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# If a, b and c are distinct positive integers, what is the value of (a

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Math Expert
Joined: 02 Sep 2009
Posts: 42629

Kudos [?]: 135833 [0], given: 12715

If a, b and c are distinct positive integers, what is the value of (a [#permalink]

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05 Aug 2017, 23:57
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If a, b and c are distinct positive integers, what is the value of (a + b + c)?

(1) $$2^{(2a+c)} + 3^b = 91$$

(2) $$2^{(a+2b)} + 3^{(\frac{c}{4})} = 13$$
[Reveal] Spoiler: OA

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Kudos [?]: 135833 [0], given: 12715

Director
Joined: 18 Aug 2016
Posts: 598

Kudos [?]: 181 [0], given: 138

GMAT 1: 630 Q47 V29
GMAT 2: 740 Q51 V38
Re: If a, b and c are distinct positive integers, what is the value of (a [#permalink]

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06 Aug 2017, 03:24
Bunuel wrote:
If a, b and c are distinct positive integers, what is the value of (a + b + c)?

(1) $$2^{(2a+c)} + 3^b = 91$$

(2) $$2^{(a+2b)} + 3^{(\frac{c}{4})} = 13$$

(1)
$$2^{(2a+c)} + 3^b = 91$$
91 can only be 64 + 27
2a+c = 6 and b=3
now (a,b,c) can only be (1,3,4) (distinct positive integers)

Sufficient

(2)
$$2^{(a+2b)} + 3^{(\frac{c}{4})} = 13$$
13 can only be 4+9
c/4 = 2
c=8
a+2b = 2 (not possible) cannot identify the value of a+b as b or a cannot be 0
Not sufficient

A
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Luckisnoexcuse

Kudos [?]: 181 [0], given: 138

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Joined: 02 Apr 2014
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Kudos [?]: 19 [0], given: 554

Re: If a, b and c are distinct positive integers, what is the value of (a [#permalink]

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07 Nov 2017, 12:29
Hi Bunuel, how come statement 2 is valid given a,b,c distinct positive integers?

thanks

Kudos [?]: 19 [0], given: 554

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Re: If a, b and c are distinct positive integers, what is the value of (a [#permalink]

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07 Nov 2017, 12:46
1
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hellosanthosh2k2 wrote:
Hi Bunuel, how come statement 2 is valid given a,b,c distinct positive integers?

thanks

Hey hellosanthosh2k2

B is not valid, that is the reason the answer is Option A.
If you have some other problem do let me know!

As already explained, a+2b = 2 is possible in 2 cases
case 1
a=0,b=1
case 2
b=0,a=2
As c has the value of 8, the value of the expression a+b+c could be 9 or 10

Hence, Option B is not sufficient
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Kudos [?]: 752 [1], given: 20

Re: If a, b and c are distinct positive integers, what is the value of (a   [#permalink] 07 Nov 2017, 12:46
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