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# Mr. McCall selects a number that is two-digit and positive. If the num

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Math Expert
Joined: 02 Sep 2009
Posts: 47157
Mr. McCall selects a number that is two-digit and positive. If the num  [#permalink]

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07 Jul 2018, 09:42
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Difficulty:

35% (medium)

Question Stats:

59% (01:48) correct 41% (01:41) wrong based on 32 sessions

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Mr. McCall selects a number that is two-digit and positive. If the number is prime, he assigns that many problems for homework. If the number is not prime, he assigns 8 more problems than the number for homework. If he assigns 97 problems for homework, which of the following could be the number he selected?

I. 89
II. 97
III. 105

A. I only
B. I and II only
C. II only
D. II and III only
E. I and III only

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Math Expert
Joined: 02 Aug 2009
Posts: 6258
Re: Mr. McCall selects a number that is two-digit and positive. If the num  [#permalink]

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07 Jul 2018, 10:28
Bunuel wrote:
Mr. McCall selects a number that is two-digit and positive. If the number is prime, he assigns that many problems for homework. If the number is not prime, he assigns 8 more problems than the number for homework. If he assigns 97 problems for homework, which of the following could be the number he selected?

I. 89
II. 97
III. 105

A. I only
B. I and II only
C. II only
D. II and III only
E. I and III only

check if 97 is a PRIME number
TIP :- check all prime numbers till $$\sqrt{97}~\sqrt{100}$$~10..

97 is odd, so not div by 2
9+7=16, so not div by 3
units digit is not 5, so not div by 5
97+70+27... 27 is not div by 7..so not div by 7
hence 97 is prime
so TWO cases
1) number picked up was 97 itself
2) number picked up was 97-8=89, but then 89 should not be a prime

check for 89 in similar manner
it is also prime, so case (2) is out

Only 97 possible

C
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Re: Mr. McCall selects a number that is two-digit and positive. If the num  [#permalink]

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07 Jul 2018, 11:13
Bunuel wrote:
Mr. McCall selects a number that is two-digit and positive. If the number is prime, he assigns that many problems for homework. If the number is not prime, he assigns 8 more problems than the number for homework. If he assigns 97 problems for homework, which of the following could be the number he selected?

I. 89
II. 97
III. 105

A. I only
B. I and II only
C. II only
D. II and III only
E. I and III only

No of problems assigned=97

Among 89,97, and 105; 89 and 97 are the prime numbers. So, 105 is eliminated.
89 can't be incremented to 97 since it's a prime; as per question algorithm stops at 89.

Hence,97 is the selected number.

Ans (C)
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PKN

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Re: Mr. McCall selects a number that is two-digit and positive. If the num  [#permalink]

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07 Jul 2018, 12:17
Any prime number p, (p >= 5), when divided by 6 leaves a remainder of 1 or 5.

Since the home work given is of 97 problems, 97 divided by 6, leaves remainder of 1. Hence 97 is a prime number.

As per logic in question, if number chosen is prime, homework is equal to number chosen. Hence number chosen was 97.

Option II is true.

Since 89 is also prime number ( as it leaves a remainder of 5 on division by 6) & 97 = 89 + 8, therefore 89 is not possible.

Similarly for 105, which is not a prime number & 105 - 8 = 97, therefore 105 is also not possible.

Thanks,
GyM
Re: Mr. McCall selects a number that is two-digit and positive. If the num &nbs [#permalink] 07 Jul 2018, 12:17
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