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04 May 2022, 04:30
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Integer n is greater than 20 and less than 80, is n odd?
(1) Both digits of n are prime numbers.
(2) The sum of n’s two digits is prime number.
(1) Both digits of n are prime numbers.
(2) The sum of n’s two digits is prime number.
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04 May 2022, 05:16
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(1) The no. could be 23 or 32. Not sufficient.
(2) The no. again could be 23 or 32. Not sufficient.
(1) + (2), The no. again could be 23 or 32. Not sufficient. (E)
This was perhaps the easiest explanation to type. Lol.
(2) The no. again could be 23 or 32. Not sufficient.
(1) + (2), The no. again could be 23 or 32. Not sufficient. (E)
This was perhaps the easiest explanation to type. Lol.
04 May 2022, 05:44
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The question is, Is n odd?
The given question is a "be verb" question. The answer to such questions will be yes or no.
Data is sufficient only if we can answer the question with a definite yes or a definite no.
From the question stem, 20 < n < 80.
Let us evaluate the statements.
Statement-1: Both digits of n are prime numbers.
Let us try with examples to establish an argument and then work on a counter-argument to contradict the earlier established argument.
Example: Assume n to be 23. Here both 2,3 are prime and n is odd. So the answer to the question is YES.
Counter-Example: Assume n to be 32. Here 3,2 are prime and n is even. So the answer to the question is NO.
Because a counter-example exists, we cannot answer the question with a definite yes or a definite no.
So, statement-1 alone is not sufficient.
Choice-A and Choice-D can be eliminated.
Statement-2: The sum of n’s two digits is a prime number.
We can use the same examples used above.
Example: Assume n to be 23. Here the sum of 2 and 3 is prime and n is odd. So the answer to the question is YES.
Counter-Example: Assume n to be 32. Here the sum of 3 and 2 is prime and n is even. So the answer to the question is NO.
Because a counter-example exists, we cannot answer the question with a definite yes or a definite no.
So, statement-2 alone is not sufficient.
Choice-B can be eliminated.
Combining the statements, we have both digits of n as prime numbers and the sum of n’s two digits is a prime number.
We can again use the same examples we have used above.
Example: Assume n to be 23. Here 2, 3 are prime, the sum of 2, and 3 is prime and n is odd. So the answer to the question is YES.
Counter-Example: Assume n to be 32. Here 3, 2 are prime, the sum of 3, and 2 is prime and n is even. So the answer to the question is NO.
Because a counter-example exists, we cannot answer the question with a definite yes or a definite no.
So, Statement-1 & 2 together are not sufficient.
Choice-C can be eliminated.
So, the answer is Choice-E.
Statements (1) and (2) TOGETHER are not sufficient.
The given question is a "be verb" question. The answer to such questions will be yes or no.
Data is sufficient only if we can answer the question with a definite yes or a definite no.
From the question stem, 20 < n < 80.
Let us evaluate the statements.
Statement-1: Both digits of n are prime numbers.
Let us try with examples to establish an argument and then work on a counter-argument to contradict the earlier established argument.
Example: Assume n to be 23. Here both 2,3 are prime and n is odd. So the answer to the question is YES.
Counter-Example: Assume n to be 32. Here 3,2 are prime and n is even. So the answer to the question is NO.
Because a counter-example exists, we cannot answer the question with a definite yes or a definite no.
So, statement-1 alone is not sufficient.
Choice-A and Choice-D can be eliminated.
Statement-2: The sum of n’s two digits is a prime number.
We can use the same examples used above.
Example: Assume n to be 23. Here the sum of 2 and 3 is prime and n is odd. So the answer to the question is YES.
Counter-Example: Assume n to be 32. Here the sum of 3 and 2 is prime and n is even. So the answer to the question is NO.
Because a counter-example exists, we cannot answer the question with a definite yes or a definite no.
So, statement-2 alone is not sufficient.
Choice-B can be eliminated.
Combining the statements, we have both digits of n as prime numbers and the sum of n’s two digits is a prime number.
We can again use the same examples we have used above.
Example: Assume n to be 23. Here 2, 3 are prime, the sum of 2, and 3 is prime and n is odd. So the answer to the question is YES.
Counter-Example: Assume n to be 32. Here 3, 2 are prime, the sum of 3, and 2 is prime and n is even. So the answer to the question is NO.
Because a counter-example exists, we cannot answer the question with a definite yes or a definite no.
So, Statement-1 & 2 together are not sufficient.
Choice-C can be eliminated.
So, the answer is Choice-E.
Statements (1) and (2) TOGETHER are not sufficient.
