Quantitative Reasoning

Number System

Medium

Find the length of the longest rod which can be used to measure exactly the lengths 5 m 13 cm, 11 m 34 cm and 12 m 15 cm.

11 cm

9 cm

1 m 3 cm

27 cm

✅ Correct Option: 4

Convert all lengths to cm: 513, 1134, 1215. Longest rod that measures all exactly is their HCF. $513 = 3^3 \times 19$ , $1134 = 2 \times 3^4 \times 7$ , $1215 = 3^5 \times 5$ . Common factor is $3^3 = 27$ . So HCF = 27 cm.

2022: 20 Aug Shift 1

$296 \times 296 - 204 \times 204 = ?$

2026: 22 May Shift 2

Match List-I with List-II

List-I (Statements/Expressions etc.)	List-II (Values, etc.)
(A) Find the sum of the first 20 odd natural numbers.	(I) 285
(B) How many prime numbers are there between 100 and 200?	(II) 0
(C) Find the sum of the squares of the digits from 1 to 9.	(III) 400
(D) Find the unit's digit in the product $81 \times 82 \times 83 \times ... ... ... \times 89$ ?	(IV) 21

Choose the correct answer from the options given below:

2025: 15 May Shift 1

Which of the following is/are prime numbers?

(A) 241

(B) 337

(D) 571

Choose the correct answer from the options given below:

2025: 27 May Shift 1

Match List-I with List-II

List-I	List-II
(A) Remainder when $17^{35234}$ is divided by 8	(I) 0
(B) Remainder when 4444 is divided by 9	(II) 1
(C) Unit's digit of $(34)^{15} + (34)^{16}$	(III) 2
(D) Unit digit of $7^4 - 9^3$	(IV) 7

Choose the correct answer from the options given below:

2026: 21 May Shift 2

In number system 3√2, is?

2025: 19 May Shift 2

The sum of all prime numbers less than 20 is:

Find the length of the longest rod which can be used to measure exactly the lengths 5 m 13 cm, 11 m 34 cm and 12 m 15 cm.

Solution

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