Source: Official Guide for GMAT Review 2016 Problem Solving; #14

2

# If 893 × 78 = p, which of the

If 893 × 78 = p, which of the following is equal to 893 × 79?

### 2 Explanations

1

John Robertson

Did the problem a similar way the second time I solved it. First time though, and I'm not sure if this is a good way to think about it as in it'll work across different problems but:

->893x78 is 78 "iterations" of 893, and it's equal to p, whatever p is.
->893x79 is 79 "iterations" of 893, so really just one additional 893 to the previous 78 "iterations" of 893 equalling p. So, it's just the previous answer p, plus another 893. If it was 893 x 80, it would be (p + 893 + 893), etc.

Solved it this way the first time, but I think training yourself to spot easy number manipulations that link the given info to the question, like 79=(78+1), substitute and distribute is probably a better groove to get in to.

Jan 15, 2017 • Comment

Cydney Seigerman, Magoosh Tutor

Hi John! Overall, the approach you described and the method Jeffrey posted original are saying the same thing :) The key is to recognize that 893x79 has one more factor of 893 is has one more "iteration" 893 than 893x78. In this way, we can compare two such products by breaking up the number we're multiplying by (e.g. 79 = 78 + 1 or 80 = 70 + 2) in order to find the value of the final product. Now that you've recognized this pattern in your practice, you should more easily identify situations in which you can break up larger numbers and subsequently distribute to rewrite expressions, like we do here :)

2

Jeffrey Braganza

893 x 78 = P (given)
893 x 79 = ?
893 x (78 + 1)
= 893x78 + 893
=P + 893

Dec 31, 2015 • Comment

Cydney Seigerman, Magoosh Tutor

Great job! Thanks for contributing to the forum :)

Tamer Karam

Sam Kinsman, Magoosh Tutor

Hi Tamer,

The key here is to notice that 893 x 79 is the same as
893 x (78 + 1). We can then write 893 x (78 + 1) as (893 x 78) + (893 x 1). So we have:

893 x 79
893 x (78 + 1)
(893 x 78) + (893 x 1)
(893 x 78) + 893

We know that 893 x 78 = P, so:

(893 x 78) + 893
P + 893

So 893 × 79 = P + 893

I hope this helps! :)