If n is a positive integer such that the units (ones) digit of

Question

If n is a positive integer such that the units (ones) digit of  n^2+4n  is 7 and the units digit of n is not 7, what is the units digit of n+3?

A. 1

B. 2

C. 3

D. 4

E. 5

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$!vakumar.m · Answer

If n is a positive integer such that the units (ones) digit of n^2+ 4n is 7 and the units digit of n is not 7, what is the units digit of n+3? 
We can note that for n with 7 or 9 as unit digit, n^2 + 4n will have 7 at units digit. But, the units digit of n is not 7. Hence, units digit of n has to be 9.
Then, units digit of n+3 is 2.
Answer B

Karan0912 · Answer

Best way here is to try digits in n^2 + 4n that give you 7 in units place. Trick is it would never be an even number (Try it!). So on trying you'd get n =7 or n=9.
The question also gives you that n is not equal to 7. Hence n=9.
So unit's digit of n+3 = 9+3 =12 ... is 2.

AbbyJ · Answer

is there any shorter way to solve this, rather than listing all unit digits of n^2 for 1 to 10, followed by unit digits in multiples of 4n for all n from 1 to 10?

amanbachhawat · Answer

AbbyJ

n^2 + 4n has units digit ending with 7 i.e. it is odd. Since 4n has to even, n^2 and therefore n are odd numbers.

N's unit digit could end in 1,3,5 or 9 (Since the question states that the unit digit of n is not 7).

On trial and error basis, we find that for n = 9 in the units digit, n^2 + 4n returns 7 in the units digit.

Therefore, n +3 (9+3,19+3,29+3...) will return 2 in the units digit. Ans B.

AbbyJ · Answer

Thanks Aman! That helps

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youcouldsailaway · Answer

Once we rewrite  n^2 +n  as  n(n+4) , we can see that taking  n  as any even one digit, two digit, three digit.... number - the above equation will always give an even number. Whereas, if we were to take  n  as any odd one digit, two digit, three digit.... number, the only  n  nos. that we can take are the ones that either have 7 or 9 in the units place. Since we can't take 7, we will take only those  n's  whose units digit is 9 and adding three to such a number will give a number which has 2 in the units place.

If n is a positive integer such that the units (ones) digit of

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GMAT Problem Solving (PS) Questions

If n is a positive integer such that the units (ones) digit of

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