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06 Jul 2022, 01:30
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
63% (02:17) correct
37%
(02:11)
wrong
based on 46
sessions
History
Date
Time
Result
Not Attempted Yet
x units of Product A costs y dollars.
y units of Product B costs x dollars.
Which product A or B costs more?
(1) \(x^2 + 1 > y^2\)
(2) \(x^2 > y^2 + 1\)
Are You Up For the Challenge: 700 Level Questions
y units of Product B costs x dollars.
Which product A or B costs more?
(1) \(x^2 + 1 > y^2\)
(2) \(x^2 > y^2 + 1\)
Are You Up For the Challenge: 700 Level Questions
06 Jul 2022, 02:09
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Pre-thinking
Though not explicitly stated, "Which product A or B costs more" means “Which product A or B costs more per unit".
Also x>0 and y>0. (Only later did I realize that x and y must be integers as well.)
Unit price for A: y/x
Unit price for B: x/y
If we can definitely tell that x>y or x<y, we can definitely answer the question.
(1)Only
x^2>y^2-1
It is possible that x>y. (For example, x=3, y=2)
But it is also possible that x=y. (For example, x=y=3)
(2)Only
x^2>y^2+1
We can certainly tell that x>y
Sufficient
The answer is thus (B).
Though not explicitly stated, "Which product A or B costs more" means “Which product A or B costs more per unit".
Also x>0 and y>0. (Only later did I realize that x and y must be integers as well.)
Unit price for A: y/x
Unit price for B: x/y
If we can definitely tell that x>y or x<y, we can definitely answer the question.
(1)Only
x^2>y^2-1
It is possible that x>y. (For example, x=3, y=2)
But it is also possible that x=y. (For example, x=y=3)
(2)Only
x^2>y^2+1
We can certainly tell that x>y
Sufficient
The answer is thus (B).
Sushil117
Joined: 04 Mar 2020
Last visit: 13 Nov 2023
Posts: 256
Given Kudos: 100
Location: India
Schools: Smith Ivey Alberta '23 HEC Montreal Rotman '23
GPA: 3.3
06 Jul 2022, 12:27
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(1) x^2+1>y^2
1> (y+x)(y-x)
(y+x) is +ve . (y-x) can 0,-1,-2....
insufficient to determine if x>= y
(2) x2>y2+1
(x-y)(y+x)>1
can only happen if x>y
sufficient
IMO B
1> (y+x)(y-x)
(y+x) is +ve . (y-x) can 0,-1,-2....
insufficient to determine if x>= y
(2) x2>y2+1
(x-y)(y+x)>1
can only happen if x>y
sufficient
IMO B
