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# The number 123,k50 is a 6-digit integer, and k is a positive 1 digit i

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6811
GMAT 1: 760 Q51 V42
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The number 123,k50 is a 6-digit integer, and k is a positive 1 digit i  [#permalink]

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02 Apr 2018, 01:16
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Difficulty:

15% (low)

Question Stats:

80% (01:10) correct 20% (01:10) wrong based on 95 sessions

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[GMAT math practice question]

The number 123,k50 is a 6-digit integer, and k is a positive 1 digit integer. Which of the following cannot be a factor of 123,k50?

A. 2
B. 3
C. 4
D. 5
E. 6

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"Only $149 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" examPAL Representative Joined: 07 Dec 2017 Posts: 868 The number 123,k50 is a 6-digit integer, and k is a positive 1 digit i [#permalink] ### Show Tags 02 Apr 2018, 01:22 MathRevolution wrote: [GMAT math practice question] The number 123,k50 is a 6-digit integer, and k is a positive 1 digit integer. Which of the following cannot be a factor of 123,k50? A. 2 B. 3 C. 4 D. 5 E. 6 As we're asked 'which cannot be a factor' we'll look to the relevant divisibility tests. This is a Precise approach. The number ends is 0 and therefore will always be divisible by 2 and 5. (A), (D) are eliminated. If the sum of 1,2,3,k,5,0 is divisible by 3, then the number will be divisible by 3. This happens for at least one k, for example k = 1. (B) is eliminated. If the number is divisible by both 2 and 3, it is divisible by 6. Based on the above, we know that this can happen and therefore (E) is eliminated. (C) must be our answer. Alternatively, a number is divisible by 4 if its last two digits are divisible by 4. Since 50 is not divisible by 4, neither is our number. Once again, (C) is our answer. _________________ Manager Joined: 05 Feb 2016 Posts: 144 Location: India Concentration: General Management, Marketing WE: Information Technology (Computer Software) Re: The number 123,k50 is a 6-digit integer, and k is a positive 1 digit i [#permalink] ### Show Tags 02 Apr 2018, 01:55 MathRevolution wrote: [GMAT math practice question] The number 123,k50 is a 6-digit integer, and k is a positive 1 digit integer. Which of the following cannot be a factor of 123,k50? A. 2 B. 3 C. 4 D. 5 E. 6 A number is divisible by 4 only if its last two digits are divisible by 4. Since 50 is not divisible by 4. (C) is our answer Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6811 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: The number 123,k50 is a 6-digit integer, and k is a positive 1 digit i [#permalink] ### Show Tags 04 Apr 2018, 01:51 => The last two digits tell us whether the number is divisible by $$4$$. Since $$50$$ is not a multiple of $$4$$, the number cannot be a multiple of $$4$$. Therefore, the answer is C. Answer: C Let’s see why the number could be divisible by each of the other options: A: Since the units digit is an even number, the whole number is a multiple of $$2$$. B: A number is divisible by $$3$$ if the sum of its digits is divisible by $$3$$. If $$k = 4$$, then the sum of the digits is $$1 + 2 + 3 + 4 + 5 + 0 = 15$$, which is a multiple of $$3$$, and so the number is a multiple of $$3$$. D: Since the units digit is a multiple of $$5$$, the number is a multiple of $$5$$. E: If $$k = 4$$, the number is divisible by $$3$$ as seen in part B. Since it is also divisible by $$2$$ (see part A), the number is divisible by $$6.$$ _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$149 for 3 month Online Course"
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Re: The number 123,k50 is a 6-digit integer, and k is a positive 1 digit i  [#permalink]

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17 Apr 2018, 15:30
MathRevolution wrote:

The number 123,k50 is a 6-digit integer, and k is a positive 1 digit integer. Which of the following cannot be a factor of 123,k50?

A. 2
B. 3
C. 4
D. 5
E. 6

We may recall that an integer is divisible by 4 if the last two digits are divisible by 4.

For example, 1,224 is divisible by 4 since 24/4 = 6.

Since 50 are the last two digits of 123,k50, and 50 is not divisible by 4, 123,k50 is not divisible by 4 regardless what digit k is.

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Re: The number 123,k50 is a 6-digit integer, and k is a positive 1 digit i &nbs [#permalink] 17 Apr 2018, 15:30
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