If integer n is a 2-digit number, is n divisible by 9? (1) When n is d

Question

If integer n is a 2-digit integer, is n divisible by 9?

(1) When n is divided by 3 the remainder is 2.
(2) When n is divided by 7 the remainder is 1.

Is the integer n divisible by 9? n is a two digit number.

1) When n is divided by 3 the remainder is 2

2) When n is divided by 7 the remainder is 1.

EgmatQuantExpert · Answer

Solution 
  Given:  
 • n is a 2-digit integer

To find:  
 • Whether ‘n’ is divisible by 9 or not
 o Whether n is of the of  9k_1  or not

Analysing Statement 1  
“When ‘n’ is divided by 3, the remainder is 2”
 • Implies,  n = 3k_2 + 2 
• This cannot be divisible by 9, for any value of  k_2

Therefore, statement 1 is sufficient

Analysing Statement 2  
“When ‘n’ is divided by 7, the remainder is 1”
 •  n = 7k_3 + 1 
 • If  k_3 = 5 , then n is divisible by 9
• If  k_3 = 4 , then n is not divisible by 9

Therefore, statement 2 is not sufficient

Hence, the correct answer is Option A

Answer: A

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Archit3110 · Answer

from 1 :

values of n which when divided by 3 leaves remainder 2 will not be divisible by 9 , sufficient

From 2: 
values of n when divided by 7 which leaves remainder as 1 may or may not be divisble by 9 ; eg 15 , 36 so in sufficient

IMO A

MathRevolution · Answer

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution. Visit https://www.mathrevolution.com/gmat/lesson for details. Since we have 1 variable (n) and 0 equations, D is most likely to be the answer. So, we should consider each condition on its own first. Condition 1) Since n is not divisible by 3, it is not divisible by 9. The answer is 'no'. Since condition 1) yields a unique solution, it is sufficient Since 'no' is also a unique answer by CMT (Common Mistake Type) 1, the condition 1) is sufficient. Condition 2) If n = 36, then n is divisible by 9 and the answer is 'yes. If n = 8, then n is not divisible by 9 and the answer is 'no'. Since condition 2) does not yield a unique solution, it is not sufficient Therefore, A is the answer. If the original condition includes “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations” etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C or E.

bumpbot · Answer

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If integer n is a 2-digit number, is n divisible by 9? (1) When n is d

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If integer n is a 2-digit number, is n divisible by 9? (1) When n is d

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