Which of the following CANNOT yield an integer when divided : GMAT Problem Solving (PS)
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# Which of the following CANNOT yield an integer when divided

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Which of the following CANNOT yield an integer when divided [#permalink]

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21 Feb 2014, 00:08
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The Official Guide For GMAT® Quantitative Review, 2ND Edition

Which of the following CANNOT yield an integer when divided by 10 ?

(A) The sum of two odd integers
(B) An integer less than 10
(C) The product of two primes
(D) The sum of three consecutive integers
(E) An odd integer

Problem Solving
Question: 109
Category: Arithmetic Operations on rational numbers
Page: 75
Difficulty: 600

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Kudos [?]: 96557 [1] , given: 10753

Re: Which of the following CANNOT yield an integer when divided [#permalink]

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21 Feb 2014, 00:08
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SOLUTION

Which of the following CANNOT yield an integer when divided by 10 ?

(A) The sum of two odd integers
(B) An integer less than 10
(C) The product of two primes
(D) The sum of three consecutive integers
(E) An odd integer

In order an integer to be divisible by 10=2*5, the integer must be divisible by 2 (and 5), so it must be even, thus an odd integer is never divisible by 10 (or another way, an integer to be divisible by 10 its units digit must be 0, thus it must be even).

(A) The sum of two odd integers. Not true: for example, 5+5=10 --> 10 IS divisible by 10.
(B) An integer less than 10. Not true: for example 0 IS divisible by 10.
(C) The product of two primes. Not true: 2*5=10 --> 10 IS divisible by 10.
(D) The sum of three consecutive integers. Not true: for example, -1+0+1=0 --> 0 IS divisible by 10.

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Re: Which of the following CANNOT yield an integer when divided [#permalink]

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21 Feb 2014, 02:00
1
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IMO (E)
A) The sum of two odd integers - It could or could not yield integer: 3+5=8 or 25+5=30
B) An integer less than 10 - It could or could not yield integer: 3 or -30
C) The product of two primes -It could or could not yield integer: 2*3=6 or 5*2=10
D) The sum of three consecutive integers -It could or could not yield integer: 2+3+4=9 or 9+10+11=30
(E) An odd integer - it can't yield integer when divided by 10: Number should contain at least one 2 and 5 to yield an integer.
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Re: Which of the following CANNOT yield an integer when divided [#permalink]

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22 Feb 2014, 00:22
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We can test examples as below:

A) 15+5 is divisible by 10
B) -10 is divisble by 10
C) 2*5 is divisible by 10
D) (19+20+21) is divisible by 10
E) All odd integers are not divisible by 10

Math Expert
Joined: 02 Sep 2009
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Kudos [?]: 96557 [0], given: 10753

Re: Which of the following CANNOT yield an integer when divided [#permalink]

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22 Feb 2014, 05:32
SOLUTION

Which of the following CANNOT yield an integer when divided by 10 ?

(A) The sum of two odd integers
(B) An integer less than 10
(C) The product of two primes
(D) The sum of three consecutive integers
(E) An odd integer

In order an integer to be divisible by 10=2*5, the integer must be divisible by 2 (and 5), so it must be even, thus an odd integer is never divisible by 10 (or another way, an integer to be divisible by 10 its units digit must be 0, thus it must be even).

(A) The sum of two odd integers. Not true: for example, 5+5=10 --> 10 IS divisible by 10.
(B) An integer less than 10. Not true: for example 0 IS divisible by 10.
(C) The product of two primes. Not true: 2*5=10 --> 10 IS divisible by 10.
(D) The sum of three consecutive integers. Not true: for example, -1+0+1=0 --> 0 IS divisible by 10.

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Re: Which of the following CANNOT yield an integer when divided [#permalink]

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15 Mar 2015, 14:29
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Re: Which of the following CANNOT yield an integer when divided   [#permalink] 15 Mar 2015, 14:29
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