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15 Jun 2021, 04:00
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
71% (02:02) correct
29%
(02:08)
wrong
based on 124
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What is the digit in the unit’s place of \((98^{43} * 122^{22}) + 729^{59} + 2^{543}\)?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
15 Jun 2021, 04:07
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Only the units digit of each base will matter if we only need the units digit of the answer, so we can instead find the units digit of
(8^43)(2^22) + 9^59 + 2^543
and since for any base, units digits repeat in 'blocks of four' (i.e. for any integer base b, the units digit of b^x and b^(x+4) is always the same) we can reduce each exponent by any multiple of 4 without affecting the answer. So we just need the units digit of
(8^3)(2^2) + 9^3 + 2^3
and since the units digit of 8^3 is 2, and the units digit of 9^3 is 9, we get
2*4 + 9 + 8 = 25, which has a units digit of 5.
I have never once seen numbers this inelegant in an official GMAT question, though.
Posted from my mobile device
(8^43)(2^22) + 9^59 + 2^543
and since for any base, units digits repeat in 'blocks of four' (i.e. for any integer base b, the units digit of b^x and b^(x+4) is always the same) we can reduce each exponent by any multiple of 4 without affecting the answer. So we just need the units digit of
(8^3)(2^2) + 9^3 + 2^3
and since the units digit of 8^3 is 2, and the units digit of 9^3 is 9, we get
2*4 + 9 + 8 = 25, which has a units digit of 5.
I have never once seen numbers this inelegant in an official GMAT question, though.
Posted from my mobile device
15 Jun 2021, 04:39
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Actually IanStewart, these questions seem to belong to an Indian Entrance exam called NMAT which is also conducted by the GMAC.
Even I was a little confused when I saw these questions appear with the NMAT tag.
Even I was a little confused when I saw these questions appear with the NMAT tag.
