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# M16-32

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Math Expert
Joined: 02 Sep 2009
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16 Sep 2014, 01:00
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Difficulty:

65% (hard)

Question Stats:

47% (01:26) correct 53% (00:58) wrong based on 127 sessions

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If $$a$$ and $$b$$ are positive, $$\frac{a}{b}$$ is what percent of $$ab$$?

(1) $$|b - 2| = 4$$

(2) $$b^2 - 3b - 18 = 0$$

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16 Sep 2014, 01:00
Official Solution:

We have to find $$(\frac{\frac{a}{b}}{ab})*100\% = (\frac{1}{b^2})*100\%$$. To answer the question we need to know $$b^2$$.

Statement (1) by itself is sufficient. From S1 it follows that $$b$$ is either 6 or -2. But the stem stipulates that $$b$$is positive. Thus, $$b = 6$$.

Statement (2) by itself is sufficient. From S2 it follows that $$b$$ is either 6 or -3. But the stem stipulates that $$b$$ is positive. Thus, $$b = 6$$.

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06 Oct 2014, 06:23
Good question.
I felt in trap. While solving i missed that it is given that a and b are positive.

Indeed each choice is correct
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21 Jun 2015, 06:46
IMO in Statement 2 solutions would be -6 and 3, not 6 and -3, nope ?
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21 Jun 2015, 10:49
mike34170 wrote:
IMO in Statement 2 solutions would be -6 and 3, not 6 and -3, nope ?

No, the two solutions of b^2−3b−18=0 are -3 and 6. You could simply plug the values to test your doubt.
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17 Aug 2016, 01:17
I think this is a poor-quality question and the explanation isn't clear enough, please elaborate. What is wrong in these steps.

10% of 200 = 20, in the similar lines.

x% of ab = a/b
or (x/100) * (ab) = a/b

we have to find x here.
x/100 = 1/b^2

since b is positive, b = 10 and x = 1.
So 1 % ab = a/b.

Since we found b = 10, none of the statements s1 and s2 matches b = 10, so I choose option E as the correct answer.

I know , I cann't challenge bunuel's explanation.Please point me where I have gone wrong
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17 Aug 2016, 01:37
1
dharan wrote:
I think this is a poor-quality question and the explanation isn't clear enough, please elaborate. What is wrong in these steps.

10% of 200 = 20, in the similar lines.

x% of ab = a/b
or (x/100) * (ab) = a/b

we have to find x here.
x/100 = 1/b^2

since b is positive, b = 10 and x = 1.
So 1 % ab = a/b.

Since we found b = 10, none of the statements s1 and s2 matches b = 10, so I choose option E as the correct answer.

I know , I cann't challenge bunuel's explanation.Please point me where I have gone wrong

The red part is not correct. x = 1/b^2*100. How did you get from here that x=1 and b=10? We got from each of the statements that b=6, which gives the value of x. So each statement is sufficient.
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17 Aug 2016, 02:50
Bunuel wrote:
dharan wrote:
I think this is a poor-quality question and the explanation isn't clear enough, please elaborate. What is wrong in these steps.

10% of 200 = 20, in the similar lines.

x% of ab = a/b
or (x/100) * (ab) = a/b

we have to find x here.
x/100 = 1/b^2

since b is positive, b = 10 and x = 1.
So 1 % ab = a/b.

Since we found b = 10, none of the statements s1 and s2 matches b = 10, so I choose option E as the correct answer.

I know , I cann't challenge bunuel's explanation.Please point me where I have gone wrong

The red part is not correct. x = 1/b^2*100. How did you get from here that x=1 and b=10? We got from each of the statements that b=6, which gives the value of x. So each statement is sufficient.

Thanks for your response. Here is how I got b = 10 and x =1

x/100 = x/10^2 = 1/b^2
So if b = 10 then x = 1.
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17 Aug 2016, 02:53
dharan wrote:
Bunuel wrote:
dharan wrote:
I think this is a poor-quality question and the explanation isn't clear enough, please elaborate. What is wrong in these steps.

10% of 200 = 20, in the similar lines.

x% of ab = a/b
or (x/100) * (ab) = a/b

we have to find x here.
x/100 = 1/b^2

since b is positive, b = 10 and x = 1.
So 1 % ab = a/b.

Since we found b = 10, none of the statements s1 and s2 matches b = 10, so I choose option E as the correct answer.

I know , I cann't challenge bunuel's explanation.Please point me where I have gone wrong

The red part is not correct. x = 1/b^2*100. How did you get from here that x=1 and b=10? We got from each of the statements that b=6, which gives the value of x. So each statement is sufficient.

Thanks for your response. Here is how I got b = 10 and x =1

x/100 = x/10^2 = 1/b^2
So if b = 10 then x = 1.

IF b=10... Why 10? Why not 1 or 100, or 1/2?

We know that b is not 10, it's 6, for which you get the value of x.
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17 Aug 2016, 03:16
I agree, Since there are two variables x and b . we need two equations.

equation 1 : x/10^2 = 1 / b^2
equation 2 : either of the 2 statements to get b value.

The mistake I did is, from equation 1. I equated 10^2 = b^2, and found b = 10. I thought that is the only 'b' value I can get. Some where I felt that by substituting values I can find x and b values. Not sure, why I did like that. May be I was trying to utilize question stem more efficiently and ended up with wrong choice.

Appreciate your patience and detailed explanation
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05 Jun 2017, 20:13
how exactly do you solve statement 2 to get values of B ?
I am confused
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05 Jun 2017, 22:54
mbsingh wrote:
how exactly do you solve statement 2 to get values of B ?
I am confused

This is factorisation of a quadratic equation.
If we are given a quadratic equation of the form: ax^2 + bx + c = 0
we need to figure out two such quantities whose sum is 'bx' and whose product is acx^2.

Lets understand with the help of given question.
We have to solve: b^2 - 3b - 18 = 0
We should think of two quantities whose sum is '-3b' and whose product is b^2*(-18) or -18b^2

These two are -6b and 3b (their sum is -3b and their product is -18b^2. Now we will re-write the given equation like this:
b^2 -6b + 3b - 18 = 0 . (notice that from first two terms, 'b' is common, and from the last two terms, '3' is common)
b(b-6) + 3(b-6) = 0 (now taking b-6 common from both)
(b-6)(b+3) = 0

So we have successfully factorised the equation. Now product of two quantities (b-6) and (b+3) equals 0 which means:
either b-6=0 which gives b=6
Or b+3=0 which gives b=-3

Thats how we get two values of b. Hope this helps.
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06 Jul 2017, 11:44
Bunuel wrote:
If $$a$$ and $$b$$ are positive, $$\frac{a}{b}$$ is what percent of $$ab$$?

(1) $$|b - 2| = 4$$

(2) $$b^2 - 3b - 18 = 0$$

The answer is relatively very simple. Point to remember a and b are positive. The question is asking $$a/b$$= x% of $$ab$$, find x.
We can further simplify - expression $$a/b = x/100 * ab$$
----> $$100/b^2$$ = x
All we have to know is b. So we can rephrase the question WHAT IS THE VALUE OF b?

1) $$|b - 2| = 4$$
b = 6 or b = -2
But since b>0, b=6 Suff

2) $$b^2 - 3b - 18 = 0$$

Solving we will get b =6 or -4
Again b>0, hence b = 6 Suff

option D winner
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06 Jul 2017, 13:30
Bunuel wrote:
If $$a$$ and $$b$$ are positive, $$\frac{a}{b}$$ is what percent of $$ab$$?

(1) $$|b - 2| = 4$$

(2) $$b^2 - 3b - 18 = 0$$

We are looking for the value of $$\frac{1}{b^2} * 100$$

(1) $$|b - 2| = 4$$

Gives two values b = 6 & -2 as b is positive b = 6

Hence (1) =====> is SUFFICIENT

(2) [m]b^2 - 3b - 18 = 0

Gives two values b = 6 & -3 as b is positive b = 6

Hence (1) =====> is SUFFICIENT

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06 Dec 2017, 16:07
Bunuel,

On a totally side note, I had read it in MGMAT that in DS, the two answer choices must be fragments (missing parts) of the same problem. I think that would mean that the two options cannot contradict each other, or give different answers. In this case, option 1 gives -2 as one of the answers, and option 2 gives -3 as one of the answers. Shouldn't they be same? I mean.. if solving option 1 gives 6 and -2 as the answer, then the equation of option 2 should be formed in such a way (e.g. b^2 - 4b - 12 = 0) that we get same 6 and -2 as the answers. Is my understanding right?
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06 Dec 2017, 20:59
chaudhurysr wrote:
Bunuel,

On a totally side note, I had read it in MGMAT that in DS, the two answer choices must be fragments (missing parts) of the same problem. I think that would mean that the two options cannot contradict each other, or give different answers. In this case, option 1 gives -2 as one of the answers, and option 2 gives -3 as one of the answers. Shouldn't they be same? I mean.. if solving option 1 gives 6 and -2 as the answer, then the equation of option 2 should be formed in such a way (e.g. b^2 - 4b - 12 = 0) that we get same 6 and -2 as the answers. Is my understanding right?

Yes, on the GMAT, two data sufficiency statements always provide TRUE information and these statements never contradict each other. Here the statement do not contradict. (1) says that b is 6 OR -2, (2) says that b is 6 OR -3. f we take them together then we get that b is 6. No contradiction.
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06 Dec 2017, 22:06
Bunuel wrote:
chaudhurysr wrote:
Bunuel,

On a totally side note, I had read it in MGMAT that in DS, the two answer choices must be fragments (missing parts) of the same problem. I think that would mean that the two options cannot contradict each other, or give different answers. In this case, option 1 gives -2 as one of the answers, and option 2 gives -3 as one of the answers. Shouldn't they be same? I mean.. if solving option 1 gives 6 and -2 as the answer, then the equation of option 2 should be formed in such a way (e.g. b^2 - 4b - 12 = 0) that we get same 6 and -2 as the answers. Is my understanding right?

Yes, on the GMAT, two data sufficiency statements always provide TRUE information and these statements never contradict each other. Here the statement do not contradict. (1) says that b is 6 OR -2, (2) says that b is 6 OR -3. f we take them together then we get that b is 6. No contradiction.

Yes, agreed that there is no contradiction. But still the answers are different (1) 6 OR -2 vs (2) 6 or -3, Hence I was wondering if this is okay.
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06 Dec 2017, 22:40
chaudhurysr wrote:
Bunuel wrote:
chaudhurysr wrote:
Bunuel,

On a totally side note, I had read it in MGMAT that in DS, the two answer choices must be fragments (missing parts) of the same problem. I think that would mean that the two options cannot contradict each other, or give different answers. In this case, option 1 gives -2 as one of the answers, and option 2 gives -3 as one of the answers. Shouldn't they be same? I mean.. if solving option 1 gives 6 and -2 as the answer, then the equation of option 2 should be formed in such a way (e.g. b^2 - 4b - 12 = 0) that we get same 6 and -2 as the answers. Is my understanding right?

Yes, on the GMAT, two data sufficiency statements always provide TRUE information and these statements never contradict each other. Here the statement do not contradict. (1) says that b is 6 OR -2, (2) says that b is 6 OR -3. f we take them together then we get that b is 6. No contradiction.

Yes, agreed that there is no contradiction. But still the answers are different (1) 6 OR -2 vs (2) 6 or -3, Hence I was wondering if this is okay.

Yes, there is nothing wrong. For example, consider the following question:

What is the value of x?

(1) x^2 = 4
(2) (x - 2)(x - 1) = 0.

From (1) x = 2 or x = -2.
From (1) x = 2 or x = 1.

(1)+(2) x can only be 2 to satisfy both statements. Sufficient.

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07 Dec 2017, 10:22
Bunuel wrote:

Yes, there is nothing wrong. For example, consider the following question:

What is the value of x?

(1) x^2 = 4
(2) (x - 2)(x - 1) = 0.

From (1) x = 2 or x = -2.
From (1) x = 2 or x = 1.

(1)+(2) x can only be 2 to satisfy both statements. Sufficient.

Okay! Thank you for clarifying!
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