Two wires of lengths 10 m 54 cm and 11 m 56 cm are both cut into pieces of length x cm each where x ...........

Quantitative Aptitude (MTS) LCM, HCF

Two wires of lengths 10 m 54 cm and 11 m 56 cm are both cut into pieces of length x cm each, where x is an integer. Find the

maximum value of x.

This questions was previously asked in

SSC MTS 21st July 2022 Shift-3

Let's solve the problem step by step:

- First, convert lengths to cm:

- 10 m 54 cm = 1054 cm

- 11 m 56 cm = 1156 cm

- Both wires are cut into pieces of length x cm (x is an integer), so x must divide both 1054 and 1156 exactly.

- We need the greatest possible value of x = HCF (Highest Common Factor) of 1054 and 1156

- Find the HCF:

- 1156 - 1054 = 102

- 1054 ÷ 102 = 10 remainder 34

- 102 ÷ 34 = 3 remainder 0

(So, HCF = 34)

- Let's check options:

- 1, 42: 42 does not divide 1054 or 1156 exactly.

- 2, 56: 56 does not divide 1054 or 1156 exactly.

- 3, 34: 34 divides both 1054 and 1156 exactly!

- 4, 28: 28 does not divide 1054 or 1156 exactly.

- The correct answer is Option 3, 34.

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