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13 Jun 2025, 12:03
Kudos
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
(N/A)
Question Stats:
100% (00:31) correct
0% (00:00) wrong based on 1 sessions
History
Date
Time
Result
Not Attempted Yet
Quantity A
(x + 2)(x - 2)
Quantity B
GMAT-Club-Forum-u9u48ywr.png [ 22.9 KiB | Viewed 224 times ]
(x + 2)(x - 2)
Quantity B
Attachment:
GMAT-Club-Forum-u9u48ywr.png [ 22.9 KiB | Viewed 224 times ]
15 Jun 2025, 00:09
Kudos
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Given and to find:
Solution:
Let's simplify Quantity B since that looks a lot more complex:
Finally, we need to compare (x^2 - 4) with -5.
Let's put them side by side with a '?' in between (a placeholder for = or > or <)
Correct Answer: Quantity A is greater.
Shweta Koshija
GMAT, GRE, SAT Coach for 10+ years
- Two quantities (A and B).
- We need to compare the two.
Solution:
Let's simplify Quantity B since that looks a lot more complex:
- Numerator: -5(x^2 - 25)(x - 1)
- -5(x - 5)(x + 5)(x - 1) --- Using the identity of difference of squares.
- Denominator: (x + 5)(x^2 – 6x + 5)
- We can factor x^2 – 6x + 5 into (x – 1)(x – 5)
- So, the denominator becomes (x + 5)(x – 1)(x – 5)
- Thus, Quantity B: –5(x + 5)(x – 5)(x – 1) / (x + 5)(x - 1)(x - 1)
- Canceling out the common factors, we are left with only –5
- So, Quantity B = –5
- Quantity A: (x + 2)(x – 2)
- Again, using the identity of Difference of squares, we have Quantity A = x^2 – 4
Finally, we need to compare (x^2 - 4) with -5.
Let's put them side by side with a '?' in between (a placeholder for = or > or <)
- x^2 - 4 ? - 5
- Adding 4 on both sides, this comparison is equivalent to x^2 ? -1
- Now, we are sure that x^2 is ALWAYS greater than -1.
- So, Quantity A is always greater than Quantity B.
Correct Answer: Quantity A is greater.
Shweta Koshija
GMAT, GRE, SAT Coach for 10+ years
19 Jun 2025, 12:43
Kudos
Bookmarks
OE
Using FOIL, Quantity A can be rewritten as \(x^2 - 4.\) Quantity B needs to be simplified. In the numerator, \(x^2 - 25\) can be factored into \((x + 5)(x - 5).\) In the denominator, \(x^2 - 6x + 5\) can be factored into \((x - 5)(x - 1).\) The fraction can then be simplified by canceling out common factors in the numerator and denominator:
So, Quantity B is equal to -5. Without knowing what x is, it might seem that Quantity A and Quantity B cannot be compared. However, when x is squared, the result cannot be negative. The smallest value it could have is 0. Subtracting 4, the smallest possible value of Quantity A is -4. That means Quantity A must be greater than or equal to -4. Any such number will always be greater than -5, so Quantity A will always be greater than Quantity B, no matter what x is. That makes (A) the correct answer.
Answer: A
GMAT-Club-Forum-xl54r2e7.png [ 49.98 KiB | Viewed 159 times ]
Using FOIL, Quantity A can be rewritten as \(x^2 - 4.\) Quantity B needs to be simplified. In the numerator, \(x^2 - 25\) can be factored into \((x + 5)(x - 5).\) In the denominator, \(x^2 - 6x + 5\) can be factored into \((x - 5)(x - 1).\) The fraction can then be simplified by canceling out common factors in the numerator and denominator:
So, Quantity B is equal to -5. Without knowing what x is, it might seem that Quantity A and Quantity B cannot be compared. However, when x is squared, the result cannot be negative. The smallest value it could have is 0. Subtracting 4, the smallest possible value of Quantity A is -4. That means Quantity A must be greater than or equal to -4. Any such number will always be greater than -5, so Quantity A will always be greater than Quantity B, no matter what x is. That makes (A) the correct answer.
Answer: A
Attachment:
GMAT-Club-Forum-xl54r2e7.png [ 49.98 KiB | Viewed 159 times ]
