MGMAT - The Power of Percents

[bml1105]

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



OA: B

[bml1105]

How come A isn't sufficient.

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

So ab = (a/100)(100/a) = 1

Then 1 X c (which is an integer) = c (an integer)

What am I doing wrong?

[bml1105]

Nevermind I saw my mistake. b% is different than b on it's own. Tricky tricky MGMAT!

[Brent@GMATPrepNow]

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
OA: B

Hey bml1105,

Once you've transcribed a question, be sure to confirm that you did so correctly.
You missed the crucial "power of" notation (^) above.

Cheers,
Brent

[Brent@GMATPrepNow]

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: https://www.gmatprepnow.com/module/gmat- ... cy?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

Answer = B

Cheers,
Brent

For even more information on rephrasing the target question, you can read this article I wrote for BTG: https://www.beatthegmat.com/mba/2014/06/ ... t-question

[nasahtahir]

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: https://www.gmatprepnow.com/module/gmat- ... cy?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

Answer = B

Cheers,
Brent

For even more information on rephrasing the target question, you can read this article I wrote for BTG: https://www.beatthegmat.com/mba/2014/06/ ... t-question

Hi
"So, if c is a multiple of 10,000, then abc MUST be a multiple of 10,000 "
How are you so sure that a&b are also multiples of 10,000? why must?

Hash.

[Brent@GMATPrepNow]

Hi
"So, if c is a multiple of 10,000, then abc MUST be a multiple of 10,000 "
How are you so sure that a&b are also multiples of 10,000? why must?

Hash.

If c is a multiple of 10,000, then we can write c = (10,000)(k), where k is some integer.
So, abc = (a)(b)(10,000)(k) = (10,000)(abk)
Since we can write abc as 10,000 times some integer (abk), we can be certain that abc is a multiple of 10,000

RELATED VIDEO
- Divisor Rules: https://www.gmatprepnow.com/module/gmat ... /video/831

Cheers,
Brent