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SSC CGL 2024 PYQ — Question 66

SSC CGL - 23 Sep 2024 - Shift 3 • Quantitative Aptitude • Q66

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If 3x + 2y = 10 and 2xy = 7, then find the value of 3x - 2y. (if 3x - 2y > 0)

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Correct answer: A

Explanation

The correct answer is option 1 i.e. 4.

2xy = 7

⇒ xy = 7/2   .....(1)

3x + 2y = 10

⇒ (3x + 2y)2 = 102 = 100

⇒ 9x2 + 12xy + 4y2 = 100   .....(2)

Now, (3x - 2y)2 = 9x2 - 12xy + 4y2

⇒ (3x - 2y)2 = (9x2 + 12xy + 4y2) - 24xy

⇒ (3x - 2y)2 = 100 - 24(7/2) = 100 - 84 = 16

⇒ 3x - 2y = √16 = 4

Therefore, the required value is 4.