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RenB
Joined: 13 Jul 2022
Last visit: 02 Mar 2026
Posts: 389
Given Kudos: 304
Location: India
Concentration: Finance, Nonprofit
Schools: Stanford '26 Wharton '26 (D) Booth '26 (D) Yale '26 (D) CBS '26 (A$$$) Darden '26 (WL) HBS '26 (D) Ross '26 (A$$$$) LBS '26 (D) Tuck '26 (A$$) Kellogg '26 (A)
GMAT Focus 1: 715 Q90 V84 DI82 
GPA: 3.74
WE:Corporate Finance (Consulting)
Schools: Stanford '26 Wharton '26 (D) Booth '26 (D) Yale '26 (D) CBS '26 (A$$$) Darden '26 (WL) HBS '26 (D) Ross '26 (A$$$$) LBS '26 (D) Tuck '26 (A$$) Kellogg '26 (A)
GMAT Focus 1: 715 Q90 V84 DI82
Posts: 389
26 Sep 2023, 04:37
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
68% (02:26) correct
32%
(02:40)
wrong
based on 154
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If m and n are positive single-digit numbers such that the units' digit of m^2 and m^4 is the same and the difference between the units' digit of n^3 and n^4 is zero, then what is the units' digit of m+n?
(1) m = n
(2) m is divisible by 5
(1) m = n
(2) m is divisible by 5
28 Sep 2023, 20:11
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RenB
\(m^2\) and \(m^4 \) having same digits mean that m digit has a repetition after two consecutive powers or after every power.
Thus m could be 1,4,5,6,9.
\(n^3\) and \(n^4 \) having same digits mean a set of consecutive powers give same units digit, meaning n would give units digit equal to itself every time.
Thus m could be 1,5,6.
We are looking for m+n.
(1) m = n
The answer could be 1+1 or 5+5 or 6+6, that is possible answers are 2 or 5.
(2) m is divisible by 5
m is 5. Nothing about n
Combined.
m=n=5
Suff
02 Sep 2024, 10:06
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chetan2u
chetan2u how did you deduce these statements? Did you try it out for a few numbers and then concluded it would be true for all such numbers?
1. \(m^2\) and \(m^4 \) having same digits mean that m digit has a repetition after two consecutive powers or after every power.
Thus m could be 1,4,5,6,9.
2. \(n^3\) and \(n^4 \) having same digits mean a set of consecutive powers give same units digit, meaning n would give units digit equal to itself every time.
I actually started computing the given powers for all numbers in the 1-9 to reach the answer, which was correct but it took me a ton of time to get to the answer. Any tips on how to improve speed in such types of questions?
