If (x^2+1)y=3, which of the following is not...

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BTGmoderatorLU: Moderator; Posts: 2505; Joined: Sun Oct 15, 2017 1:50 pm; Followed by:6 members

If (x^2+1)y=3, which of the following is not...

by BTGmoderatorLU » Wed Nov 22, 2017 2:27 pm

If (x^2+1)y=3, which of the following is not a possible value for y?

A. 3/2
B. 2
C. 8/3
D. 3
E. 7/2

The OA is E.

I'm confused with this PS question. Please, can any expert assist me with it? Thanks in advanced.

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Source: Beat The GMAT — Problem Solving | Wed Nov 22, 2017 2:27 pm

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Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 am; Location: Grand Central / New York; Thanked: 470 times; Followed by:34 members

by Jay@ManhattanReview » Wed Nov 22, 2017 8:29 pm

LUANDATO wrote:If (x^2+1)y=3, which of the following is not a possible value for y?

A. 3/2
B. 2
C. 8/3
D. 3
E. 7/2

The OA is E.

I'm confused with this PS question. Please, can any expert assist me with it? Thanks in advanced.

We have y(x^2 + 1) = 3

=> x^2 + 1 = 3/y => x^2 = 3/y - 1 => x = âˆš(3/y - 1)

x = âˆš[(3 - y)/y]

Since x is a real number, y must be less than equal to 3, else (3 - y) would be a negative number and x would then be an imaginary number.

Thus, any value greater than 3 is not qualified for y. The correct answer is 7/2 = 3.5.

The correct answer: E

Hope this helps!

-Jay
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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Sat Oct 12, 2019 4:01 pm

BTGmoderatorLU wrote:If (x^2+1)y=3, which of the following is not a possible value for y?

A. 3/2
B. 2
C. 8/3
D. 3
E. 7/2

The OA is E.

I'm confused with this PS question. Please, can any expert assist me with it? Thanks in advanced.

We are given that (x^2 + 1)y = 3.

Since x^2 is always nonnegative, we see that x^2 + 1 must always be greater than or equal to 1. Thus, in order for the product of a number greater than or equal to 1 and y to be 3, y has to be less than or equal to 3. Thus, y cannot equal 7/2.

Answer: E

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