Question: Remainder when Divided by 7

Comment on Remainder when Divided by 7

My approach was similar to second one but from given conditions, we can infer that (x-1) when divided by 5 & 7 will leave remainder as 0. Since 5&7 both are prime, the first no. that can satisfy the given condition came to be (x-1) = 35( divisible by 5&7). => x=36. This gives q=7. Thus q/7 leaves remainder 0.
gmat-admin's picture

Great approach!

My approach is like this.
Once we equate both equations of x, we get 5q = 7k. Once looking at this, we will get 35 in our mind where 5 and 7 meets. So q=7 and k=5.
Then, q/7 means 7/7 which leaves remainder 0.
gmat-admin's picture

Great approach.
here sir i did this
unit digit of 12^12= 6
unit digit of 13^13 = 3
unit digit of 12^12 +13^13 will be 9
and unit digit of (14^14*15^15) will be 0
but 14^14*15^15 > 12^12+13^13
when we subtract two numbers last digit would be 10-9 = 1
eg 20-9 last digit will be 1 30-9 will be 1
sir is this approach correct?
gmat-admin's picture

That's a perfectly valid solution. Nice work!


dear Brent what will happen if we take the value of x as 1 instead of 36 can you write it to me.
gmat-admin's picture

Great question! Let's find out what happens.

GIVEN: When positive integer x is divided by 5, the quotient is q and the remainder is 1.
If x = 1, then q = 0 (since 5 divides into 1 ZERO times with remainder 1)

QUESTION: What is the remainder when q is divided by 7?
Since q = 0, the remainder will be 0, when 0 is divided by 7.

Answer: A


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