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 Your Progress

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.

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

The Next Quiz will start on 7:30AM IST 16nd Feb (15th Feb, 9PM EST). The Quiz will be Live for 12 hrs. We will also have a webinar on the Quiz Questions on 10 PM, IST 16 Feb (11:30 AM, EST 16 Feb)

Want to score 90 percentile or higher on GMAT CR? Attend this free webinar to learn how to pre-think assumptions and solve the most challenging questions in less than 2 minutes.

Want to solve 700+ level Algebra questions within 2 minutes? Attend this free webinar to learn how to master the most challenging Inequalities and Absolute Values questions in GMAT

Re: If a, b, and c are positive integers such that a < b < c, is a% of b%
[#permalink]

Show Tags

19 Jun 2015, 03:16

Bunuel 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

Kudos for a correct solution.

Not quite sure if I got this right:

Statement 1: rewrite as b = 100/a >>> which is a*b = 100 Plug in some numbers a=2 and b=50, i.e. c > 50 in THIS case because c > b 2%*50%*55 if C is for example 55, the result will NOT be an integer. However if C is 100, the result will be integer. Therefore insufficient.

Statement 2: alone insufficent (nothing about a).

Together: Statement 2 says that c = 100b. Combined with the information above, this will always be integer. Even if a = 1 and b = 100.

Re: If a, b, and c are positive integers such that a < b < c, is a% of b%
[#permalink]

Show Tags

20 Jun 2015, 02:31

Bunuel 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

Kudos for a correct solution.

Hello, Answer to this question will be C. Both statements combined are sufficient.

Statement 2 : C=100b not sufficient as there is no information about a. Calculating b% of c will be b/100 *100b which will give b^2. But can't be solved further as no information about a.

Statement 1 : It gives us ab=100. No information about c as well as a and b can assume different values.

Combining both Statement 1 and Statement 2 are sufficient.

b% of c = b^2 a% of b% = a/100 *b^2 => ab^2/100 => a*b*b/100 =>ab*b/100 =>100b/100 => b which is an integer.

Hence combining both statements we can say that it is an integer.

Prosper!!! GMATinsight Bhoopendra Singh and Dr.Sushma Jha e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772 Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi http://www.GMATinsight.com/testimonials.html

If a, b, and c are positive integers such that a < b < c, is a% of b%
[#permalink]

Show Tags

22 Jun 2015, 05:52

3

1

Bunuel 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 = 100^b

Kudos for a correct solution.

Question : is a% of b% of c an integer?

Question : is (a/100)*(b/100)*c and Integer?

Question : is (a*b*c)/(100*100) and Integer?

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

i.e. b = (100/a) i.e. ab/100 = 1 which if we substitute in the Expression of Question, we are left with c/100 but c/100 may or may not be an Integer

Hence NOT SUFFICIENT

Statement 2: c = 100^b

if we substitute this value of c in the Expression of Question, we are left with \(\frac{(a*b*100^b)}{(100*100)}\) SInce a, b, and c are positive Integers and a < b < c

i.e. Minimum value of a = 1 and Minimum value of b = 2

i.e. Numerator in the expression \(\frac{(a*b*100^b)}{(100*100)}\) is a multiple of \(100^2\) which cancels the \(100^2\) in denominator and renders and Integer result a multiple of \(a*b\)

Prosper!!! GMATinsight Bhoopendra Singh and Dr.Sushma Jha e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772 Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi http://www.GMATinsight.com/testimonials.html

Re: If a, b, and c are positive integers such that a < b < c, is a% of b%
[#permalink]

Show Tags

23 Aug 2015, 12:09

1

2

OA:

You can rephrase the question as follows:

Is \(\frac{a}{100}*\frac{b}{100}*c\) an integer?

Is \(\frac{abc}{100^2}\) an integer?

\(100^2\) can also be thought of as \((102)^2\) or \(10^4\), which in turn can be broken down into primes: \(2^45^4\)

Thus, an alternative rephrase is as follows:

Does the product abc contain four 2’s and four 5’s?

(1) INSUFFICIENT: Simplifying the statement and analyzing it with regards to divisibility, you get

ab = 100

ab = \(2^25^2\)

Thus the product ab contains two 2’s and two 5’s, but it is uncertain whether the inclusion of c in the product would add the two more 2’s and two more 5’s needed to satisfy the question.

(2) SUFFICIENT: Simplifying the statement by breaking it down into primes, you get:

c = \((2^25^2)^b\)

This means that c contains a set of two 2’s and two 5’s, b number of times. That is, if b = 1, c contains only two 2’s and two 5’s, however, if b = 2, c contains two sets for a total of four two’s and four 5’s, etc. Looking back at the given, a < b < c and all three are positive integers, thus the minimum value for b is 2. That means that c alone must have at least four 2’s and four 5’s and therefore so will the product abc.

NOTE that this is a very tempting C-trap. Statement (1) provides information about a and b, and statement (2) provides information about c, appearing to complete the picture.

Re: If a, b, and c are positive integers such that a < b < c, is a% of b%
[#permalink]

Show Tags

15 Nov 2016, 21:24

1

This is like one of mine favourite trick questions where C seems like the only option just because we have been in a hurry. So, dissecting what the question is asking for we know that a<b<c and luckily they all are positive integers (Aah! lot of test cases gone )

Now : we have a situation where abc/10000= integer. In other works abc=10000n

Statement 1: ab=100 awesome but what about C. if c=100 yay we are done, but if c=17 Ouch we are not. so we have a yes no situation NS

Statement2: c=100^b if b=1 then c=100 and a=? oh we are messed up a little here. but hey wait doesn't the question stem say A<b<c and all of them are sweet and neat positive intergers. So b is definitely more than 1 and any value of b>1 will be sufficient to prove our case

Re: If a, b, and c are positive integers such that a < b < c, is a% of b%
[#permalink]

Show Tags

07 Apr 2017, 15:15

This is a beautifully confusing question stem. At first glance this question might appear to be about percentages or inequalities, but it's really about divisibility. "Is a% of b% of c an integer" can be translated into:

(a/100) * (b/100) * (c) => abc/10000

That's a little easier. Is the product of a, b, and c divisible by 10000?

1) the product of a and b is 100, but we don't know if c is a positive multiple of 10 NOT SUFFICIENT

2) because of the constraints in the stem, we know that b is an integer greater than or equal to 2. Thus, c is an integer multiple of 100^2. Since a and be are integers, the product of a, b, and c is an integer multiple of 100^2, and is definitely divisible by 10000. SUFFIECIENT

Re: If a, b, and c are positive integers such that a < b < c, is a% of b%
[#permalink]

Show Tags

11 Apr 2017, 21:01

Inference from the given data: Question is asking whether abc = 10,000XK (where as K>0) a<b<c (min value of a =1 => min b= 2) 1. no value about c . So Not Suff.

2. C = b power of 100. it is given that b=2, So c= 10000 (min) & a = + ve integer. if we substitute we will get unique answer to the given question. So Suff. B

Re: If a, b, and c are positive integers such that a < b < c, is a% of b%
[#permalink]

Show Tags

09 Jul 2017, 08:33

1

You can rephrase the question as follows:

Is an integer?

Is an integer?

1002 can also be thought of as (102)2 or 104, which in turn can be broken down into primes: 2454

Thus, an alternative rephrase is as follows:

Does the product abc contain four 2’s and four 5’s?

(1) INSUFFICIENT: Simplifying the statement and analyzing it with regards to divisibility, you get

ab = 100

ab = 2252

Thus the product ab contains two 2’s and two 5’s, but it is uncertain whether the inclusion of c in the product would add the two more 2’s and two more 5’s needed to satisfy the question.

(2) SUFFICIENT: Simplifying the statement by breaking it down into primes, you get:

c = (2252)b

This means that c contains a set of two 2’s and two 5’s, b number of times. That is, if b = 1, c contains only two 2’s and two 5’s, however, if b = 2, c contains two sets for a total of four two’s and four 5’s, etc. Looking back at the given, a < b < c and all three are positive integers, thus the minimum value for b is 2. That means that c alone must have at least four 2’s and four 5’s and therefore so will the product abc.

NOTE that this is a very tempting C-trap. Statement (1) provides information about a and b, and statement (2) provides information about c, appearing to complete the picture.

Re: If a, b, and c are positive integers such that a < b < c, is a% of b%
[#permalink]

Show Tags

18 Jan 2018, 06:46

1

Top Contributor

Bunuel 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 = 100^b

Kudos for a correct solution.

Target question:Is a% of b% of c an integer?

This is a great candidate for rephrasing the target question. Aside: See our video with tips on rephrasing the target question (below)

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

Re: If a, b, and c are positive integers such that a < b < c, is a% of b%
[#permalink]

Show Tags

25 May 2019, 00:32

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________