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Updated on: Wed Nov 30, 2022 11:04 am
Originally posted by manavsaraf001 on Wed Nov 30, 2022 10:59 am.
Last edited by Bunuel on Wed Nov 30, 2022 11:04 am, edited 1 time in total.
Last edited by Bunuel on Wed Nov 30, 2022 11:04 am, edited 1 time in total.
Renamed the topic and edited the question.
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A
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Difficulty:
95%
(hard)
Question Stats:
16% (01:48) correct
84%
(02:24)
wrong
based on 49
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What is the tens digit of N, where N = (177)^322+k ? (k is a positive integer)?
(1) The units digit of N is divisible by 3.
(2) The tens digit of N is divisible by 4.
(1) The units digit of N is divisible by 3.
(2) The tens digit of N is divisible by 4.
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
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Thu Dec 01, 2022 4:28 am
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manavsaraf001
The number is \(177^{(322+k)}\)
Of course, knowing tens digit would require a pattern in last 2 digits or division by 100, so let us check.
\(7^1=07\)…..last two digits 07
\(7^2=49\)…..last two digits 49
\(7^3=343\)…..last two digits 43
\(7^4=2401\)…..last two digits 01
Next would be 2401*7, that is 07, and the pattern is formed.
Pattern is 07, 49, 43, 01, 07……
Only possibility of tens digit is 4 or 0.
(1) The units digit of N is divisible by 3.
Units digit are 7,9,3,1, out of which 9 and 3 are multiples of 3.
Possibilities: 49 or 43.
So, the tens digit has to be 4 in each case.
Sufficient
(2) The tens digit of N is divisible by 4.
Both 0 and 4 are divisible by 4.
Insufficient
A
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