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.

Answer C

a% of b% of c = abc/(100*100)
stmt 1 - b = (a/100)^(-1) so b= 100/a substituting above we get a% of b% of c = c/100 - so not suff

stmt 2 - substituting c = 100b we get b2a/100 - not sufficient

combining 1 and 2 we get b2a/100 = 100
ans C

Sorry guys, it's (2) \(c = 100^b\) NOT (2) c = 100b . Edited the original post. Please try again.
_________________

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.

The correct answer is (B).

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

YAY B is the correct answer.

+kudos if you like my explanation.

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

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

Answer: B

RELATED VIDEO

_________________