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Given that p is a positive even integer with a positive [#permalink]

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08 Aug 2006, 13:59

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Given that p is a positive even integer with a positive units digit, if the units digit of p^3 minus the units digit of p^2 is equal to 0, what is the units digit of p + 3?

A. 3 B. 6 C. 7 D. 9 E. It cannot be determined from the given information.

Unit digit of p^3 = unit digit of x^3
Unit digit of p^2 = unit digit of x^2

Their difference is 0 (As given). This is possible only if unit digit is 1 or 0. But since p is an even integer. So unit digit of p =0
hence unit digit of p+3 = 3
_________________

(Unit digit of p^3) - (Unit digit of p^2) = 0 if the units digit is 0, 1, 5, 6.

The answer in these cases would be 3, 4, 8, 9.

Even if 0 is neither posive or negative, we still have 3 options left.

However, only 9 is mentioned from among these choices, so could be D as well... any suggestions?
_________________

Uh uh. I know what you're thinking. "Is the answer A, B, C, D or E?" Well to tell you the truth in all this excitement I kinda lost track myself. But you've gotta ask yourself one question: "Do I feel lucky?" Well, do ya, punk?

Unit digit of p^3 = unit digit of x^3 Unit digit of p^2 = unit digit of x^2

Their difference is 0 (As given). This is possible only if unit digit is 1 or 0. But since p is an even integer. So unit digit of p =0 hence unit digit of p+3 = 3

What the heck I was thinking

Answer should be D because last digit of p must be +ve and even.
_________________

Given that p is a positive even integer with a positive units digit, if the units digit of p^3 minus the units digit of p^2 is equal to 0, what is the units digit of p + 3?

A 3 B 6 C 7 D 9 E It cannot be determined from the given information.

please explain

unit digits could be 0, 1, 5 and 6 but only 6 satisfies the conditions given in the question. so D make sense..

Given that p is a positive even integer with a positive units digit, if the units digit of p^3 minus the units digit of p^2 is equal to 0, what is the units digit of p + 3?

A 3 B 6 C 7 D 9 E It cannot be determined from the given information.

please explain

If units digit = 6 then units(216)-units(36) = 0
p+3 = 9

Re: Given that p is a positive even integer with a positive [#permalink]

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28 Sep 2013, 12:31

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Given that p is a positive even integer with a positive units digit, if the units digit of p^3 minus the units digit of p^2 is equal to 0, what is the units digit of p + 3?

A. 3 B. 6 C. 7 D. 9 E. It cannot be determined from the given information.

p is a positive even integer with a positive units digit --> the units digit of p can be 2, 4, 6, or 8 --> only options C and E are left.

In order the units digit of p^3 - p^2 to be 0, the units digit of p^3 and p^2 must be the same. Thus the units digit of p can be 0, 1, 5 or 6.

Intersection of values is 6, thus the units digit of p + 3 is 6 + 3 = 9.

Re: Given that p is a positive even integer with a positive [#permalink]

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03 Oct 2015, 20:59

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
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Re: Given that p is a positive even integer with a positive [#permalink]

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17 Jun 2016, 03:12

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Bunuel wrote:

u2lover wrote:

Given that p is a positive even integer with a positive units digit, if the units digit of p^3 minus the units digit of p^2 is equal to 0, what is the units digit of p + 3?

A. 3 B. 6 C. 7 D. 9 E. It cannot be determined from the given information.

p is a positive even integer with a positive units digit --> the units digit of p can be 2, 4, 6, or 8 --> only options C and E are left.

In order the units digit of p^3 - p^2 to be 0, the units digit of p^3 and p^2 must be the same. Thus the units digit of p can be 0, 1, 5 or 6.

Intersection of values is 6, thus the units digit of p + 3 is 6 + 3 = 9.

Answer: B.

Apologies for seeing a mistake,shouldn't the answer choice be option D

Given that p is a positive even integer with a positive units digit, if the units digit of p^3 minus the units digit of p^2 is equal to 0, what is the units digit of p + 3?

A. 3 B. 6 C. 7 D. 9 E. It cannot be determined from the given information.

p is a positive even integer with a positive units digit --> the units digit of p can be 2, 4, 6, or 8 --> only options C and E are left.

In order the units digit of p^3 - p^2 to be 0, the units digit of p^3 and p^2 must be the same. Thus the units digit of p can be 0, 1, 5 or 6.

Intersection of values is 6, thus the units digit of p + 3 is 6 + 3 = 9.

Answer: B.

Apologies for seeing a mistake,shouldn't the answer choice be option D

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