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16 Sep 2014, 01:28
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If \(x^4 = 29x^2 - 100\), then which of the following is NOT a product of three possible values of \(x\)?
I. -50
II. 25
III. 50
A. \(I\) only
B. \(II\) only
C. \(III\) only
D. \(I\) and \(II\) only
E. \(I\) and \(III\) only
I. -50
II. 25
III. 50
A. \(I\) only
B. \(II\) only
C. \(III\) only
D. \(I\) and \(II\) only
E. \(I\) and \(III\) only
RenanBragion
GMAT 1: 760 Q48 V46
Posts: 130
Updated on: 02 Apr 2025, 16:56
Originally posted by RenanBragion on 12 Jun 2020, 03:50.
Last edited by RenanBragion on 02 Apr 2025, 16:56, edited 2 times in total.
Last edited by RenanBragion on 02 Apr 2025, 16:56, edited 2 times in total.
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Great question
An alternative approach:
\(x^4 - 29x^2 + 100 = 0\)
Create a variable \( y = x^2 \)
\(x^4 - 29x^2 + 100 \)
\(y^2-29y+100 = 0\)
y = 25 or y = 4
Substitute the values of y in the equation \( y = x^2 \)
Find X:
If y = 25 then x = 5 or x = -5
If y = 4 then x = 2 or x = -2
An alternative approach:
\(x^4 - 29x^2 + 100 = 0\)
Create a variable \( y = x^2 \)
\(x^4 - 29x^2 + 100 \)
\(y^2-29y+100 = 0\)
y = 25 or y = 4
Substitute the values of y in the equation \( y = x^2 \)
Find X:
If y = 25 then x = 5 or x = -5
If y = 4 then x = 2 or x = -2
General Discussion
16 Sep 2014, 01:28
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Bookmarks
Official Solution:
If \(x^4 = 29x^2 - 100\), then which of the following is NOT a product of three possible values of \(x\)?
I. -50
II. 25
III. 50
A. \(I\) only
B. \(II\) only
C. \(III\) only
D. \(I\) and \(II\) only
E. \(I\) and \(III\) only
Rearrange and factor for \(x^2\): \((x^2-25)(x^2-4)=0\).
Thus, we find that \(x=5\), \(x=-5\), \(x=2\), or \(x=-2\).
For the given options:
I. \(-50 = 5*(-5)*2\);
III. \(50 = 5*(-5)*(-2)\);
However, 25 cannot be expressed as a product of three of these values. Thus, only 25 is NOT a product of three possible values of \(x\).
Answer: B
If \(x^4 = 29x^2 - 100\), then which of the following is NOT a product of three possible values of \(x\)?
I. -50
II. 25
III. 50
A. \(I\) only
B. \(II\) only
C. \(III\) only
D. \(I\) and \(II\) only
E. \(I\) and \(III\) only
Rearrange and factor for \(x^2\): \((x^2-25)(x^2-4)=0\).
Thus, we find that \(x=5\), \(x=-5\), \(x=2\), or \(x=-2\).
For the given options:
I. \(-50 = 5*(-5)*2\);
III. \(50 = 5*(-5)*(-2)\);
However, 25 cannot be expressed as a product of three of these values. Thus, only 25 is NOT a product of three possible values of \(x\).
Answer: B
