If x is positive and y is 1 more than the square of x, then

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pm; Followed by:23 members

If x is positive and y is 1 more than the square of x, then

by BTGmoderatorDC » Thu Oct 11, 2018 7:11 pm

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If x is positive and y is 1 more than the square of x, then what is the value of x in terms of y?

$$A.\ y^2\ -\ 1$$
$$B.\ y^2\ +\ 1$$
$$C.\ \sqrt{y}-\ 1$$
$$D.\ \sqrt{y\ -\ 1}$$
$$E.\ \sqrt{y\ +\ 1}$$

OA D

Source: Princeton Review

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Source: Beat The GMAT — Problem Solving | Thu Oct 11, 2018 7:11 pm

Byjus: Newbie | Next Rank: 10 Posts; Posts: 9; Joined: Fri Aug 17, 2018 10:11 pm

answer

by Byjus » Fri Oct 12, 2018 1:41 am

Hi,

It's a straight forward question.

Given,

x is positive and y = x^2 + 1

y = x^2 +1

x^2 = y-1

x = sqrt(y-1)

So the answer is D.

OR

We can try numbers too.

If x = 1 then y = 2.

When we substitute y = 2 in the answer choices we should get "x" value as 1.

A. y^2 - 1 = 4 - 1 = 3. Eliminate.

B. y^2 + 1 = 4 + 1 = 5. Eliminate.

C. âˆš(y)âˆ’ 1 = âˆš2 - 1 = not an integer. Eliminate.

D. âˆš(y - 1) = âˆš(2 - 1) = 1. Hold on.

E. âˆš(y + 1) = âˆš(2 + 1) = 3. Eliminate.

So the answer is D.

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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 » Thu Oct 18, 2018 5:17 pm

BTGmoderatorDC wrote:If x is positive and y is 1 more than the square of x, then what is the value of x in terms of y?

$$A.\ y^2\ -\ 1$$
$$B.\ y^2\ +\ 1$$
$$C.\ \sqrt{y}-\ 1$$
$$D.\ \sqrt{y\ -\ 1}$$
$$E.\ \sqrt{y\ +\ 1}$$

We can create the equation:

y = 1 + x^2

y - 1 = x^2

âˆš(y - 1) = x

Answer: D

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