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21 Apr 2021, 07:15
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Difficulty:
35%
(medium)
Question Stats:
70% (01:54) correct
30%
(01:52)
wrong
based on 87
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What is the largest five-digit number which is divisible by 17?
(A) 99,999
(B) 99,994
(C) 99,993
(D) 99,992
(E) 99,991
(A) 99,999
(B) 99,994
(C) 99,993
(D) 99,992
(E) 99,991
belagavi
Joined: 15 Feb 2021
Last visit: 25 May 2024
Posts: 95
Given Kudos: 58
Schools: Kenan-Flagler '26 (II) Broad'26 (WL)
02 May 2021, 21:45
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I solved it this way. I picked one of the numbers i.e. 99991 and divided it by 17. I got a remainder of 14, this means 99991 falls short of being a multiple of 17 by 3 because (17-14 = 3). Simply add 3 to 99991 to get 99994 which is the largest five digit multiple of 17.
03 May 2021, 00:32
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Let's break the five-digit numbers into multiples of 17 and consider 99,999 is divisible by 17.
Since we need five - digits: 5000 * 17 = 85,000. [As 6 * 17 = 102]
We are 99,999 - 85,000 = 14,999 short.Closest number here will be 17 * 8 = 136.
=> 17 * 800 = 13,600
=> Now we are short of 14,999 - 13,600 = 1,399.Closest number here will be 17 * 8 = 136
=> 17 * 80 = 1,360
=> Now we are short of 1,399-1,360= 39.Closest number to 39 divisible by 17 is 34.
We have an excess of 5 and hence, 99,999 - 5 = 99,994 is the largest number divisive by 17.
Answer B
Since we need five - digits: 5000 * 17 = 85,000. [As 6 * 17 = 102]
We are 99,999 - 85,000 = 14,999 short.Closest number here will be 17 * 8 = 136.
=> 17 * 800 = 13,600
=> Now we are short of 14,999 - 13,600 = 1,399.Closest number here will be 17 * 8 = 136
=> 17 * 80 = 1,360
=> Now we are short of 1,399-1,360= 39.Closest number to 39 divisible by 17 is 34.
We have an excess of 5 and hence, 99,999 - 5 = 99,994 is the largest number divisive by 17.
Answer B
