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Sajjad1994
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What is the largest possible positive integer value of a that satisfie 22 Oct 2020, 03:41
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C
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65% (02:13) correct 35% (02:10) wrong based on 132 sessions

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What is the largest possible positive integer value of a that satisfies \(a^2+5b = 315\); where b is a prime number?

(A) 4

(B) 5

(C) 10

(D) 15

(E) 17
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C
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Mona2019
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What is the largest possible positive integer value of a that satisfie Updated on: 22 Oct 2020, 11:08
Originally posted by Mona2019 on 22 Oct 2020, 04:04.
Last edited by Mona2019 on 22 Oct 2020, 11:08, edited 1 time in total.
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Let's go by option,
A can't be 17, as if we subtract 17^2 from 315, we won't be getting a number that is divisible by 5 (5b)

So E is not the answer

If a is 15, 5b becomes 90, thus B is 18 which is not prime.

If a is 10, b is 43,
So C is the answer, IMO

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What is the largest possible positive integer value of a that satisfie 22 Oct 2020, 11:02
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Mona2019

If a is 15, 5b becomes 90, thus B is 16 which is not prime.
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I think you meant to say b is 18 (not 16), but otherwise your solution is perfect.
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What is the largest possible positive integer value of a that satisfie 22 Oct 2020, 11:07
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IanStewart
Mona2019

If a is 15, 5b becomes 90, thus B is 16 which is not prime.

I think you meant to say b is 18 (not 16), but otherwise your solution is perfect.
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Yes, you are right. Thanks for pointing it out. I don't know I have the habit of making such silly mistakes. I am trying to cope with the time crunch and I am suffering from these silly things instead.

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What is the largest possible positive integer value of a that satisfie 22 Oct 2020, 11:23
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Mona2019

Yes, you are right. Thanks for pointing it out. I don't know I have the habit of making such silly mistakes. I am trying to cope with the time crunch and I am suffering from these silly things instead.
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That's a very common issue, and it's worth paying attention to if you want to maximize your score. Many test takers rush through easier questions to try to save time, and sometimes make careless errors and get easier questions wrong. But on an adaptive test like the GMAT, the worst thing you can do is answer an easy question incorrectly. It's much more important to be right than to be fast, especially on lower-level questions, and if you need to save time on the test, the best way to do it (to optimize your score) is to move on more quickly from very hard questions, if you don't see how to solve them, rather than to try to solve lower level problems more quickly. Hope that helps! :)
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What is the largest possible positive integer value of a that satisfie 22 Oct 2020, 11:30
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Mona2019

Yes, you are right. Thanks for pointing it out. I don't know I have the habit of making such silly mistakes. I am trying to cope with the time crunch and I am suffering from these silly things instead.

That's a very common issue, and it's worth paying attention to if you want to maximize your score. Many test takers rush through easier questions to try to save time, and sometimes make careless errors and get easier questions wrong. But on an adaptive test like the GMAT, the worst thing you can do is answer an easy question incorrectly. It's much more important to be right than to be fast, especially on lower-level questions, and if you need to save time on the test, the best way to do it (to optimize your score) is to move on more quickly from very hard questions, if you don't see how to solve them, rather than to try to solve lower level problems more quickly. Hope that helps! :)
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Yes , it definitely helps. Thank you for helping me out. :)

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What is the largest possible positive integer value of a that satisfie 22 Oct 2020, 11:36
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Since the question asks for the largest value of 'a', let's start with the largest option provided.

17^2 = 289 which when subtracted from 315 does not yield any number of the form of 5*b where b is a prime number.

Next comes 15, the square of which is 225. 315-225 gives 90, which makes b = 18, which is non prime.

10 satisfies both these criteria and hence should be our answer.
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What is the largest possible positive integer value of a that satisfie 22 Oct 2020, 11:59
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Lets start with the largest numbers:

(E) 17^2 = 289. We can eliminate this choice because 5b ends in 0 or 5.

(D) 15^2 = 225. 315 - 225 = 90. B = 18, which is not prime.

(C) 10^ = 100. 315 - 100 = 215. 215 / 5 = 43.

C is correct.
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