GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 21 Oct 2018, 03:39

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 50007
If a, b and c are distinct positive integers, what is the value of (a  [#permalink]

### Show Tags

06 Aug 2017, 00:57
1
4
00:00

Difficulty:

95% (hard)

Question Stats:

35% (03:07) correct 65% (02:36) wrong based on 154 sessions

### HideShow timer Statistics

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

_________________
Director
Joined: 18 Aug 2016
Posts: 625
Concentration: Strategy, Technology
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]

### Show Tags

06 Aug 2017, 04:24
1
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
_________________

We must try to achieve the best within us

Thanks
Luckisnoexcuse

Senior Manager
Joined: 02 Apr 2014
Posts: 471
GMAT 1: 700 Q50 V34
Re: If a, b and c are distinct positive integers, what is the value of (a  [#permalink]

### Show Tags

07 Nov 2017, 13:29
Hi Bunuel, how come statement 2 is valid given a,b,c distinct positive integers?

thanks
Senior PS Moderator
Joined: 26 Feb 2016
Posts: 3188
Location: India
GPA: 3.12
Re: If a, b and c are distinct positive integers, what is the value of (a  [#permalink]

### Show Tags

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
_________________

You've got what it takes, but it will take everything you've got

SVP
Joined: 12 Dec 2016
Posts: 1710
Location: United States
GMAT 1: 700 Q49 V33
GPA: 3.64
If a, b and c are distinct positive integers, what is the value of (a  [#permalink]

### Show Tags

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.
If a, b and c are distinct positive integers, what is the value of (a &nbs [#permalink] 23 Dec 2017, 14:01
Display posts from previous: Sort by