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What is the smallest number which when increased by 3 is divisible by
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01 Dec 2015, 04:36
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What is the smallest number which when increased by 3 is divisible by 27, 35, 25 and 21?
(A) 3272
(B) 3572
(C) 4122
(D) 4722
(E) 4922
(A) 3272
(B) 3572
(C) 4122
(D) 4722
(E) 4922
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Re: What is the smallest number which when increased by 3 is divisible by
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01 Dec 2015, 05:47
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Prime factorization of numbers
27 = 3^3
35 = 5*7
25 = 5^2
21 = 3*7
Smallest number divisble by above 4 numbers will be LCM = 3^3 * 5^2 * 7 = 4725
Now , the number we need is 3 less than 4725 , therefore the number is 4722
Answer D
27 = 3^3
35 = 5*7
25 = 5^2
21 = 3*7
Smallest number divisble by above 4 numbers will be LCM = 3^3 * 5^2 * 7 = 4725
Now , the number we need is 3 less than 4725 , therefore the number is 4722
Answer D
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Re: What is the smallest number which when increased by 3 is divisible by
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01 Dec 2015, 12:21
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The problem can be reduced if we add 3 to the answer options and check divisibility rule of 3 ( Since 27 is a multiple of 3)
I am deliberately not involving in checking the divisibility rule for 5 and 7 since all the answer options have units digit as 5 and divisibility by 7 is a cumbersome 3 step process, where as divisibility by 3 is simply the sum of all the digits of the number.
(A) 3272 -> 3272+3 = 3275 Sum of the digits is 17 which is not divisible by 3.
(B) 3572 -> 3572+3 = 3575 Sum of the digits is 20 which is not divisible by 3.
(C) 4122 -> 4122+3 = 4125 Sum of the digits is 12 which is divisible by 3 { Keep this option for now }
(D) 4722 -> 4722+3 = 4725 Sum of the digits is 18 which is divisible by 3 { Keep this option for now }
(E) 4922 -> 4922+3 = 4925 Sum of the digits is 20 which is not divisible by 3
Now check options (C) and (D)
C) 4125 / 27 = Not completely divisible , so this is not the answer.
D) 4725 / 27 = 175 Completely divisible , so this is our answer.
I am deliberately not involving in checking the divisibility rule for 5 and 7 since all the answer options have units digit as 5 and divisibility by 7 is a cumbersome 3 step process, where as divisibility by 3 is simply the sum of all the digits of the number.
(A) 3272 -> 3272+3 = 3275 Sum of the digits is 17 which is not divisible by 3.
(B) 3572 -> 3572+3 = 3575 Sum of the digits is 20 which is not divisible by 3.
(C) 4122 -> 4122+3 = 4125 Sum of the digits is 12 which is divisible by 3 { Keep this option for now }
(D) 4722 -> 4722+3 = 4725 Sum of the digits is 18 which is divisible by 3 { Keep this option for now }
(E) 4922 -> 4922+3 = 4925 Sum of the digits is 20 which is not divisible by 3
Now check options (C) and (D)
C) 4125 / 27 = Not completely divisible , so this is not the answer.
D) 4725 / 27 = 175 Completely divisible , so this is our answer.