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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here. # Suppose n is a two-digit positive integer with units digit 5  Question banks Downloads My Bookmarks Reviews Important topics
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TAGS: Intern Joined: 17 Feb 2018
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Suppose n is a two-digit positive integer with units digit 5 [#permalink]
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Question Stats: 72% (01:21) correct 27% (02:18) wrong based on 18 sessions
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. Intern Joined: 10 Sep 2018
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Re: Suppose n is a two-digit positive integer with units digit 5 [#permalink]
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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.

Intern Joined: 27 Oct 2018
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Re: Suppose n is a two-digit positive integer with units digit 5 [#permalink]
n = 10u+5
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Re: Suppose n is a two-digit positive integer with units digit 5 [#permalink]
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.

Manager Joined: 08 Dec 2018
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Re: Suppose n is a two-digit positive integer with units digit 5 [#permalink]
10U+5=n
So, E=[(10U+5)^2-25]/100
by calculation,E= U^2+U. GRE Prep Club Tests Editor Affiliations: Partner at MyGuru LLC.
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Re: Suppose n is a two-digit positive integer with units digit 5 [#permalink]
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Expert's post
Quote:
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.
_________________

Stefan Maisnier Re: Suppose n is a two-digit positive integer with units digit 5   [#permalink] 19 May 2019, 08:46
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