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Re: If a, b, and c are positive integers such that a < b < c, is a% of b% [#permalink]
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19 Jun 2015, 04:16
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.
Answer C
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Re: If a, b, and c are positive integers such that a < b < c, is a% of b% [#permalink]
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20 Jun 2015, 03:31
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.
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If a, b, and c are positive integers such that a < b < c, is a% of b% [#permalink]
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22 Jun 2015, 06:52
2
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 \(a*b\)
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Re: If a, b, and c are positive integers such that a < b < c, is a% of b% [#permalink]
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23 Aug 2015, 13:09
1
1
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]
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15 Nov 2016, 22:24
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]
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07 Apr 2017, 16:15
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]
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11 Apr 2017, 22:01
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]
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09 Jul 2017, 09:33
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]
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18 Jan 2018, 07:46
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
Answer: B
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Re: If a, b, and c are positive integers such that a < b < c, is a% of b%
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18 Jan 2018, 07:46