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If n is a two-digit number, in which n = x^y. If x + y < 8,
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26 Oct 2017, 23:49
26 Oct 2017, 23:49
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Question Stats:
29% (02:09) correct
70% (01:51) wrong based on 123 sessions
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If n is a two-digit number, in which n = x^y. If x + y < 8, and x and y are positive integers greater than one, then the units digit of n could be which of the following?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
(F) 5
(G) 6
(H) 7
(I) 8
(J) 9
Kudos for correct solution.
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
(F) 5
(G) 6
(H) 7
(I) 8
(J) 9
Kudos for correct solution.
Show: :: OA
(B), (C), (E), (F), (G) and (H).
ShowHide Answer
Official Answer
B,C,E,F,G,H
Re: If n is a two-digit number, in which n = x^y. If x + y < 8,
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27 Oct 2017, 05:00
27 Oct 2017, 05:00
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x and y are strictly greater than 1 and their sum is less than 8, thus we are left with numbers 2, 3, 4, 5 so as they are all above 1 and their sum is 7 at maximum. Then, we can mix them using the fact that n = x^y.
In this way,
2^4 = 16 so (G)
2^5 = 32 so (C)
3^3 = 27 so (H)
3^4 = 81 so (B)
4^3 = 64 so (E)
5^2 = 25 so (F)
since we have to look at the unit digits!
In this way,
2^4 = 16 so (G)
2^5 = 32 so (C)
3^3 = 27 so (H)
3^4 = 81 so (B)
4^3 = 64 so (E)
5^2 = 25 so (F)
since we have to look at the unit digits!
General Discussion
Re: If n is a two-digit number, in which n = x^y. If x + y < 8,
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27 Oct 2017, 10:52
27 Oct 2017, 10:52
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Bunuel wrote:
If n is a two-digit number, in which n = x^y. If x + y < 8, and x and y are positive integers greater than one, then the units digit of n could be which of the following?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
(F) 5
(G) 6
(H) 7
(I) 8
(J) 9
Kudos for correct solution.
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
(F) 5
(G) 6
(H) 7
(I) 8
(J) 9
Kudos for correct solution.
Show: :: OA
(B), (C), (E), (F), (G) and (H).
Here
X cannot be greater than 5 , because if X= 6 then y can neither be 1 nor 2 as this will nullify the statement.
therefore the possible values are
x=2 then y=5,4 i.e \(2^5\), \(2^4\) = 32 , 16 (\(2^3\), \(2^2\) are not two digit number)
x=3 then y=3,4 i.e \(3^3\) , \(3^4\) = 27, 81
x=4 then y=2,3 i.e \(4^2\) , \(4^3\) = 16 , 64
x=5 then y=2 i.e \(5^2\) = 25
Thus the unit digit are = 1,2,4,6,7
