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

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06 Aug 2017, 00:57
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95% (hard)

Question Stats:

36% (03:06) correct 64% (02:41) wrong based on 143 sessions

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

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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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06 Aug 2017, 04:24
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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
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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, 13:29
Hi Bunuel, how come statement 2 is valid given a,b,c distinct positive integers?

thanks
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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, 13:46
1
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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If a, b and c are distinct positive integers, what is the value of (a  [#permalink]

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23 Dec 2017, 14:01
it seems that there is no faster way to calculate. It tooks me 3.5 min. Also, the assumption here is that the value of (a+b+c) must have a value. In other words, if there is no value, then the statement is insufficient. For this reason, B is wrong.
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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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09 Mar 2019, 02:42
Luckisnoexcuse wrote:
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

In my opinion even A is not sufficient.

in A we get 2A+C=6

We get two possible solutions to the above ie. A=1,C=4 or A=2, C=2.

With two possible solutions, we get two different values of A+B+C

Re: If a, b and c are distinct positive integers, what is the value of (a   [#permalink] 09 Mar 2019, 02:42
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# If a, b and c are distinct positive integers, what is the value of (a

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