# Know the GMAT Code: Working Backwards

*by*, Jul 21, 2017

Do you know how to Work Backwards on Problem Solving (PS) problems? More important, do you know *when* to work backwardsand when not to? To get a really high score on this test, youve got to Know the Code in order to get through the questions efficiently.

Ive got two problems for you to try from the GMATPrep free question set. On one, working backwards is a great option. On the othernot so much. If you think you already know this strategy, test out your skills by trying both problems and articulating (out loud, so you know that you really know it!) how to know where you can work backwards and where you shouldnt try.

If you dont already know how to work backwards, just go ahead and try both problems however youd like and then well learn all about this strategy.

Ready? Set your timer for 4 minutes and Go!

*If [pmath](2^x)(2^y) = 8[/pmath] and [pmath](9^x)(3^y) = 81[/pmath], then [pmath](x, y) =[/pmath](A) (1, 2)

(B) (2, 1)

(C) (1, 1)

(D) (2, 2)

(E) (1, 3)

If [pmath]x^2= 2y^3[/pmath] and [pmath]2y = 4[/pmath], what is the value of [pmath]x^2+ y[/pmath] ?(A) -14

(B) -2

(C) 3

(D) 6

(E) 18

Okay, what do you think? Dont just keep reading. Take a stand noweven if youre not sure, just guess. (That goes for your actual answers and what you think re: when to work backwards.) Making yourself take a guess invests you more in the outcomeand helps you to better retain what youre about to learn.

Lets do this!

Were going to do the first one first. Glance at the problem. PS. Exponents. Glance at the answers pairs? Is this like coordinate plane or something?

Read. No, its not actually geometryits just writing the *x* and *y* answers this way. Jot down the given equations.

Note that I didn't repeat the parentheses in the equations when I jotted this down because Im confident that I wont make a mistake by removing them. (Though I could make a different mistake!) If you arent confident about that, then keep using the parentheses.

All right, lets think about what weve got here.

Variables in the exponents. I can solve algebraically by getting the bases on each side to be equal and then dropping the bases and setting the exponents equal to each other. Anything else?

Glance at those answers again. Theres something pretty awesome about them.

First, the answers actually give you the possible values for the only two variables in this problem, [pmath]x[/pmath]and [pmath]y[/pmath]. This is the classic sign that you can work backwards, if you want to: The answer choices give you the actual value for at least one discrete variable in the problem.

But, in this case, it gets even better! In order to work backwards, you *have* to have that first criterion (actual value for one discrete variable), but there are additional criteria that make the problem easier to do this way. First, the values should be nice numberstheyre not too hard to plug back into the problem. In this case, the possibilities are 1, 2, and 3 as nice as it gets. :)

Second, tell me what the possible values for [pmath]x[/pmath] are.

Check it out! Although there are 5 answer choices, there are only 2 distinct possibilities for [pmath]x[/pmath]: 1 or 2. Just try them both and youll be done in about 1 minute.

[pmath]{2^1}{2^y}= 8[/pmath]

[pmath]2^y= 4[/pmath]

[pmath]y = 2[/pmath]

For the first equation, when [pmath]x = 1[/pmath], [pmath]y = 2[/pmath], which matches answer (A). Is that actually the correct answer?

Try the numbers in the second equation to see. If they work, answer (A) is correct. If they dont, then [pmath]x[/pmath] must equal 2, and youll have to plug into one of the two equations to find out what [pmath]y[/pmath] equals.

[pmath]{9^x}{3^y}= 81[/pmath]

[pmath]{9^1}{3^2}= 81[/pmath]

[pmath]9*9 = 81[/pmath] CORRECT!

The pairing (1, 2) does work for the second equation, so the correct answer is (A).

You can of course also solve this problem algebraically, and the algebra is not super hard on this one. But given that you only have to try a *maximum* of two numbersand that those two numbers are 1 and 2working backwards should still be a serious consideration.

Since I told you at the beginning that only one problem could be done by working backwards, you now know that you cant use this technique for the second one. Why? Use what youve learned so far to articulate the answer to my question, then join me next time, when well dive into the full solution!

## Key Takeaways for Knowing the Code:

(1) If the answers give you possible values for (at least) one discrete variable in the problem, then you can work backwards. Should you? If the numbers are also nice numbers for the problem, then you should seriously consider it. :)

(2) Practice working backwards enough that you learn how to spot other signs that WB is a great strategy for a particular problem. In this case, the paired answers meant that we had to try only 2 (really easy) numbersdoesnt get a lot better than that. Even if you felt fine doing this one algebraically, that *lesson* is a great lesson to learn so that you know how to spot this characteristic on harder problems in future.

(3) Turn that knowledge into Know the Code flash cards:

* GMATPrep questions courtesy of the Graduate Management Admissions Council. Usage of this question does not imply endorsement by GMAC.

###### Recent Articles

###### Archive

- February 2020
- January 2020
- December 2019
- November 2019
- October 2019
- September 2019
- August 2019
- July 2019
- June 2019
- May 2019
- April 2019
- March 2019
- February 2019
- January 2019
- December 2018
- November 2018
- October 2018
- September 2018
- August 2018
- July 2018
- June 2018
- May 2018
- April 2018
- March 2018
- February 2018
- January 2018
- December 2017
- November 2017
- October 2017
- September 2017
- August 2017
- July 2017
- June 2017
- May 2017
- April 2017
- March 2017
- February 2017
- January 2017
- December 2016
- November 2016
- October 2016
- September 2016
- August 2016
- July 2016
- June 2016
- May 2016
- April 2016
- March 2016
- February 2016
- January 2016
- December 2015
- November 2015
- October 2015
- September 2015
- August 2015
- July 2015
- June 2015
- May 2015
- April 2015
- March 2015
- February 2015
- January 2015
- December 2014
- November 2014
- October 2014
- September 2014
- August 2014
- July 2014
- June 2014
- May 2014
- April 2014
- March 2014
- February 2014
- January 2014
- December 2013
- November 2013
- October 2013
- September 2013
- August 2013
- July 2013
- June 2013
- May 2013
- April 2013
- March 2013
- February 2013
- January 2013
- December 2012
- November 2012
- October 2012
- September 2012
- August 2012
- July 2012
- June 2012
- May 2012
- April 2012
- March 2012
- February 2012
- January 2012
- December 2011
- November 2011
- October 2011
- September 2011
- August 2011
- July 2011
- June 2011
- May 2011
- April 2011
- March 2011
- February 2011
- January 2011
- December 2010
- November 2010
- October 2010
- September 2010
- August 2010
- July 2010
- June 2010
- May 2010
- April 2010
- March 2010
- February 2010
- January 2010
- December 2009
- November 2009
- October 2009
- September 2009
- August 2009