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

 It is currently 20 Oct 2019, 20:04 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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  If a, b and c are distinct positive integers, what is the value of (a

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 58434
If a, b and c are distinct positive integers, what is the value of (a  [#permalink]

Show Tags

1
7 00:00

Difficulty:   95% (hard)

Question Stats: 36% (03:06) correct 64% (02:41) wrong based on 143 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) $$2^{(a+2b)} + 3^{(\frac{c}{4})} = 13$$

_________________
Current Student P
Joined: 18 Aug 2016
Posts: 603
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

1
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  P
Joined: 02 Apr 2014
Posts: 468
Location: India
Schools: XLRI"20
GMAT 1: 700 Q50 V34 GPA: 3.5
Re: If a, b and c are distinct positive integers, what is the value of (a  [#permalink]

Show Tags

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

thanks
Senior PS Moderator V
Joined: 26 Feb 2016
Posts: 3335
Location: India
GPA: 3.12
Re: If a, b and c are distinct positive integers, what is the value of (a  [#permalink]

Show Tags

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
VP  P
Joined: 12 Dec 2016
Posts: 1492
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

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.
Intern  B
Joined: 24 Jun 2018
Posts: 35
Re: If a, b and c are distinct positive integers, what is the value of (a  [#permalink]

Show Tags

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
Display posts from previous: Sort by

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

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne  