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If n is a two-digit number, in which n = x^y. If x + y < 8, and x and

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If n is a two-digit number, in which n = x^y. If x + y < 8, and x and  [#permalink]

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New post 24 May 2019, 01:41
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A
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E

Difficulty:

  55% (hard)

Question Stats:

62% (02:20) correct 38% (01:56) wrong based on 37 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?

I. 5
II. 6
III. 7

A. I only
B. II only
C. III only
D. I and III only
E. I, II and III
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Re: If n is a two-digit number, in which n = x^y. If x + y < 8, and x and  [#permalink]

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New post 24 May 2019, 01:54
X+Y < 8

X=5 and Y=2
N= 5^2 = 25
So, units digit can be 5

X=4 and Y=2
N= 4^2 = 16
So, units digit can be 6

X=3 and Y=3
N=3^3 = 27
So, units digit can be 7

Hence, 5,6, and 7 can be the units digit.
Option E

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Re: If n is a two-digit number, in which n = x^y. If x + y < 8, and x and  [#permalink]

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New post 24 May 2019, 03:50
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?

I. 5
II. 6
III. 7

A. I only
B. II only
C. III only
D. I and III only
E. I, II and III


so I took numbers to solve this question.
since x+y < 8

took 5 and 2
\(5^2\)= 25
I is possible

took 2 and 4
\(2^4\)=16.. so II is also possible

ideally one should stop at this point because the only option that has I and II is E.

Just to double check, one can use 3 and 3
\(3^3\) = 27

Please give me Kudos :)
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Re: If n is a two-digit number, in which n = x^y. If x + y < 8, and x and  [#permalink]

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New post 24 May 2019, 08:38
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?

I. 5
II. 6
III. 7

A. I only
B. II only
C. III only
D. I and III only
E. I, II and III


n is a two digit number, let's see if we can form a two digit number by x^y when x+y<8

Let's try to get 5 in unit digit= 5^2, possible. 5+2<8
Let's try to get 6 in unit digit= 2^4, possible. 2+4<8
Let's try to get 7 in unit digit= 3^3, possible. 3+3<8
E, all I II and III possible.
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Re: If n is a two-digit number, in which n = x^y. If x + y < 8, and x and   [#permalink] 24 May 2019, 08:38
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