If the square root of the product of three distinct positive

Question

If the square root of the product of three distinct positive integers is equal to the largest of the three numbers, what is the product of the two smaller numbers?

(1) The largest number of the three distinct numbers is 12.
(2) The average (arithmetic mean) of the three numbers is 20/3

gayathri · Answer

I think its A.

Translating the question stem: x<y<z and sqrt(xyz) = z ie: xyz = z^2 or xy = z

S(1): z = 12 => xy = 12 sufficient
S(2): x+y+z = 20 insufficient

ruhi · Answer

I'll go with D.

agree with whatever gayathri said except statement 2---

x+y+z=20

we know xy=z.

hence, x+y+xy=20
lets try n find two values for x and y such that the above eq. is satisfied.
its possible only when x=6, y=2 or x=2 and y=6. eitherways, xy=12.
hence, statement 2 is SUFFICIENT.

Hence, D.

twixt · Answer

Will go with D too.

1st statement is enough ok

2nd statement means that, assuming a, b, c are the 3 positive integers, ab=c and (a+b+c)/3=20/3 id est a+b+ab=20 : this is true only if a=2 and b=6 or a =6 and b=2 (ab=12)

So statement 2 is enough

Dookie · Answer

Yes, the answer is D. I thought this was a trick one

Well done!

gayathri · Answer

My bad again

I seem to have this problem with DS where I rush to the answer too soon

If the square root of the product of three distinct positive

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards