BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

DS Divisibility

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Master | Next Rank: 500 Posts
Posts: 358
Joined: Thu Apr 18, 2013 9:46 am
Location: Jeddah, Saudi Arabia
Thanked: 42 times
Followed by:7 members
GMAT Score:730

DS Divisibility

by faraz_jeddah » Sun May 26, 2013 11:36 pm
If a,b,c are integers all greater than 1, and 15^8 = a * (b)^c. What is the value of c?

1 - a is not divisible by 5
2 - b is not divisible by 3

I will post the OA after some discussion.

My approach

(3)^8 * (5)^8 = a * (b)^c

Statement 1 tells us a cannot have a 5 in its factor.
Statement 2 tells us b cannot have a 3 in its factor.

Since all are greater than 1
By comparing the equations a = 3^8 ; b =5
Hence c = 8.

IMO C
Top
Source: — Data Sufficiency |
User avatar
Junior | Next Rank: 30 Posts
Posts: 26
Joined: Sat Oct 31, 2009 10:52 am
Location: rourkela
Thanked: 1 times

by sanjayism » Mon May 27, 2013 5:12 am
answer is c; its correct
kumar sanjay
Top
User avatar
Master | Next Rank: 500 Posts
Posts: 358
Joined: Thu Apr 18, 2013 9:46 am
Location: Jeddah, Saudi Arabia
Thanked: 42 times
Followed by:7 members
GMAT Score:730

by faraz_jeddah » Mon May 27, 2013 5:20 am
sanjayism wrote:answer is c; its correct
Nope the OA is E
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

by Brent@GMATPrepNow » Mon May 27, 2013 5:53 am
faraz_jeddah wrote:If a,b,c are integers all greater than 1, and 15^8 = a * (b)^c. What is the value of c?

(1) a is not divisible by 5
(2) b is not divisible by 3

Target question: What is the value of c?

Given: a,b,c are integers all greater than 1, and 15^8 = a * (b)^c

Here are a few possibilities:
15^8 = (3^8)(5^8)
15^8 = (5^8)(3^8)
15^8 = (3^8)(25^4) since 25 = 5^2, we get (3^8)(25^4) = (3^8)(5^2)^4 = (3^8)(5^8) = 15^8
15^8 = (3^8)(625^2) since 625 = 5^4, we get (3^8)(625^2) = (3^8)(5^4)^2 = (3^8)(5^8) = 15^8

Okay, now onto the question

Statement 1: a is not divisible by 5
There are several sets of values that meet this condition. Here are two:
Case a: 15^8 = (3^8)(5^8), in which case a = 3^8, b = 5 and c = 8
Case b: 15^8 = (3^8)(25^4), in which case a = 3^8, b = 25 and c = 4
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: b is not divisible by 3
There are several sets of values that meet this condition. Here are two:
Case a: 15^8 = (3^8)(5^8), in which case a = 3^8, b = 5 and c = 8
Case b: 15^8 = (3^8)(25^4), in which case a = 3^8, b = 25 and c = 4
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined:
There are still different sets of values that meet this condition. Here are two:
Case a: 15^8 = (3^8)(5^8), in which case a = 3^8, b = 5 and c = 8
Case b: 15^8 = (3^8)(25^4), in which case a = 3^8, b = 25 and c = 4
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer = E

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
User avatar
Master | Next Rank: 500 Posts
Posts: 141
Joined: Fri Sep 07, 2012 10:25 pm
Location: NY
Thanked: 5 times
Followed by:1 members

by hutch27 » Mon May 27, 2013 6:24 am
That was a tricky question, where's it from
Top
Post new topic Post Reply
• Page 1 of 1