HCF and LCM – Railway Maths

Total Questions: 50

31. The LCM and the HCF of two numbers, x and y, are 286 and 2, respectively. If the sum of these two numbers is 48, then the value of 1/x + 1/y is: [Group D 06/10/2022 (Evening)]

Correct Answer: (d) 12/143
Solution:

LCM of x and y = 286
HCF of x and y = 2
We know,
Product of two numbers = HCF × LCM
xy = 286 × 2 ⇒ xy = 572
1/x + 1/y = (x + y) / xy = 48 / 572 = 12 / 143

32. K is the product of the greatest and the smallest of the numbers [NTPC CBT II Level 6 (09/05/2022) Shift 1]

Correct Answer: (b) 27
Solution:

1/4 , 2/3 , 4/5 , 5/8 , 3/4
Taking the L.C.M of denominator

[4, 3, 5, 8, 4] = 120

¼ × 120, ⅔ × 120, ⁴⁄₅ × 120, ⁵⁄₈ × 120, ¾ × 120

30, 80, 96, 75, 90
From the above result we can see that 30 is the smallest and 96 is the largest number.
So, ¼ is the smallest number and ⁴⁄₅ is the largest number.
So the product of the numbers is,

¼ × ⁴⁄₅ = ¹⁄₅

Now the value of (¹/ₖ + 4)(¹/ₖ − 2) = (5 + 4)(5 − 2) = 9 × 3 = 27

33. In a school there are 360, 520 and 280 students in classes 5, 6, and 7 respectively. Buses are to be hired to take these students for a trip. Find the maximum number of students who can be accommodated in each bus if each bus must take the same number of students, and each bus should have students from the same class. [NTPC CBT II Level 6 (09/05/2022) Shift 2]

Correct Answer: (b) 40
Solution:

Required number = HCF (360, 520, 280) ⇒ 40

34. If x = 2³ × 3² × 5 × 7³, y = 2² × 3³ × 5² × 7², and z = 2⁴ × 3 × 5³ × 7, Then the HCF of x, y and z is: [NTPC CBT II Level 3 (14/06/2022) Shift 1]

Correct Answer: (a) 420
Solution:

x = 2³ × 3² × 5 × 7³
y = 2² × 3³ × 5² × 7²
z = 2⁴ × 3 × 5³ × 7
HCF = 2² × 3 × 5 × 7 = 420

35. In a school, the number of students in Grades 6, 7 and 8 was 184, 276, and 322, respectively. Students in each grade were divided into different sections, but every section across grades had the same number of students. For each section, a class teacher was appointed. What was the minimum number of class teachers required for the purpose? [NTPC CBT II Level 5 (15/06/2022) Shift 1]

Correct Answer: (d) 17
Solution:

Grade 6 = 184
Grade 7 = 276
Grade 8 = 322
HCF of 184, 276 and 322 = 46
Minimum number of class teacher
= 184/46 + 276/46 + 322/46 = 17

36. Find the HCF of (a – b)(a + 2b), (a² – b²)(a + 2b), (a + b), (a² – b²), where a > b > 0 [NTPC CBT II Level 3 (17/06/2022) Shift 1]

Correct Answer: (d) a – b
Solution:

(a − b)(a + 2b), (a² − b²)(a + 2b), (a + b)(a² − b²)
(a − b) is common in all, hence,
H.C.F is (a − b)

37. When 4230, 5986 and 9059 are divided by the greatest number m, the remainder in each case is n. What is the value of (m – n)? [NTPC CBT II Level 3 (17/06/2022) Shift 2]

Correct Answer: (a) 160
Solution:

5986 − 4230 = 1756
9059 − 4230 = 4829
9059 − 5986 = 3073
H.C.F of 1756, 4829 and 3073 = 439 (that is m)
So, on dividing 4230, 5986 and 9059 by 439 we get, 279 (that is n) as remainder.
Now, m − n = 439 − 279 = 160

38. The smallest square number which is exactly divisible by 12, 15 and 18 is [NTPC CBT – I (28/12/2020) (Evening)]

Correct Answer: (c) 900
Solution:

The LCM of 12, 15 and 18 is = 180 (2² × 3² × 5)
The smallest square number which is exactly divisible by 12, 15 and 18 is
= 180 × 5 = 900

39. 24 mango trees, 56 apple trees and 72 orange trees have to be planted in rows such that each row contains the same number of trees of one variety only. Find the minimum number of rows in which the above mentioned trees may be planted? [NTPC CBT – I (04/01/2021) (Evening)]

Correct Answer: (a) 19
Solution:

HCF of (24, 56, 72) = 8
Total number of trees = 24 + 56 + 72 = 152
Number of rows = 152 / 8 = 19

40. Find the HCF of 2/3, 4/9, 8/15, 10/21 [NTPC CBT - I 11/01/2021 (Morning)]

Correct Answer: (b) 2/315
Solution: