Is A B? (1) AX BX (2) X

Question

Is A > B?

(1) AX > BX

(2) X < 0

amanvermagmat · Answer

Statement 1 AX > BX or AX - BX > 0 or X*(A-B) > 0 So Either both X > 0 and A - B > 0 (which means here A>B) OR both X < 0 and A - B < 0 (which means here A B or A < B till we know whether X is positive or negative. Insufficient . Statement 2 This is clearly insufficient on its own. Combining the two statements, since we know that X < 0 so it must be the second case and thus A < B. This gives us NO as an answer to the question asked. Sufficient . Hence C answer

Mo2men · Answer

Is A > B?

(2) X < 0

No info about A & B

Insufficient

(1) AX > BX

AX - BX > 0

x (A-B) > 0

Case 1:

X > 0 & A - B > 0...then A > B............Answer is Yes

Case 2:

X< 0 & A - B < 0....then A < B............Answer is No

Insufficient

Combine 1 & 2

From Statement :X<0.This means case 2 from statement 1

Sufficient

Answer: C

MathRevolution · Answer

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Since we have 3 variables (A, B and X) and 0 equations, E is most likely to be the answer. So, we should consider conditions 1) & 2) together first.

Conditions 1) & 2):
Since AX > BX and X < 0, we have A < B by dividing both sides by X.

Since ‘no’ is also a unique answer by CMT (Common Mistake Type) 1, both conditions are sufficient, when used together.

Since this question is a statistics question (one of the key question areas), CMT (Common Mistake Type) 4(A) of the VA (Variable Approach) method tells us that we should also check answers A and B.

Condition 1):
A = 2, B = 1, X = 1: The answer is Yes.
A = -2, B = -1, X = -1: The answer is No.

The condition 1) is not sufficient, since the answer is not unique.

Condition 2):
Since we don't have information about A and B, the condition 2) is not sufficient.

Therefore the answer is C.

In cases where 3 or more additional equations are required, such as for original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, conditions 1) and 2) usually supply only one additional equation. Therefore, there is an 80% chance that E is the answer, a 15% chance that C is the answer, and a 5% chance that the answer is A, B or D. Since E (i.e. conditions 1) & 2) are NOT sufficient, when taken together) is most likely to be the answer, it is generally most efficient to begin by checking the sufficiency of conditions 1) and 2), when taken together. Obviously, there may be occasions on which the answer is A, B, C or D.

energetics · Answer

Yes/No Question: is a>b?

(1) ax>bx
Test values:
If a=4 and b=2 and x = 1, then 4>2 and 4>2 yes
If a=2 and b=4 and x = -1, then -2>4 and 2>4, no
Insufficient

(2) x < 0, no info about a or b, Insufficient.

(3) If x < 0 then we get No as in statement 1
Logically, whenever we compare 2 negative numbers, the one closer to 0 is greater. This is reversed when we compare their positive equivalents since now the answer farther from 0 is greater. So the answer is No, sufficient.

Is A > B? (1) AX > BX (2) X < 0

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