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# If x is a two-digit number, is x < 84? (1) The sum of the tens’ and th

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Joined: 02 Sep 2009
Posts: 58340
If x is a two-digit number, is x < 84? (1) The sum of the tens’ and th  [#permalink]

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25 Sep 2018, 05:29
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Difficulty:

55% (hard)

Question Stats:

62% (01:47) correct 38% (01:31) wrong based on 35 sessions

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If x is a two-digit number, is x < 84?

(1) The sum of the tens’ and the unit digit of x is a prime number.
(2) Each of the two digits of x is a prime number

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Re: If x is a two-digit number, is x < 84? (1) The sum of the tens’ and th  [#permalink]

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25 Sep 2018, 20:31
i think its B.

1)The sum of the tens’ and the unit digit of x is a prime number. - several examples; the number can be 29 (sum 11) -yes, 92 (sum 11) -no ; hence insufficient
2)Each of the two digits of x is a prime number -we have only 4 single digit prime numbers -2,3,5,7 -any combination of these numbers would yield a number not greater than 84 - Sufficient.
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Re: If x is a two-digit number, is x < 84? (1) The sum of the tens’ and th  [#permalink]

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25 Sep 2018, 23:22
Bunuel wrote:
If x is a two-digit number, is x < 84?

(1) The sum of the tens’ and the unit digit of x is a prime number.
(2) Each of the two digits of x is a prime number

Question: Is x < 84?

Statement 1: The sum of the tens’ and the unit digit of x is a prime number
if x = 12, sum of digits = 3 and x < 84 i.e. answer to the question is YES
if x = 98, sum of digits = 17 and x > 84 i.e. answer to the question is NO
NOT SUFFICIENT

Statement 2: Each of the two digits of x is a prime number
Single digit Prime numbers are 2, 3, 5, 7
and no two digit number can be formed using these prime single digit numbers which is greater than 84 hence
SUFFICIENT

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Re: If x is a two-digit number, is x < 84? (1) The sum of the tens’ and th   [#permalink] 25 Sep 2018, 23:22
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