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# X is the sum of 5 consecutive positive integers a, b, c, d, e such

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DS Forum Moderator
Joined: 21 Aug 2013
Posts: 1412
Location: India
X is the sum of 5 consecutive positive integers a, b, c, d, e such  [#permalink]

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27 Jun 2018, 20:50
1
00:00

Difficulty:

65% (hard)

Question Stats:

62% (02:30) correct 38% (02:14) wrong based on 17 sessions

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X is the sum of 5 consecutive positive integers a, b, c, d, e such that a < b < c < d < e. Is X divisible by 14?

(1) 'e' is even.

(2) 'a' gives a remainder of 5 when divided by 7.
Math Expert
Joined: 02 Aug 2009
Posts: 7100
Re: X is the sum of 5 consecutive positive integers a, b, c, d, e such  [#permalink]

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27 Jun 2018, 22:34
amanvermagmat wrote:
X is the sum of 5 consecutive positive integers a, b, c, d, e such that a < b < c < d < e. Is X divisible by 14?

(1) 'e' is even.

(2) 'a' gives a remainder of 5 when divided by 7.

a<b<c<d<e and all are consecutive integers, so a+b+c+d+e = 5c

(1) 'e' is even.
that means c is also even as c=e-2
if c is a multiple of 7 example 14,28 .. ans is YES
if c is not a multiple of 7 say 4, 5c=5*4=20, ans is NO
insuff

(2) 'a' gives a remainder of 5 when divided by 7
so c will give a remainder of a+2 as c=a+2
or c gives a remainder of 5+2=7, so c is div by 7
if c is an odd number say 7,21 etc... ans is NO
if c is an even number say 14,28.. ans is YES
insuff

combined
statement I tells us that c is even and statement II tells us that c is div by 7, so c is div by 2*7=14
and hence X, which is 5c, is div by 14
sufficient

C
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Re: X is the sum of 5 consecutive positive integers a, b, c, d, e such &nbs [#permalink] 27 Jun 2018, 22:34
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