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a% of b% of c an integer?

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j_shreyans Legendary Member Default Avatar
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a% of b% of c an integer?

Post Sun Jun 07, 2015 5:22 am
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.

Please advise and correct me.

Thanks,

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theCEO Master | Next Rank: 500 Posts Default Avatar
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Post 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!

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theCEO Master | Next Rank: 500 Posts Default Avatar
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Post 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

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theCEO Master | Next Rank: 500 Posts Default Avatar
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Post 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!

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theCEO Master | Next Rank: 500 Posts Default Avatar
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Post 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

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Post 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.

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Post 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/

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EdM in Mind, Brain, and Education
Harvard Graduate School of Education


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Post 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.

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Harvard Graduate School of Education


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Post 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

Answer = B

Cheers,
Brent

For even more information on rephrasing the target question, you can read this article I wrote for BTG: http://www.beatthegmat.com/mba/2014/06/30/rephrasing-the-target-question

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