I know that 140 divided by 7 = 20
140 - 7 = 133, so 133 divided by 7 = 19
So, 135 divided by 7 equals 19 with remainder 2

What about 135 divided by 19?
Well, we learned earlier that 133 divided by 7 = 19
This ALSO means that 133 divided by 19 = 7
So, 135 divided by 19 equals 7 with remainder 2

We get:
Quantity A: 2
Quantity B: 2

Answer:
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this was quite a simple i dnt think we are luckey enough to get such questions in exam

I agree. However, It is useful to cement the concepts. it is never a waste of time.

Regards
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It would be possible to see a similar question (on the first quant section at least) on test day.


Cheers,
Brent
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Both values are equal

C

C

I am sorry, I am unable to understand the process of solving it.

Will it be wise to use calculator to solve this type of question in actual GRE.

yes, why not.

However, a question like this, using directly the calculator to solve it, is quite improbable.

Regards
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it is interesting question

I used the calculator just to try out and the results are somewhat misleading in terms of answering the question correctly:

135/7=19.285...
135/19=7.105263...

so in this case you would get differing remainders. How come the two methods result in different answers?

The explanation lies in how remainders, divisors and decimals are related through division.

Take as an example the expression 17 ÷ 5. We know through long division that the divisor 5 goes into the dividend 17 three times with 2 left over, so the quotient could be written as 3 remainder 2. However, the quotient were we to put 17 ÷ 5 in the calculator would be 3.4 as a decimal.

Why is this??

It's because the decimal leftover 0.4 = 2/5 as a fraction, which is also equal to the remainder 2 out of the divisor of 5.

So, for all division : remainder / divisor must = quotient decimal leftover as a fraction.

Let's now apply this concept to the decimals left over in the problem.

As already established, 135 ÷ 7 = 19 remainder 2 and if you take that remainder of 2 and divide it by the divisor of 7 you get a decimal leftover of 0.285714 repeating.

Then, since 135 ÷ 19 = 7 remainder 2 you would instead take that remainder of 2 and divide it by the divisor of 19 to get a decimal leftover of 0.105263...

Hope this sufficiently explains the relationship between remainders and decimals in division!
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Great insight Sir.

Regards
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