If n and r are positive integers and r is the remainder when 27 is div

Shoyland , n cannot be 4. You have to have a quotient of 2 and you need to be as close to 27. So n×2 is a number which is closest to 27 and leaves a remainder . If n is 4 then quotient cannot be 2 as 4x6=24 so quotient would have been 6 and remainder 3 .

It cannot be even 9 as 9x3=27 it goes in completely . It can be 10 or more but not even 14 as 14x2=28 which goes over 27.

So 9<n<14 is the range.

Posted from my mobile device

target determine value of r
#1
When 20 is divided by n, the remainder is 7.
possible value of n is 13 ; so now when 27 divided by n '13' we get r as '1'
sufficient
#2
When 27 is divided by n, the quotient is 2 and the remainder is r.
27=n*2+r
here value of n can be any integer value from 1 to 13 and remainder can be from 1 to 25 ; insufficeint
option A is correct

Forget the conventional way to solve DS questions.

We will solve this DS question using the variable approach.

Remember the relation between the Variable Approach, and Common Mistake Types 3 and 4 (A and B)[Watch lessons on our website to master these approaches and tips]

Step 1: Apply Variable Approach(VA)

Step II: After applying VA, if C is the answer, check whether the question is key questions.

StepIII: If the question is not a key question, choose C as the probable answer, but if the question is a key question, apply CMT 3 and 4 (A or B).

Step IV: If CMT3 or 4 (A or B) is applied, choose either A, B, or D.

Let's apply CMT (2), which says there should be only one answer for the condition to be sufficient. Also, this is an integer question and, therefore, we will have to apply CMT 3 and 4 (A or B).

To master the Variable Approach, visit https://www.mathrevolution.com and check our lessons and proven techniques to score high in DS questions.

Let’s apply the 3 steps suggested previously. [Watch lessons on our website to master these 3 steps]

Step 1 of the Variable Approach: Modifying and rechecking the original condition and the question.

We have to find remainder 'r' when '27' is divided by integer 'n'.

Second and the third step of Variable Approach: From the original condition, we have 2 variables (n and r ). To match the number of variables with the number of equations, we need 2 equations. Since conditions (1) and (2) will provide 1 equation each, C would most likely be the answer.

But we know that this is a key question [Integer question] and if we get an easy C as an answer, we will choose A or B.

Let’s take a look at each condition.

Condition(1) tells us that When 20 is divided by n, the remainder is 7.

=> 20 = n*p + 7

=> Then n = 13.

=> 27 divided by '13' will give remainder r = 1

Since the answer is unique , the condition is sufficient by CMT 2.


Condition(2) tells us that when 27 is divided by n, the quotient is 2 and the remainder is r.

=> 27 = 2 * n + r
=> If n = 10 => 27 divided by 20 will give remainder 7.
=> If n = 11 => 27 divided by 22 will give remainder 5.


Since the answer is not unique , the condition is not sufficient by CMT 2.


Condition (1) alone is sufficient.

So, A is the correct answer.

Answer: A