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In how many ways can 141 be divided into two parts such that one part 03 Jan 2021, 15:57
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C
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55% (hard)

Question Stats:

60% (02:18) correct 40% (02:43) wrong based on 144 sessions

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In how many ways can 141 be divided into two parts such that one part is divisible by 5 and the remaining part is divisible by 9?

A. 1
B. 2
C. 3
D. 4
E. 5
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C
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In how many ways can 141 be divided into two parts such that one part 03 Jan 2021, 16:07
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There are only 3 ways in which first number is divisible by 5 and second part is divisble by 9

(105,36), (60,81) and (15,126)

Ans C
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In how many ways can 141 be divided into two parts such that one part 03 Jan 2021, 16:08
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Since 5 and 9 are co prime numbers, their LCM is 5 x 9 = 45. Since 141 can be divided by 45 3 times (45 x 3 = 135, which is less than 141), so 141 can be split into two such numbers in 3 ways.

The numbers are -
15 + 127 = 141
60 + 81 = 141
105 + 36 = 141

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In how many ways can 141 be divided into two parts such that one part 03 Jan 2021, 22:44
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Given, 5*x +9*y= 141
So, LCM (5,9) = 45 and 141/45~ So, we will have 3 to 4 solutions of the equation.

Trail and error= (x,y) = (3,14), then the other solutions by compensating x and y coefficient (12,9) or (21,4)

So, We have 3 solutions. I think C. :)
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In how many ways can 141 be divided into two parts such that one part 14 Jun 2024, 00:57
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5x+9y=141.
5x=141-9y

This is a multiple of 5 if last digit is either 0 or 5.

Only option is 141- x1 or 141 -x6

=> 9x9 gives 81 , 9x4 & 9x14 gives 6 as last digit,

Hence 3 values

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