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# Each of a, b, and c is a positive integer, 3b < a, and a + b = c. What

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Math Expert
Joined: 02 Sep 2009
Posts: 51280
Each of a, b, and c is a positive integer, 3b < a, and a + b = c. What  [#permalink]

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25 Jul 2018, 23:22
00:00

Difficulty:

45% (medium)

Question Stats:

64% (01:50) correct 36% (01:31) wrong based on 45 sessions

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Each of a, b, and c is a positive integer, 3b < a, and a + b = c. What is the value of b?

(1) c = 8
(2) a = 7

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Math Expert
Joined: 02 Aug 2009
Posts: 7112
Re: Each of a, b, and c is a positive integer, 3b < a, and a + b = c. What  [#permalink]

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26 Jul 2018, 00:24
Each of a, b, and c is a positive integer, 3b < a, and a + b = c. What is the value of b?

(1) c = 8
so $$a+b=8$$.......
now a>3b....least value of b is 1
so a>3b or a>3......so $$(>3)+1=8........(>3)=7$$....YES
but if b is 2,
a>3*2 or a>6, so $$(>6)+2=8..........(>6)=6$$.....NO
so ONLY possibility of b is 1
sufficient

(2) a = 7
can be any value of b and c
insuff

A
_________________

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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Posts: 314
Re: Each of a, b, and c is a positive integer, 3b < a, and a + b = c. What  [#permalink]

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26 Jul 2018, 11:59
From 1, we get the only possible value of b=1, since 3b<a. Sufficient.
From 2, we get b=1 or b=2, since a=7. Not Sufficient.

Hence, A.
Re: Each of a, b, and c is a positive integer, 3b < a, and a + b = c. What &nbs [#permalink] 26 Jul 2018, 11:59
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