A man has four copper rods whose lengths are 52 m, 65 m, 78 m, 91 m, respectivel

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Question
A man has four copper rods whose lengths are 52 m, 65 m, 78 m, 91 m, respectively. This man wants to cut pieces of same length from each of four rods. what is the least number of total pieces if he is to cut without any wastage?
Options
A. 23
B. 24
C. 22
D. 20

Correct Answer

22

Explanation

The pieces cut from four rods is least, so length of the pieces is the HCF of 52, 65, 78 and 91 which is 13.
? Number of pieces cut =(52 + 65 + 78 + 91)/13 = 22

Problems on H.C.F and L.C.M

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1.
What is the LCM of (x ² - y ² - z ² - 2yz), (x ² - y ² + z ² + 2xz) and (x ² + y ² - z ² - 2xy)?
Options
A. (x + y + z) (x + y - z) (x - y + z)
B. (x + y + z) (x - y - z) (x - y + z)
C. (x + y + z) (x + y - z) (x - y - z)
D. (x + y - z) (x - y - z) (x - y + z)

2.
A, B and C start at the same time in the same direction to run around in 252s, B in 308s and C in 198s, all starting at the same point. After what time will they meet again at the starting point?
Options
A. 26 min and 18s
B. 42 min and 36s
C. 45 min
D. 46 min and 12s

3.
There are five hobby clubs in a college viz. photography, yachting, chess, electronics and gardening. The gardening group meets every second day, the electronics group meets every third day, the chess group meets every fourth day, the yachting group meets every fifth day and the photography group meets every sixth day. How many times do all the five groups meets on the same day within 180 days?
Options
A. 3
B. 5
C. 10
D. 18

4.
Four metal rods of lengths 78 cm, 104 cm, 117 cm and 169 cm are to be cut into parts of equal length. Each part must be as long as possible. What is the maximum number of pieces that can be cut?
Options
A. 27
B. 36
C. 43
D. 480

5.
The traffic lights at three different road crossings changes after every 48 sec., 72 sec. and 108 sec. respectively. If they all change simultaneously at 8 : 20 : 00 hrs, then they will again change simultaneously at?
Options
A. 8 : 27 : 12 hrs.
B. 8 : 27 : 24 hrs.
C. 8 : 27 : 36 hrs.
D. 8 : 27 : 48 hrs.

6.
A, B, and C start at the same time in the same direction to run around a circular stadium. A completes a round in 252s, B in 308s and C in 198s, all starting of the same point. After what time will they meet again at the string point?
Options
A. 26 min and 18s
B. 42 min and 36s
C. 45 min
D. 46 min and 12s

7.
A person has completely put each of three liquids 403 L of petrol, 456 L of diesel and 496 L of mobile oil in in bottles of equal size without mixing any of the above three types of liquids such that each bottle is completely filled. What is the least possible number of bottles required?
Options
A. 34
B. 44
C. 46
D. None of these

8.
30 pineapple trees, 45 orange tree and 60 mango trees have to be planted in rows such that each row contains the same number of trees of one variety only. What is minimum number number of row in which the trees may be planted?
Options
A. 10
B. 15
C. 25
D. 9

9.
If HCF of x ³ - 10m ² + 31x - 30m and x ² - 8mx + 15 is a linear polynomial, then what is the value of m?
Options
A. 2
B. 3
C. 1
D. 4

10.
What is the um of the digits of the least number which when divided by 54 leaves 35 as remainder, when divided by 80 leaves 61 as remainder and when divided by 119 leaves 100 leaves 100 as remainder?
Options
A. 21
B. 19
C. 23
D. 28

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