Both a and b are positive; what is the value of a? (1) 150

Question

Both a and b are positive; what is the value of a?

(1) 150 percent of a equals 450 percent of b.

(2) ab is the cube of a positive integer.

medanova · Answer

1) --> 150×a=450×b --> a=3b
insufficient because a could be any positive value

(2)-->ab=X³ also insufficient

Combining both (1) and (2) :
a=3b
ab=X³ 
-->3b×b=X³ 
It's easy to see that a and b could both equal 3, then we will have 3×3×3=3³ 
But b could be also 24 (2×2×2×3), then a=3×2×2×2×3 and ab= 2×2×2×3 × 3× 2×2×2×3, which is (2×2×3)×(2×2×3)×(2×2×3)=(2×2×3)³

so still not sufficient to determine the value of a, therefore answer should be E

vitamingmat · Answer

could you be more clear on the 2nd option...

from 2) 3b^2 = X^3
=======> now i should have a value of b whose square times of 3 = x power of 3

i think b = 3 satiesfies the equation..wecan get the value of A from B....
=======> in your case 24 = 2*2*2*3 
=======> 3* 2^3 === > which is not equal to b^2

so the ans is : b alone....

please let me know if i am wrong...

scheol79 · Answer

You are actually solving for 1) and 2) together.

2) alone gives you nothing more than ab=k^3

My answer is E

1) a=3b (insuff)
2) ab=k^3 (insuff)

1)+2) solving for a
a*(a/3)=k^3
a^2=3k^3
a = root square(3k^3) or k*rootsquare(3k) 
I stared at this for a few seconds then decided it was insufficient.

OA plz

medanova · Answer

vitamingmat, 
sorry for the late answer, I just came back from a short holiday.

a =3b
ab=X³

case 1
if b=3 then a=3x3 -->ab=3³ 
case 2
if b=2x2x2x3 then a=3x2x2x2x3 --> ab=3³x2³x2³=(3x2x2)³

There are multiple cases apart from case 1 and 2 and it is not possible so determine the value of a even when both statements are combined.
I hope now it is clear.

harshdeep12 · Answer

Both a and b are positive; what is the value of a?

(1) 150 percent of a equals 450 percent of b.

(2) ab is the cube of a positive integer.

a) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
b) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
c) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
d) EACH statement ALONE is sufficient.
e) Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.

Can someone help me find a quick and a crisp solution to find this. PLease explain your answers.

BeingHan · Answer

C. 
From statement 1 A/B =3. Not sufficient.
From statement 2 AB= X^3 Not sufficient.
Combining 1 and 2. A=3k. B =k
AB= 3k^2=X^3. Which leads to k=3 only. As A and B can't be negative. So sufficient as A =9.

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chetan2u · Answer

Hi,.
 BeingHan , you should be careful when we are dealing with VARIABLES..

To get answer we require some numeric value and not just RATIO..

Statement I gives us a ratio 1.5a=4.5b.....a=3b
Insuff..
Statement II gives ab=x^3, where x is an integer..
Again insufficient..

Combined..
3b*b=x^3..
Easy to think B as 3... BUT nowhere it is given a and b are INTEGERS..
B can be 1/√3, then x becomes 1..
So insufficient

E

BeingHan · Answer

Yes. True. Thanks for the swift explanation.

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harshdeep12 · Answer

Hey Chetan2u-
This is great. thanks for such an amazing explanation. When i was solving this question, it took me around 6 minutes to get this. Ideally, what would you suggest to improve timings on such questions please. thanks and appreciate the help

chetan2u · Answer

Hi,

It is with practice that you would improve timings.. First point..
Second, would be to think alternative methods when you do any Q..

Specifically to this Q..
1) whenever you have variables, always check if it is mentioned integer or not, positive or negative..
2) even POSITIVE and non negative are different. So check for all this.
3) RATIO can never give you a numeric value of a variable.
4) watch out for that C trap. If the Q invited you to go for C, look once again.

Bunuel · Answer

Merging topics. Please refer to the discussion above.

harshdeep12 · Answer

Hey Bunuel and Chetan2u- I had a question here. When i was analyzing this question, i was thinking of a situation when a and b are positive integers. The trap answer in that case seems to be C. But i think, even if the question restricted the values of a and b to be integers, i think the answer would be still insufficient.(the initial question never mentioned such a restriction)

For example: x^3=3*b*b. I can think of two cases(obviously there would be more- one when we can take b as 3 and the other when we take b as 3^4. Hence we can have two or more values of a.Am i going the right way? Please throw some light. Thanks again.

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Both a and b are positive; what is the value of a? (1) 150

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