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SSC CGL 2024 PYQ — Question 53

SSC CGL - 19 Sep 2024 - Shift 3 • Quantitative Aptitude • Q53

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Simplify (25)4+1250+1−(25)2(25)2+25+1(25)^4+1250+1−(25)^2\over (25)^2+25+1.

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Correct answer: B

Explanation

The correct answer is option 2 i.e. 601.

 (25)4+1250+1−(25)2(25)2+25+1(25)^4+1250+1−(25)^2\over (25)^2+25+1=(25)4+2(25)2+1−(25)2(25)2+25+1={(25)^4+2(25)^2+1−(25)^2\over (25)^2+25+1}

=(25)4+(25)2+1(25)2+25+1={(25)^4+(25)^2+1\over (25)^2+25+1}=(252+25+1)(252−25+1)(252+25+1)=\frac{\left(25^2+25+1\right)\left(25^2-25+1\right)}{\left(25^2+25+1\right)}   

[∵ a4 + a2 + 1 = (a2 + a + 1)(a2 - a + 1)]

= 252 - 25 + 1 = 625 - 25 + 1 = 601