If x y, then which of the following could be true?

Question

If  x > y , then which of the following could be true?

I.  |x|*|y|*x < |x*y|*y 
II.  |x|*|y|*x > |x*y|*y 
III.  |x|*|y|*x = −|x*y|*y

(A) I only
(B) II only
(C) III only
(D) I and II only
(E) II and III only

av1901 · Answer

For could be true, we only need to find one true condition and that is enough to state that this statement could be true If x>y, it can imply the following conditions (valid for both integers as well as for fractions): i) x and y both are negative ii) x and y both are positive iii) x is positive and y is negative I. |x|*|y|*x < |x*y|*y We can already see that if both x and y are the same sign and integers then this will obviously never satisfy because x > y and there are 2 (x) on the left and 1 on the right. We can see for fractions and see if it works out If x=1/2 and y=1/4 then we get 1/16 < 1/32 which is FALSE If x=-1/2 and y=-1/4 then we get -1/32 < -1/16 which is also FALSE If x=1/2 and y=-1/2 then we get Positive < Negative which is also FALSE So, this statement cannot be true II. |x|*|y|*x > |x*y|*y This is reverse of the previous statement, and since that gave false for all, we can take any one example from that and it will give true If x=1/2 and y=1/4 then we get 1/16 < 1/32 which is TRUE So, this statement can be true III. |x|*|y|*x = −|x*y|*y Since there is equal to sign, we need to try equal absolute values and let us try x as positive and y as negative because there is a negative sign involved in the RHS of the equation If x=1/2 and y=-1/2 then we get 1/8 = -(1/4)*(-1/2) which is TRUE So, this statement can be true So, II and III can be true Answer - E

SaquibHGMATWhiz · Answer

Solution:

We are given  x>y

I.  |x|*|y|*x < |x*y|*y 
  Multiplying  |x*y|  or  |x|*|y|  on both sides of  x>y , we will get  |x|*|y|*x > |x*y|*y  
 Thus, this inequality is never true

II.  |x|*|y|*x > |x*y|*y 
  We have already analyzed above that this inequality is true

III.  |x|*|y|*x = −|x*y|*y 
  Let us assume x = 2 and y = -2 
 Then this equation is true

Hence the right answer is    Option E

glagad · Answer

I solved this problem using a property of Modulus - |x| * |y| = |x * y| (you can try to proof this with some numbers)

Given - x>y

St 1 - |x|∗|y|∗x<|x∗y|∗y
>> Eliminate |x*y| from both the sides ( know that |x * y| > 0 and thus can be eliminated in this inequality safely)
>> We get x < y
However, we know that its not given and goes against the given constraint
Hence St 1 Cant be true.

St 2 - |x|∗|y|∗x>|x∗y|∗y
>> Eliminate |x*y| from both the sides
>> We get x > y
Aligns with given constraint in the question
Hence St 2 can be true.

St3 => |x|∗|y|∗x=−|x∗y|∗y

>> |x|∗|y|∗x + |x∗y|∗y = 0
>> |x*y| * (x+y) = 0

>> x or y =0 OR x +y = 0, x > -y
Both of these conditions are possible based on the constraint given in the questions
Hence St 3 Cant be true.

Hence I & III

If x > y, then which of the following could be true?

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

GMAT Problem Solving (PS) Questions