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# If n is an integer between 10 and 99, is n < 80?

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If n is an integer between 10 and 99, is n < 80?  [#permalink]

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15 Jan 2012, 22:49
3
11
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Difficulty:

25% (medium)

Question Stats:

78% (01:22) correct 22% (01:27) wrong based on 520 sessions

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If n is an integer between 10 and 99, is n < 80?

(1) The sum of the two digits of n is a prime number.
(2) Each of the two digits of n is a prime number.

I know this must be easy. The answer is B (statement 2 is sufficient alone, while statement 1 is not). Doesn't that lead to tons of possible values of n?
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Joined: 02 Sep 2009
Posts: 50672
Re: If n is an integer between 10 and 99, is n < 80?  [#permalink]

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16 Jan 2012, 02:25
6
2
If n is an integer between 10 and 99, is n < 80?

(1) The sum of the two digits of n is a prime number.
(2) Each of the two digits of n is a prime number.

I know this must be easy. The answer is B (statement 2 is sufficient alone, while statement 1 is not). Doesn't that lead to tons of possible values of n?

If n is an integer between 10 and 99. Is n < 80?

Notice that n is an integer between 10 and 99 means that n is two-digit integer.

(1) The sum of the two digits of n is a prime number. Clearly insufficient: for example 83>80 and 38<80.

(2) Each of the two digits of n is a prime number --> greatest one digit prime is 7, thus max value of n is 77, which is less than 80. Sufficient.

I am lost on this one. Prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, etc. There are several values that satisfy the conditions of 10>n>80 while both digits are prime numbers, for instance 23, 32, 57, etc. Is that the reason that we can eliminate #2? Similarly, not to sound stupid, but is 67 then the only integer that meets the conditions of #1? Thanks.

We are told that n is a two-digit integer and each of these two digits is a prime, so n can be: 22, 23, 25, 27, ... and as greatest one digit prime is 7, thus max value of n is 77.

As what n could be taking in account statement (1):
23 --> 2+3=5=prime;
25 --> 2+5=7=prime;
29 --> 2+9=11=prime;
...

Hope it's clear.
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Re: If n is an integer between 10 and 99, is n < 80?  [#permalink]

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15 Jan 2012, 23:28
4
If n is an integer between 10 and 99, is n < 80?

(1) The sum of the two digits of n is a prime number.
(2) Each of the two digits of n is a prime number.

I know this must be easy. The answer is B (statement 2 is sufficient alone, while statement 1 is not). Doesn't that lead to tons of possible values of n?

1. let n be 67 then 6+7 = 13 (prime) and n < 80
but if n is 89 then 8+9 =17 (prime) and n >80. hence insuff

2. 8 and 9 are not prime so n < 80 as no value above 80 satisfies stmnt 2
hence suff

B
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Re: If n is an integer between 10 and 99, is n < 80?  [#permalink]

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15 Jan 2012, 23:38
kp1811 wrote:
If n is an integer between 10 and 99, is n < 80?

(1) The sum of the two digits of n is a prime number.
(2) Each of the two digits of n is a prime number.

I know this must be easy. The answer is B (statement 2 is sufficient alone, while statement 1 is not). Doesn't that lead to tons of possible values of n?

1. let n be 67 then 6+7 = 13 (prime) and n < 80
but if n is 89 then 8+9 =17 (prime) and n >80. hence insuff

2. 8 and 9 are not prime so n < 80 as no value above 80 satisfies stmnt 2
hence suff

B

I am lost on this one. Prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, etc. There are several values that satisfy the conditions of 10>n>80 while both digits are prime numbers, for instance 23, 32, 57, etc. Is that the reason that we can eliminate #2? Similarly, not to sound stupid, but is 67 then the only integer that meets the conditions of #1? Thanks.
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Re: If n is an integer between 10 and 99, is n < 80?  [#permalink]

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16 Jan 2012, 02:21
1
1
kp1811 wrote:
If n is an integer between 10 and 99, is n < 80?

(1) The sum of the two digits of n is a prime number.
(2) Each of the two digits of n is a prime number.

I know this must be easy. The answer is B (statement 2 is sufficient alone, while statement 1 is not). Doesn't that lead to tons of possible values of n?

1. let n be 67 then 6+7 = 13 (prime) and n < 80
but if n is 89 then 8+9 =17 (prime) and n >80. hence insuff

2. 8 and 9 are not prime so n < 80 as no value above 80 satisfies stmnt 2
hence suff

B

I am lost on this one. Prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, etc. There are several values that satisfy the conditions of 10>n>80 while both digits are prime numbers, for instance 23, 32, 57, etc. Is that the reason that we can eliminate #2? Similarly, not to sound stupid, but is 67 then the only integer that meets the conditions of #1? Thanks.

67 is not the only number for #1

we can have several numbers satisfying this condition like 23,32, 12, 21,43,34

also for stmnt 2 any number = or > than 80 will have 8 or 9 as ten's digit which are not prime and don't agree with stmnt 2
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Re: If n is an integer between 10 and 99, is n < 80?  [#permalink]

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16 Jan 2012, 02:26
Just got this. Way easier than I was making it out to be. Thanks.
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Re: If n is an integer between 10 and 99, is n < 80?  [#permalink]

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27 Nov 2015, 08:04
If n is an integer between 10 and 99, is n < 80?

(1) The sum of the two digits of n is a prime number.

92, 9+2=11, is 92 < 80? no
29, 2+9=11, is 11 < 80? yes

(2) Each of the two digits of n is a prime number.

Single digit primes are 2, 3, 5, 7. Any combination into a 2 digit number will be < 80

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Re: If n is an integer between 10 and 99, is n < 80?  [#permalink]

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07 Jan 2017, 22:16
If we prove none of the number greater than 80 satisfy (1) or (2) , then we can answer the question.

from 81 to 98 inclusive : there are more than 1 number satisfying statement (1) , n could take multiple values(83,85 etc), hence (1) is insufficient.
from 81 to 98 inclusive : there are no numbers which have both of the digits as prime, this satisfies (2), hence n must be less than 80.

Ans : B
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Re: If n is an integer between 10 and 99, is n < 80?  [#permalink]

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03 Jul 2017, 03:27
looks easier than done during the test.
why is that the easier questions also take more time in exam than when normally practicing
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If n is an integer between 10 and 99, is n < 80?  [#permalink]

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11 Jul 2017, 06:54
geometric wrote:
If n is an integer between 10 and 99, is n < 80?

(1) The sum of the two digits of n is a prime number.
(2) Each of the two digits of n is a prime number.

I know this must be easy. The answer is B (statement 2 is sufficient alone, while statement 1 is not). Doesn't that lead to tons of possible values of n?

If n is an integer between 10 and 99, is n < 80?

(1) The sum of the two digits of n is a prime number.

Lets take numbers:

$$76 - 7 + 6 = 13 =$$Prime $$< 80$$

$$85 - 8 + 5 = 13 =$$Prime $$> 80$$

Hence, (1) ===== is NOT SUFFICIENT

(2) Each of the two digits of n is a prime number.

$$8$$ & $$9$$ are non prime numbers

Hence, the only possibility of having both the digits as prime is when the number is $$< 80$$

Hence, (2) ===== is SUFFICIENT

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Re: If n is an integer between 10 and 99, is n < 80?  [#permalink]

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16 Sep 2018, 10:16
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Re: If n is an integer between 10 and 99, is n < 80? &nbs [#permalink] 16 Sep 2018, 10:16
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