you.
_________________

Re: Veritas Prep 10 Year Anniversary Promo Question #9 [#permalink]

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21 Sep 2012, 10:05

Divisibility rules for 11 require difference between sum of odd and even places to be divisible by 11 For n=14444, this is 9-8 = 1 only operation D n=100000, doesnt give a number divisible by 11. Hence answer is D

Re: Veritas Prep 10 Year Anniversary Promo Question #9 [#permalink]

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21 Sep 2012, 10:05

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14444/11 => the remainder = 1. A. 1-1 =0 => remainder = 0 B. 1 + 10 =11 => remainder = 0 C. 1 - 100 = -99 => remainder =0 D. 1 + 100000 = 100001 which is divisible by 11 E. Correct

Last edited by monsama on 21 Sep 2012, 10:19, edited 2 times in total.

Re: Veritas Prep 10 Year Anniversary Promo Question #9 [#permalink]

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21 Sep 2012, 10:06

Ans is E 14443 is divisible by 11.

Hence, A) n - 1 is div by 11 B) n + 10 is div by 11 C) n - 100 =n-1 - 99 is div by 11 D) n + 100,000 is div by 11 E) n - 100,000 = -85556 when divided by 11 yields a remainder of 9

Re: Veritas Prep 10 Year Anniversary Promo Question #9 [#permalink]

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21 Sep 2012, 10:12

Answer is E

A) n - 1 >>divisible by 11 B) n + 10 >>divisible by 11 C) n - 100 >>divisible by 11 D) n + 100,000 >>divisible by 11 E) n - 100,000 >> not >>divisible by 11
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Re: Veritas Prep 10 Year Anniversary Promo Question #9 [#permalink]

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21 Sep 2012, 10:12

The Answer is E. E is not divisible
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Re: Veritas Prep 10 Year Anniversary Promo Question #9 [#permalink]

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21 Sep 2012, 10:34

Quote:

To participate, please make sure you provide the correct answer (A,B,C,D,E) and explanation that clearly shows how you arrived at it. Winners will be announced the following day at 10 AM Pacific/1 PM Eastern Time.[/textarea]

If n = 14,444, which of the following operations will not yield a number that is divisible by 11?

A) n - 1 B) n + 10 C) n - 100 D) n + 100,000 E) n - 100,000

Rule: any number to be divisible by 11 the sum of digits at odd places - the sum of digits at even place should either be zero or divisible by 11. A) n - 1 = 14443 --> (1+4+3) - (4+4) = 0 B) n + 10 = 14454 --> (1+4+4) - (4+5) = 0 C) n - 100 = 14344 --> (1+3+4) - (4+4) = 0 D) n + 100,000 = 114444 --> (1+4+4) - (1+4+4) = 0 E) n - 100,000 = - 85556 --> (8+5+6) - (5+5) = 9 ----->not divisible by 11

Re: Veritas Prep 10 Year Anniversary Promo Question #9 [#permalink]

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21 Sep 2012, 11:31

Answer E:

If n = 14,444, which of the following operations will not yield a number that is divisible by 11?

A) n - 1 B) n + 10 C) n - 100 D) n + 100,000 E) n - 100,000[/quote]

My approch was to solve the question first.

n = 14444 and we need to find value which will not be divisible by 11. check for 14444 first. 14444/11 gives remainder of 1

so option 1 => n -1 will be divisible option 2 => n +10 will be divisible option 3 => n -100 = n - 1 - 99 => n - 1 and 99 both are divisible by 11. Hence n - 100 will be divisible option 4 => n +100000 => n + 10 + 99990 => n+10 and 99990 both are divisible by 11. hence n+100000 will be divisible option 5 => n -100000 will not be divisible (you can conclude either directly or can calculate the same way) n - 1 - 99999 = > n-1 is divisibe and 99990 is divisible but not 99999. 99999 will give a remainder of 9.

Re: Veritas Prep 10 Year Anniversary Promo Question #9 [#permalink]

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21 Sep 2012, 23:22

Answer E Look at only D and E - Since we are adding and subtracting the same 100000 and 100000 is not divisible by 11 the answer would be one of the 2. Now, in D apply the alternate digit sum test (Difference of odd and even sum should be 0 or divisible by 11) Sum = 114444 Even sum = 9 Odd sum = 9 Difference = 0 So, D eliminated and E is the answer