If x# = x(x + 3), what is the value of x##

Question

(A) x(x + 3)

(B) (x(x + 3))^2

(C) x(x + 3)(x^2 + 3x + 3)

(D) x(x + 3)(x + 4x)

(E) x(x + 3)(x + 6x)

EMPOWERgmatRichC · Accepted Answer

Hi sagarag,

This is an example of "Symbolism" question. We're given a symbol, told what it represents mathematically, then asked to perform a calculation with it. Since we're not given any specific values to work with, we can TEST VALUES.

We're told that X# = X(X+3)

eg
2# = 2(2+3) = 10

We're asked for the value of X##.....notice the second symbol - this means that we have to perform TWO calculations using this Symbol (the RESULT of the first calculation gets put back into the Symbol to get us the second, final result).

IF...X = 2
2## = 2(2+3) = 10
10# = 10(10+3) = 130

So we're looking for an answer that = 130 when X = 2

While these answers look "crazy", notice what they ALL have in common....X(X+3)....We do NOT have to do THAT calculation 5 times; we just have to do it ONCE and plug the result into all 5 answers.

Answer A: 10 is NOT a match
Answer B: 10^2 = 100 is NOT a match
Answer C: 10(13) = 130 IS a MATCH
Answer D: 10(10) = 100 is NOT a match
Answer E: 10(14) = 140 is NOT a match

Final Answer:  C

GMAT assassins aren't born, they're made,
Rich

manpreetsingh86 · Answer

X# = x(x+3)----------------------------1)

now while computing X## , we will put x(x+3) in place of x in equation 1.

thus, 
X## = x(x+3)(x(x+3)+3)
=x(x+3)(x^2+3x+3)

which is option C

PareshGmat · Answer

Answer = C) x(x+3)(x^2+3x+3)

X# =   x  (  x  +3)

To find the value of X##, place x(x+3) in the place of x

X\#\# = x(x+3)  = x(x+3)(x^2 + 3x + 3)

ranaazad · Answer

I don't understand the motif of this question. Nowhere does it ask to put x(x+3) in place of x.

EMPOWERgmatRichC · Answer

Hi ranaazad,

Symbolism questions sometimes ask you to use the given symbol/function more than once. Here, we're asked for the value of X##, which is the same as asking for the value of (X#)#. If you're going to approach this question algebraically, since X# = X(X+3), so you would then have to plug in "X(X+3)" into the symbol again (for the second part of the calculation) to answer the given question. You would likely find TESTing VALUES to be an easier approach.

GMAT assassins aren't born, they're made,
Rich

ranaazad · Answer

I started in the algebraic way and ended up nowhere because I didn't understand what the question was asking. Thank you for making it clear now

+1

AkshdeepS · Answer

Tricky :

Let us get it stepwise ;

Question : X## = ?

Break it : (X#)#

Solve the bracket part first:

X# = x(x+3)

Now , (X#)# = x(x+3)

x(x+3)(x^2+3x+3)

(C)

RusskiyLev · Answer

If we use 1 instead of 2, then X# = X (X + 3) = 1 * (1 + 3) = 1 * 4 = 4
In this case, X## = 4# = 4 * (4 + 3) = 4 * 7 = 28

Checking option C: X## = X (X + 3) (X^2 + 3X + 3) = 4 * (1^2 + 3 * 1 + 3) = 4 * 7 = 28
Checking option E: X## = X (X + 3) (X + 6X) = 4 * (1 + 6 * 1) = 4 * (1 + 6) = 4 * 7 = 28

In this case 2 options are suitable as you can see from an example above. What is your advice for this case?

EMPOWERgmatRichC · Answer

Hi RusskiyLev,

When dealing with a PS question - and you're TESTing VALUES - it's generally a good idea to NOT use 0 or 1. You've actually discovered the big reason why with your example: more than one answer appears to be correct. Here, one of those 2 answers IS the correct one - so if you were low on time, then you could take a guess (knowing that it's a 50/50 shot). However, if you had started with a small number that is NOT 0 or 1 (in my explanation, I used X=2), then you can get the correct answer on the first try.

It's worth noting that some PS questions (for example, certain Number Property questions) are designed so that you'll have to do a little more work to get to the correct answer - so having more than one answer 'match' what you're looking for isn't necessary a bad outcome (it might be a built-in part of how the question was written).

GMAT assassins aren't born, they're made,
Rich

kitipriyanka · Answer

Given: X# = x(x+3).....1
Find: X##?

Say X#=y
then y=x(x+3) ....2

now, we need to find y#
then replacing x in 1 with y
we get, y#=x(x+3)(x(x+3) +3)
y#=  x(x+3)(x^2+3x+3)

Hence C

kntombat · Answer

Bunuel ,  VeritasKarishma ,  chetan2u  
Could either of you explain how to solve this question algebraically, I solved it using values but would love to know the algebraic approach also.

thanks.

chetan2u · Answer

Hi  kntombat  
Algebraic way would again be very simple. 
In step II just substitute x(x+3) for x. 
x#=x(x+3)....

Step I :
x##=(x#)#=(x(x+3))#
Step II
Now substitute x as x(x+3)
So (x(x+3))#=(x(x+3))(x(x+3)+3)=x(x+3)(x^2+3x+3)

C

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

If x# = x(x + 3), what is the value of x##

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

If x# = x(x + 3), what is the value of x##

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards