Is J + K L + M ?

Question

Is J + K > L + M ?

(1) J > L + M

(2) K > L + M

LighthousePrep · Answer

This question is testing your understanding of number properties. At first glance it seems obvious that the answer would be D (both statements alone). But upon further thought, you would find that there is no restriction that the numbers have to be positive. Therefore, it is possible that any of the numbers could be negative. Knowing that, if we try to plug in some extreme examples we find that we cannot prove the statement and the correct answer is E. Here are some sample numbers I tried to plug in.

Statement 1:

J = 3
L = 2
M = 1
K = 100 or -100
Using one value of K gives me TRUE, using the second value gives me FALSE. Therefore Statement 1 is insufficient.

Statement 2:
Just like Statement 1, but switch J and K.

K = 3
L = 2
M = 1
J = 100 or -100
Using one value of J gives me TRUE, using the second value gives me FALSE. Therefore Statement 2 is insufficient.

nelo5390 · Answer

But what makes E correct, and why not C?

Bunuel · Answer

Is J + K > L + M ?

(1) J > L + M. If J = K = 1 and L + M = 0, then J + K > L + M but if If J = 1, K = -1 and L + M = 0, then J + K = L + M. Not sufficient.

(2) K > L + M. If J = K = 1 and L + M = 0, then J + K > L + M but if If J = -1, K = 1 and L + M = 0, then J + K = L + M. Not sufficient.

(1)+(2):

If J = K = 1 and L + M = 0, then J + K > L + M 
If J = K = -1 and L + M = -2, then J + K = L + M.

Not sufficient.

Answer: E.

thefibonacci · Answer

we can clearly see 1 and 2 alone are insufficient. (1)+(2) assume all terms are +ve add the inequality (j+k) > 2(l+m) assume all terms are -ve add the inequality (j+k) < 2(l+m) so E.

mkeshri185 · Answer

But how will we do this type of que in real exam? If J>L+M and K>L+M then we can say that both J and K are greater than (L+M) so on right side we have two quantities J and K which both are individually greater than (L+M). then their sum(j+k) should be logically greater than L+M?

Bunuel · Answer

Even with J > L + M and K > L + M, the sum is not forced to be greater.

Example from the solution: J = K = -1, L + M = -2.
 Then J > L + M and K > L + M, but J + K = -2, so not greater.

Is J + K > L + M ?

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