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29 Apr 2015, 04:02
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
85%
(hard)
Question Stats:
53% (02:54) correct
47%
(02:50)
wrong
based on 212
sessions
History
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In the grid above, the variables a through p are each equal to 2, 3, 5, or 7, with exactly one occurrence of each value in any row and in any column. What is the value of fgjk?
(1) bcehilno = 35^4
(2) (2.25^2)afkp = dgjm
Attachment:
Screen-Shot-2012-05-18-at-10.58.53-PM.png [ 8.69 KiB | Viewed 4920 times ]
(1) \(bcehilno = 35^4 = 5^4 * 7^4\)
This means 4 out of the 8 numbers b,c,e,h,i,l,n,o are equal to 5 and the rest 4 are equal to 7.
Since e and h are in the same row, one of them is 5 and the other one 7.
Therefore, f and g are either 2 and 3 or 3 and 2 respectively.
Similarly, j and k are 2 and 3 or 3 and 2 respectively.
So f, g, j, k are 2, 3, 3, 2 or 3, 2, 2, 3 respectively since numbers in the same row or column can't have the same value.
In both cases, \(fjgk = 2*3*3*2 = 36\)
SUFFICIENT
(2) (2.25^2)afkp = dgjm
2.25 can also be written as \(\frac{9}{4}\).
\(9^2 afkp = 4^2 dgjm\)
\(3^4 afkp = 2^4 dgjm\)
Since 3 and 2 are prime numbers, the only way LHS and RHS can be equal if \(afkp = 2^4\) and \(dgjm = 3^4\)
Therefore, a = f = k = p = 2 and d = g = j = m = 3
\(fjgk = 2*3*3*2 = 36\)
SUFFICIENT
D is the correct choice here.
This means 4 out of the 8 numbers b,c,e,h,i,l,n,o are equal to 5 and the rest 4 are equal to 7.
Since e and h are in the same row, one of them is 5 and the other one 7.
Therefore, f and g are either 2 and 3 or 3 and 2 respectively.
Similarly, j and k are 2 and 3 or 3 and 2 respectively.
So f, g, j, k are 2, 3, 3, 2 or 3, 2, 2, 3 respectively since numbers in the same row or column can't have the same value.
In both cases, \(fjgk = 2*3*3*2 = 36\)
SUFFICIENT
(2) (2.25^2)afkp = dgjm
2.25 can also be written as \(\frac{9}{4}\).
\(9^2 afkp = 4^2 dgjm\)
\(3^4 afkp = 2^4 dgjm\)
Since 3 and 2 are prime numbers, the only way LHS and RHS can be equal if \(afkp = 2^4\) and \(dgjm = 3^4\)
Therefore, a = f = k = p = 2 and d = g = j = m = 3
\(fjgk = 2*3*3*2 = 36\)
SUFFICIENT
D is the correct choice here.
General Discussion
29 Apr 2015, 05:32
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Bunuel
1) \(35^4 = 7^4*5^4\) So we can infer that all letters bcehilno are equal to \(5\) or \(7\)
and we see on the picture that \(fj\) placed in vertical row with \(b\) and \(n\) so it should be equal to \(2\) and \(3\)
and \(gk\) placed in vertical row with \(c\) and \(o\) so it should be equal to \(2\) and \(3\)
We can infer that \(fgjk\) will be equal to \(2*3*2*3=36\)
Sufficient
2) This is diagonal letters, so it should be equal numbers like \(2222\) or \(3333\) etc.
we have 4 variants: \(2^4 = 16\); \(3^4=81\); \(5^4=625\); \(7^4=\)something big, we don't need it
\(2.25^2\) equal to \(5\) and something more
and we see that \(2.25^2*2^4=3^4=81\) (I didn't check it but 5*16 = 80 and we have something more in 5 so it one possible variant I think)
so we can infer that \(fk = 2*2\) and \(gj=3*3\)
\(fgjk\) will be equal to \(2*3*2*3=36\)
Sufficient
Answer is D
