• Free Practice Test & Review
How would you score if you took the GMAT

Available with Beat the GMAT members only code

• Free Veritas GMAT Class
Experience Lesson 1 Live Free

Available with Beat the GMAT members only code

• 5-Day Free Trial
5-day free, full-access trial TTP Quant

Available with Beat the GMAT members only code

• 1 Hour Free
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

• Award-winning private GMAT tutoring
Register now and save up to \$200

Available with Beat the GMAT members only code

• Get 300+ Practice Questions

Available with Beat the GMAT members only code

• 5 Day FREE Trial
Study Smarter, Not Harder

Available with Beat the GMAT members only code

• Magoosh
Study with Magoosh GMAT prep

Available with Beat the GMAT members only code

• Free Trial & Practice Exam
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

## a% of b% of c an integer?

tagged by: Brent@GMATPrepNow

This topic has 5 expert replies and 3 member replies
j_shreyans Legendary Member
Joined
07 Aug 2014
Posted:
510 messages
Followed by:
5 members
Thanked:
3 times

#### a% of b% of c an integer?

Sun Jun 07, 2015 5:22 am
Elapsed Time: 00:00
• Lap #[LAPCOUNT] ([LAPTIME])
If a, b, and c are positive integers such that a < b < c, is a% of b% of c an integer?

(1) b=(a/100)^-1

(2) c = 100b

Statement 1 = b=(a/100)^-1

b=1/(a/100) so b = 100/a

if i put b=100/a in our target question then it will give a/100 X 100/a X c

so we will have only C and a,b,and c is positive integers it's given .

so this statement should be true.

Thanks,

Need free GMAT or MBA advice from an expert? Register for Beat The GMAT now and post your question in these forums!
theCEO Master | Next Rank: 500 Posts
Joined
17 Oct 2010
Posted:
363 messages
Followed by:
3 members
Thanked:
115 times
Sun Jun 07, 2015 5:59 am
j_shreyans wrote:
If a, b, and c are positive integers such that a < b < c, is a% of b% of c an integer?

(1) b=(a/100)^-1

(2) c = 100b

Statement 1 = b=(a/100)^-1

b=1/(a/100) so b = 100/a

if i put b=100/a in our target question then it will give a/100 X 100/a X c

so we will have only C and a,b,and c is positive integers it's given .

so this statement should be true.

Thanks,
b% of c = (bc)/100
a% of b% of c = (abc)/10,000
Is (abc)/10,000 an integer?

(1) b=(a/100)^-1
1 equation and 2 unknowns, cant solve so statement is insufficent

(2) c = 100b
1 equation and 2 unknowns, cant solve so statement is insufficent

Combining both
b=(a/100)^-1 = 100/a
ab = 100
c = 100b

(abc)/10,000 = 10,000b / 10,000 = b which is an integer
statement is sufficent

### GMAT/MBA Expert

GMATGuruNY GMAT Instructor
Joined
25 May 2010
Posted:
13378 messages
Followed by:
1781 members
Thanked:
12899 times
GMAT Score:
790
Sun Jun 07, 2015 6:24 am
The posted problem has a typo.

Quote:
If a, b, and c are positive integers such that a < b < c, is a% of b% of c an integer?

(1) b = (a/100)^(-1)

(2) c = 100^b
Does (a/100) * (b/100) * c = integer?

Test integer values such that a < b < c.

Statement 1: b = (a/100)¯¹
Thus, b = 100/a.

Test the smallest possible value for a.
Case 1: a=1
Here, b =100/1 = 100.
In this case, (a/100) * (b/100) * c = 1/100 * 100/100 * c = c/100.

If c = 200, then c/100 = 2, which is an integer.
If c = 201, then c/100 = 201/100, which is not an integer.
INSUFFICIENT.

Statement 2: c = 100^b
Test the smallest possible value for b.
Case 2: b=2
Here, a=1 and c = 100² = 10000.
In this case, (a/100) * (b/100) * c = 1/100 * 2/100 * 10000 = 2, which is an integer.

Test an extreme value for b.
Case 3: b=100
Here, c = 100¹⁰⁰.
In this case, (a/100) * (b/100) * c = a/100 * 10/100 * 100¹⁰⁰ = 10a * 100⁹⁸, which is an integer.

Cases 2 and 3 illustrate that -- given that c = 100^b -- (a/100) * (b/100) * c will always be equal to an integer value.
SUFFICIENT.

_________________
Mitch Hunt
GMAT Private Tutor
GMATGuruNY@gmail.com
If you find one of my posts helpful, please take a moment to click on the "Thank" icon.
Available for tutoring in NYC and long-distance.

Last edited by GMATGuruNY on Fri Jun 12, 2015 9:55 pm; edited 1 time in total

Thanked by: theCEO, j_shreyans
Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now.

### GMAT/MBA Expert

Brent@GMATPrepNow GMAT Instructor
Joined
08 Dec 2008
Posted:
10764 messages
Followed by:
1213 members
Thanked:
5154 times
GMAT Score:
770
Sun Jun 07, 2015 6:47 am
Quote:
If a, b, and c are positive integers such that a < b < c, is a% of b% of c an integer?

(1)b = (a/100)^-1
(2) c = 100^b
Target question: Is a% of b% of c an integer?

This is a great candidate for rephrasing the target question.
Aside: We have a free video with tips on rephrasing the target question: http://www.gmatprepnow.com/module/gmat-data-sufficiency?id=1100

a% of b% of c is the same as (a/100)(b/100)(c), which equals abc/10,000
So, we can rephrase the target question as follows:
REPHRASED target question: Is abc/10,000 an integer?

We can REPHRASE the target question even further...
RE-REPHRASED target question: Is abc a multiple of 10,000?

Statement 1: b = (a/100)^-1
In other words, b = 100/a
There are several values of a, b and c that satisfy this condition. Here are two:
Case a: a = 1, b = 100 and c = 1000, in which case abc = 100,000. Here, abc IS a multiple of 10,000
Case b: a = 1, b = 100 and c = 101, in which case abc = 10,100. Here, abc is NOT a multiple of 10,000
Since we cannot answer the RE-REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: c = 100^b
IMPORTANT: We are told that a, b and c are POSITIVE INTEGERS and that a < b < c
So, we can be certain that b > 2.
If b is greater than or equal to 2, then c (which equals 100^b) can equal 10,000 or 1,000,000 or 100,000,000 and so on.
Notice that ALL of these possible values of c are multiples of 10,000
So, if c is a multiple of 10,000, then abc MUST be a multiple of 10,000
Since we can answer the RE-REPHRASED target question with certainty, statement 2 is SUFFICIENT

Cheers,
Brent

_________________
Brent Hanneson – Founder of GMATPrepNow.com
Use our video course along with

Check out the online reviews of our course
Come see all of our free resources

Thanked by: j_shreyans
GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months!

### GMAT/MBA Expert

ceilidh.erickson GMAT Instructor
Joined
04 Dec 2012
Posted:
1634 messages
Followed by:
224 members
Thanked:
1419 times
Sun Jun 07, 2015 6:49 am
Quote:
if i put b=100/a in our target question then it will give a/100 X 100/a X c
so we will have only C and a,b,and c is positive integers it's given .
Be careful, j_shreyans - you're right that plugging the first statement into our question will cancel a and b. But as theCEO pointed out, our target question is really "is (abc)/10,000 an integer?"

You seemed to have interpreted the question as "a% of b of c" rather than "a% of b% of c." If we substitute (a/100)^-1 for b, we would get (a/100)((100/a)/100)(c). When we simplify, we're still left with c/100. Since the only constraint was a < b < c, we can't know if c is divisible by 100. Insufficient.

_________________

Ceilidh Erickson
Manhattan Prep GMAT & GRE instructor
EdM in Mind, Brain, and Education

Manhattan Prep instructors all have 99th+ percentile scores and expert teaching experience.
Sign up for a FREE TRIAL, and learn why we have the highest ratings in the GMAT industry!

Thanked by: j_shreyans
Free Manhattan Prep online events - The first class of every online Manhattan Prep course is free. Classes start every week.

### GMAT/MBA Expert

ceilidh.erickson GMAT Instructor
Joined
04 Dec 2012
Posted:
1634 messages
Followed by:
224 members
Thanked:
1419 times
Sun Jun 07, 2015 6:54 am
theCEO wrote:
(1) b=(a/100)^-1
1 equation and 2 unknowns, cant solve so statement is insufficent

(2) c = 100b
1 equation and 2 unknowns, cant solve so statement is insufficent
Be careful, theCEO! The GMAT will often mess with our expectations that we need 2 equations for 2 unknowns, 3 equations for 3 unknowns, etc. Remember that CONSTRAINTS are always given for a reason, and you didn't use the constraint that a, b, & c are positive and a < b < c. Since this is the case, as Mitch pointed out, the minimum value of b is 2, and thus the minimum value of 100^b = 10,000. This is sufficient.

So remember to always ask yourself - why did they include this restraint?

For more on how the GMAT breaks the "2 unknowns, 2 equations" rule, see here: https://www.manhattanprep.com/gmat/blog/2015/02/19/high-school-algebra-wrong-gmat-breaks-systems-equations-rules/

_________________

Ceilidh Erickson
Manhattan Prep GMAT & GRE instructor
EdM in Mind, Brain, and Education

Manhattan Prep instructors all have 99th+ percentile scores and expert teaching experience.
Sign up for a FREE TRIAL, and learn why we have the highest ratings in the GMAT industry!

Thanked by: theCEO
Free Manhattan Prep online events - The first class of every online Manhattan Prep course is free. Classes start every week.
theCEO Master | Next Rank: 500 Posts
Joined
17 Oct 2010
Posted:
363 messages
Followed by:
3 members
Thanked:
115 times
Sun Jun 07, 2015 7:10 am
ceilidh.erickson wrote:
theCEO wrote:
(1) b=(a/100)^-1
1 equation and 2 unknowns, cant solve so statement is insufficent

(2) c = 100b
1 equation and 2 unknowns, cant solve so statement is insufficent
Be careful, theCEO! The GMAT will often mess with our expectations that we need 2 equations for 2 unknowns, 3 equations for 3 unknowns, etc. Remember that CONSTRAINTS are always given for a reason, and you didn't use the constraint that a, b, & c are positive and a < b < c. Since this is the case, as Mitch pointed out, the minimum value of b is 2, and thus the minimum value of 100^b = 10,000. This is sufficient.

So remember to always ask yourself - why did they include this restraint?

For more on how the GMAT breaks the "2 unknowns, 2 equations" rule, see here: https://www.manhattanprep.com/gmat/blog/2015/02/19/high-school-algebra-wrong-gmat-breaks-systems-equations-rules/
Thanks alot Ceilid!

theCEO Master | Next Rank: 500 Posts
Joined
17 Oct 2010
Posted:
363 messages
Followed by:
3 members
Thanked:
115 times
Fri Jun 12, 2015 7:00 pm
After reviewing this post, I realize that the question asked and the question Mitch solved are different.

j_shreyans wrote:
If a, b, and c are positive integers such that a < b < c, is a% of b% of c an integer?

(2) c = 100b
GMATGuruNY wrote:
If a, b, and c are positive integers such that a < b < c, is a% of b% of c an integer?

(2) c = 100^b

### GMAT/MBA Expert

GMATGuruNY GMAT Instructor
Joined
25 May 2010
Posted:
13378 messages
Followed by:
1781 members
Thanked:
12899 times
GMAT Score:
790
Fri Jun 12, 2015 9:53 pm
Good catch.
This problem is from MGMAT.

j_shreyans wrote:
(2) c = 100b
Here, statement 2 has a typo.
In the original MGMAT problem, statement 2 reads as follows:

GMATGuruNY wrote:
(2) c = 100^b
I've amended my post above to call attention to this difference.
Even so:

theCEO wrote:
(2) c = 100b
1 equation and 2 unknowns, cant solve so statement is insufficent
Here, the portion in red mischaracterizes the task at hand.
To answer the question stem -- Is a% of b% of c an integer? -- we do no have to solve.
Rather, we have to determine whether abc is a multiple of 10,000.
A clearer line of reasoning would be as follows:
If a=1, b=2 and c=200, then abc is not a multiple of 10,000.
If a=1, b=100, and c=10,000, then abc is a multiple of 10,000.

_________________
Mitch Hunt
GMAT Private Tutor
GMATGuruNY@gmail.com
If you find one of my posts helpful, please take a moment to click on the "Thank" icon.
Available for tutoring in NYC and long-distance.

Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now.

### Best Conversation Starters

1 Vincen 152 topics
2 lheiannie07 61 topics
3 Roland2rule 49 topics
4 LUANDATO 44 topics
5 ardz24 40 topics
See More Top Beat The GMAT Members...

### Most Active Experts

1 Brent@GMATPrepNow

GMAT Prep Now Teacher

140 posts
2 Rich.C@EMPOWERgma...

EMPOWERgmat

110 posts
3 EconomistGMATTutor

The Economist GMAT Tutor

109 posts
4 GMATGuruNY

The Princeton Review Teacher

107 posts
5 DavidG@VeritasPrep

Veritas Prep

72 posts
See More Top Beat The GMAT Experts