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02 Nov 2017, 02:52
Kudos
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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:
65%
(hard)
Question Stats:
61% (02:33) correct
39%
(02:17)
wrong
based on 271
sessions
History
Date
Time
Result
Not Attempted Yet
Let *y be the operation given by *y = 4/y – y. Which of the following statements are true?
I. If 0 < y, then *y is negative.
II. If 0 < y < z, then *y > *z.
III. If 0 < y then y(*y) is less than 5.
(A) I only
(B) II only
(C) III only
(D) II and III
(E) I, II, and III
I. If 0 < y, then *y is negative.
II. If 0 < y < z, then *y > *z.
III. If 0 < y then y(*y) is less than 5.
(A) I only
(B) II only
(C) III only
(D) II and III
(E) I, II, and III
Luckisnoexcuse
Current Student
Joined: 18 Aug 2016
Last visit: 31 Mar 2026
Posts: 513
Given Kudos: 198
Concentration: Strategy, Technology
Schools: Kenan-Flagler '20 (M)
GMAT 1: 630 Q47 V29
GMAT 2: 740 Q51 V38
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02 Nov 2017, 04:30
Kudos
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Bunuel
I) let y=2 then *y = 2-2=0...not true
II) let y = 2 and z = 4 then *y=0 and *z=-3; let y=1/50 and z = 1 then *y=~200 and *z=3...true (any value above 4 gives negative *y)
III) let y=1 then y(*y)=3; y=1/50 then y(*y) =~4; y=100 then y*y is -ve....true
D
05 Nov 2017, 08:22
Kudos
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Bunuel
Let’s analyze each answer choice:
I. If 0 < y, then *y is negative.
We can let y = 1, and we have:
*1 = 4/1 - 1 = 4 - 1 = 3
We see that I is not true since *1 is not negative.
II. If 0 < y < z, then *y > *z.
We can let y = 1 and z = 2. Recall that *1 = 3 and:
*2 = 4/2 - 2 = 0
We see that *1 is greater than *2. However, let’s prove the statement algebraically.
We are given that y < z, so we have:
1/y > 1/z (recall that when we reciprocate two positive quantities, we switch the inequality sign)
and
-y > -z (recall that when we multiply two quantities by a negative number, we switch the inequality sign)
Multiplying the first inequality by 4 and adding the result to the second inequality, we have:
4/y - y > 4/z - z
*y > *z
This proves that II is true.
III. If 0 < y, then y(*y) is less than 5.
Notice that y(*y) = y(4/y - y) = 4 - y^2. Since y^2 is a nonnegative quantity, 4 - y^2 will be no more than 4, which means it’s always less than 5. So III is true.
Answer: D
