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

Question

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

Luckisnoexcuse · Answer

(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

hellosanthosh2k2 · Answer

Hi  Bunuel , how come statement 2 is valid given a,b,c distinct positive integers?

Please clarify

thanks

pushpitkc · Answer

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

chesstitans · Answer

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.

sahibr · Answer

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

Bunuel , please help

Anurag06 · Answer

Hi experts  Bunuel   VeritasKarishma   ScottTargetTestPrep

Is there any way to trace the number patterns that way?

I find it quite complicated beyond certain limit. Please help!

Thanks.

KarishmaB · Answer

A and C are distinct integers. So A = 2, C = 2 is not allowed.

KarishmaB · Answer

There aren't too many options to worry about here.
 2^{(2a+c)} + 3^b = 91 
The only powers of 3 less than 91 are 3, 9, 27 and 81. 
When subtracted from 91, they should leave a power of 2. You can arrive at 27-64 combination fairly quickly.

ScottTargetTestPrep · Answer

In either case, you can subtract consecutive powers of one base and see if you get a power of the other base. For instance, to find powers of 2 and 3 that add up to 91, let's subtract powers of 3 from 91:

91 - 3^0 = 90
91 - 3^1 = 87
91 - 3^2 = 82
91 - 3^3 = 64 (a power of 2)
91 - 3^4 = 10
91 - 3^5 = a negative number

We see that the only way to add a positive integer power of 2 and 3 and get 91 is 3^3 + 2^6 = 91.
For powers of 2 and 3 that add up to 13, let's do the same but now subtract powers of 2:

13 - 2^0 = 12
13 - 2^1 = 11
13 - 2^2 = 9 (a power of 3)
13 - 2^3 = 5
13 - 2^4 = a negative number

Again we see that the only positive integer powers of 2 and 3 that add up to 13 is 2^2 + 3^2 = 13.

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

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GMAT Data Sufficiency (DS) Questions

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

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