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# If c > d > b, is d an integer?

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Math Expert
Joined: 02 Aug 2009
Posts: 6549
If c > d > b, is d an integer?  [#permalink]

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08 Dec 2017, 01:38
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Difficulty:

65% (hard)

Question Stats:

58% (00:52) correct 42% (01:11) wrong based on 59 sessions

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If c > d > b, is d an integer?

(1) c = b + 1
(2) $$d=\frac{c+b}{2}$$

New tricky question

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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: If c > d > b, is d an integer?  [#permalink]

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08 Dec 2017, 02:04
(1) c=1,5 b=0,5 then d lie in 0,5<d<1,5 and can be 1 or 0,7 so it is unclear whether it is integer or not.
Insufficient
(2) d=(c+b)/2
c= 1,5 b=0,5 d= (1,5+0,5)/2=1 - integer
c=1,8 b=0,8 d= (1,8+0,8)/2=1,3 - NOT an integer
(1) + (2)
c= 1,5 b=0,5 d= (1,5+0,5)/2=1 - integer
c=1,8 b=0,8 d= (1,8+0,8)/2=1,3 - NOT an integer

Answer should be E I guess
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Re: If c > d > b, is d an integer?  [#permalink]

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08 Dec 2017, 10:47
chetan2u wrote:
If c > d > b, is d an integer?

(1) c = b + 1
(2) $$d=\frac{c+b}{2}$$

New tricky question

(1) If b is an integer, then c=b+1 is also an integer, else not. But in any case d might or might not be an integer. So Insufficient.

(2) d = (c+b)/2 This tells us that d is the arithmetic mean of c & b, and thus c, d, b are in Arithmetic Progression (AP). But we cant say whether any or all of them are integers or not. Eg, c, d, b could be 3, 2, 1 respectively or they could be 3.3, 3.2, 3.1 respectively. So Insufficient.

Combining the two statements, c, d, b are in AP and c=b+1. But we could have a case where d is an integer (eg, c/d/b could be 3/2.5/2 respectively) OR we could also have a case where d is NOT an integer (eg, c/d/b could be 3.5/3/2.5 respectively). So d might or might not be an integer still. Insufficient.

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Re: If c > d > b, is d an integer?  [#permalink]

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10 Dec 2017, 05:19
Another approach-
S1: c= b+1
If c and b were integers, then this statement tells c and b are consecutive integers, so d, which lies between them has to be non-integer. Then our answer to the question would be a NO. But since it is not given that c and b are integers, we have to consider the case if c and b are both non-integers with a difference of 1 (e.g.. 1.5 and 0.5), then it is possible that d is an integer and answer to question would be YES.
Thus Statement 1 is INSUFFICIENT.

S2: d = (b+c)/2

If sum of b and c is even, then d will be integer, so answer to question will be YES.
If sum of b and c is odd, then d is not an integer. So answer to question is NO.
Thus, statement 2 is INSUFFICIENT.

Combine (1) and (2), it says:
d = (2b+1)/2

One may falter here thinking, 2b+1 has to be ODD, so d is definitely not integer. However, one should not forget that b can be non-integer e.g. 1.5, and then d will be an integer. So both statements combined are INSUFFICIENT.

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Re: If c > d > b, is d an integer? &nbs [#permalink] 10 Dec 2017, 05:19
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