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Hey GMAT aspirants! We’re back with our GMAT Study Tip #2: Back Solving! Missed our Study Tip #1 on Guesstimating? Here’s where you can check it out.

The GMAT is a time-bound test. So naturally, sometimes, solving a Quant problem algebraically may consume a lot of time and hamper your overall performance. How do you get past this particular pickle? Back solving, that’s how! This is basically another time-saving strategy (like the Guesstimate), where a ‘Problem Solving’ question is solved backwards.

You should be Back Solving, only when:

- All the answer choices given for a question are numbers.
- Solving a problem algebraically is almost impossible or very tedious.

- Start with the answer choice (C) as the value asked in the question.
*This is because the options in GMAT will be in either ascending or descending order (i.e., the mid value as option C).*

Now, there will be two possibilities while solving with option C:

- Option (C) is the correct answer → and in this case you can simply move to the next question.
- Option (C) is
**not**the correct answer → then you will get to know if you are looking for a higher value or a lower value in comparison to option (C). Hence, you can eliminate at least three choices i.e. either A, B, C or C, D, E.

It’s that simple!

Now, let’ try and understand Back Solving with an example.

*Q. A man has a total of x dollars and he wants to distribute the amount among his four sons. He gives half of what he had to the first son; half of the remaining amount to the second son; half of what remained, to his third son and the remaining amount to the fourth son. If the fourth son received $10,000, what is the value of x, in dollars?*

A. 10,000

B. 20,000

C. 40,000

D. 80,000

E. 1,60,000

Note that at every stage what the man gives to his son and what remains to be further given to the other son(s) are equal. Why? Because, the man is giving one half to his son.

This problem is best solved by working backwards.

First, we will consider the answer option (C) and check if that can be the answer?

Total First Son Second Son Third Son Fourth Son

A)

B)

C) **x = $40,000 →** $20,000 → $10,000 →** **$5,000 →** **$5,000

If x = 40,000

→ The first son would get ½ of $40,000 i.e. $20,000

→ So, remaining amount is ($40,000 – $20,000) = $20,000 and the second son would get ½ of remaining i.e. ½ of $20,000 = $10,000

→ Similarly, remaining amount now is ($20,000 – $10,000) = $10,000 and the third son would get ½ of remaining i.e. ½ of $10,000 = $5,000

→ Hence, the fourth son would also get $10,000 – $5000 = $5000.

Therefore, (C) cannot be the answer as the fourth son got $10,000. So, the answer has to be > 40,000.

D) **x = $80,000 →** $40,000 → $20,000 →** **$10,000 →** **$10,000

If you can figure that double the amount of $40,000, will give the correct amount that the 4^{th} son received. Even otherwise, try the option (D) and you will get your answer.

I hope that by now, you’ve realised that the Back Solving technique is extremely useful since it saves time, it’s quite simple and helps to solve a problem without any hassles!

Stay tuned for more GMAT Study Tips!

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