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Suppose n is a two-digit positive integer with units digit 5

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alihong2010
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Suppose n is a two-digit positive integer with units digit 5 [#permalink] New post   09 Sep 2018, 19:44
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Suppose \(n\) is a two-digit positive integer with units digit 5, and tens digit u. Now, if \(E=\frac{(n^2-25)}{100}\), then express E in terms of u.

A. \(u+1\)

B. \(u^2+1\)

C. \(u^2-u\)

D. \(u^2+u\)

E. \(u^2+u+1\)

Here is how I did it:
E
=(n^2-25)/100
=[(n+5)(n-5)]/100
=[(u+1)*10*(u-1)*10]/100
=(u+1)(u-1)
=u^2-1, which is not an choice so I don't know where I did wrong.
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saifee
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Re: Suppose n is a two-digit positive integer with units digit 5 [#permalink] New post   10 Sep 2018, 10:50
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from the question, it can be said that n=10u+5.

now just plug it into the expression for E and then you'll get u^2+u after a little calculation.

answer D
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indiragre18
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Re: Suppose n is a two-digit positive integer with units digit 5 [#permalink] New post   10 Nov 2018, 07:25
answer must be D only
n = 10u+5
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AE
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Re: Suppose n is a two-digit positive integer with units digit 5 [#permalink] New post   16 Nov 2018, 18:08
saifee wrote:
from the question, it can be said that n=10u+5.

now just plug it into the expression for E and then you'll get u^2+u after a little calculation.

answer D

Please provide clear explanation.
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jelal123
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Re: Suppose n is a two-digit positive integer with units digit 5 [#permalink] New post   19 May 2019, 08:02
10U+5=n
So, E=[(10U+5)^2-25]/100
by calculation,E= U^2+U.
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Re: Suppose n is a two-digit positive integer with units digit 5 [#permalink] New post   19 May 2019, 08:46
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Suppose \(n\) is a two-digit positive integer with units digit 5, and tens digit u. Now, if \(E=\frac{(n^2-25)}{100}\), then express E in terms of u.

A. \(u+1\)

B. \(u^2+1\)

C. \(u^2-u\)

D. \(u^2+u\)

E. \(u^2+u+1\)


Anytime you have a problem with variables in the choices and the problem, consider plugging in your own easy value(s) as an alternative to an often needlessly complex textbook algebraic approach. Easy values are going to be numbers that conform to the conditions of the problem, but are not themselves in the answer choices. In this case, I might consider plugging in n = 35, which in turn means that u = 3.

Subsequently, E = (35^2 - 25) / 100 = 12.

Now, plug u = 3 into each of the choices, testing all individually, seeking a match to the found value E = 12.

A. 3 + 1 ≠ 12 | Eliminate
B. 9 + 1 ≠ 12 | Eliminate
C. 9 - 3 ≠ 12 | Eliminate
D. 9 + 3 = 12 | Hold
E. 9 + 3 + 1 ≠ 12 | Eliminate

Select Choice D as the only match to the sought value of 12.
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spirited5herry
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Re: Suppose n is a two-digit positive integer with units digit 5 [#permalink] New post   24 Sep 2023, 04:52
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n=10*u+5

(n^2-25)/100=[(n-5)*(n+5)]/100=(10*u+5-5)*(10*u+5+5)/100

=[10*u*(10*u+10)]/100

=10*u*10*(u+1)/100

=100*u*(u+1)/100

=u*(u+1)=u^2+u
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