What is the greatest positive integer that divides 554 714 and 213 leaving the remainder 43 57 and 6...........

Quantitative Aptitude (CPO) Number System

What is the greatest positive integer that divides 554, 714 and 213 leaving the remainder 43, 57 and 67, respectively?

This questions was previously asked in

SSC CPO 10th Nov 2022 Shift 2

Let’s break this problem down:

- The number we’re looking for should divide these: (554?-?43), (714?-?57), and (213?-?67), which gives us 511, 657, and 146.

- In other words, the greatest common divisor (GCD) of 511, 657, and 146.

- Here’s how the options stack up:

- Option 1 — 95: 511 ÷ 95 = 5.378..., so not a divisor.

- Option 2 — 71: 511 ÷ 71 = 7.197..., nope.

- Option 3 — 83: 511 ÷ 83 = 6.15..., not clean.

- Option 4 — 73: 511 ÷ 73 = 7, 657 ÷ 73 = 9, 146 ÷ 73 = 2. All perfect divisors.

- 73 is the biggest positive integer that fits the rule.

The correct answer is: Option 4 — 73.

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