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SSC CGL 2022 PYQ — Question 70

SSC CGL - 02 Dec 2022 - Shift 4 • Quantitative Aptitude • Q70

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Which of the following statement is correct?

  1. The value of 1002 - 992 + 982 - 972 + 962 - 952 + 942 - 932..........+ 22 - 12 is 5050
  2. If 8X + 8/X = -16 and X<0, then the value of X197 + X-197 is 2.

Show answer & explanation

Correct answer: A

Explanation

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

Explanation:

For statement I: 1002 - 992 + 982 - 972 + 962 - 952 + 942 - 932..........+ 22 - 12 

⇒ (1002 - 992) + (982 - 972) +......+(22 - 12)

⇒ (100 + 99)(100 - 99) + (98 +97)(98 - 97) + (96 + 95)(96 - 95) + .....+ (2 +1)(2 - 1)

⇒ 100 + 99 + 98 + 97 + 96 + 95 + ......+ 2 + 1

Now, we know that the sum of first 'n' ntural numbers is n(n+1)2n(n + 1) \over 2

⇒ 100(100+1)2100(100 + 1) \over 2 = 50 × 101 = 5050.

So, statement I is correct.

For statement II: 8X+8X=−168X + {8\over X }= -16

Dividing whole equationby 8, we get

⇒ X+1X=−2X + {1 \over X} = -2

Now, putting X = -1, equation is satisfied.

Hence putting X = -1 in X197 + X-197, we get

⇒ (-1)197 + (-1)-197 = -2 

Hence Statement II is incorrect.