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If x, y, and z are positive numbers, is x < y < z ?
(1) xy < yz
(2) xz < yz
(1) xy < yz
(2) xz < yz
1 and 2 are insuff by themselves; but when evaluating C, we have:
x < z
x < y
If we subtract the 2 inequalities, we get 0 < z - y ; or --> y<z
Since we now know how y and z also relate to each other, isn't this info sufficient to answer the question?
Got this from Hacks Challenge Algebra; DS; answer given is E
Please help
x < z
x < y
If we subtract the 2 inequalities, we get 0 < z - y ; or --> y<z
Since we now know how y and z also relate to each other, isn't this info sufficient to answer the question?
Got this from Hacks Challenge Algebra; DS; answer given is E
Please help
16 Apr 2014, 07:26
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brobeedle
If x, y, and z are positive numbers, is x < y < z ?
(1) xy < yz
(2) xz < yz
1 and 2 are insuff by themselves; but when evaluating C, we have:
x < z
x < y
If we subtract the 2 inequalities, we get 0 < z - y ; or --> y<z
Since we now know how y and z also relate to each other, isn't this info sufficient to answer the question?
Got this from Hacks Challenge Algebra; DS; answer given is E
Please help
(1) xy < yz
(2) xz < yz
1 and 2 are insuff by themselves; but when evaluating C, we have:
x < z
x < y
If we subtract the 2 inequalities, we get 0 < z - y ; or --> y<z
Since we now know how y and z also relate to each other, isn't this info sufficient to answer the question?
Got this from Hacks Challenge Algebra; DS; answer given is E
Please help
If x, y, and z are positive numbers, is x < y < z ?
(1) xy < yz. Since y is a positive number we can safely reduce by it: x < z. Not sufficient.
(2) xz < yz. Since z is a positive number we can safely reduce by it: x < y. Not sufficient.
(1)+(2) We know that x is less than both z and y but we don't know whether y < z. Not sufficient.
Answer: E.
The problem with your solution is that we can only subtract inequalities when their signs are in the opposite directions. Thus you cannot subtract x < y from x < z.
Adding/subtracting/multiplying/dividing inequalities: help-with-add-subtract-mult-divid-multiple-inequalities-155290.html
Similar question to practice: if-x-y-and-z-are-positive-numbers-is-x-y-z-166907.html
Hope this helps.
brobeedle
Joined: 01 Aug 2013
Last visit: 15 Feb 2022
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16 Apr 2014, 09:05
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Very helpful, thank you!
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