GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 10 Dec 2018, 11:55

# Dec 10th is GMAT Club's BDAY :-)

Free GMAT Club Tests & Quizzes for 24 hrs to celebrate together!

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

## Events & Promotions

###### Events & Promotions in December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
• ### Free lesson on number properties

December 10, 2018

December 10, 2018

10:00 PM PST

11:00 PM PST

Practice the one most important Quant section - Integer properties, and rapidly improve your skills.
• ### Free GMAT Prep Hour

December 11, 2018

December 11, 2018

09:00 PM EST

10:00 PM EST

Strategies and techniques for approaching featured GMAT topics. December 11 at 9 PM EST.

# If x and y are integers, what is the value of 2x^(6y) - 4?

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 51072
If x and y are integers, what is the value of 2x^(6y) - 4?  [#permalink]

### Show Tags

11 Nov 2017, 07:01
00:00

Difficulty:

35% (medium)

Question Stats:

71% (01:23) correct 29% (02:00) wrong based on 94 sessions

### HideShow timer Statistics

If x and y are integers, what is the value of $$2x^{(6y)} - 4$$?

(1) $$x^{(2y)} = 16$$

(2) $$xy = 4$$

_________________
PS Forum Moderator
Joined: 25 Feb 2013
Posts: 1217
Location: India
GPA: 3.82
Re: If x and y are integers, what is the value of 2x^(6y) - 4?  [#permalink]

### Show Tags

11 Nov 2017, 07:08
2
Bunuel wrote:
If x and y are integers, what is the value of $$2x^{(6y)} - 4$$?

(1) $$x^{(2y)} = 16$$

(2) $$xy = 4$$

Statement 1: $$x^{(2y)} = 16$$, cube both sides to get

$$x^{(6y)} = 16^3$$. we got the value of the variable. hence we can calculate the value of the equation. Sufficient

Statement 2: Two variables and one equation. Cannot be solved. Hence Insufficient

Option A
Intern
Joined: 30 Sep 2017
Posts: 38
Location: India
Concentration: Entrepreneurship, General Management
Schools: IIM Udaipur '17
GMAT 1: 700 Q50 V37
GPA: 3.7
WE: Engineering (Energy and Utilities)
Re: If x and y are integers, what is the value of 2x^(6y) - 4?  [#permalink]

### Show Tags

14 Nov 2017, 20:13
Statement 1: x^(2y)=16, cube both sides to get

x^(6y)=16^3. Hence 2*x^(6y)-4 = 2*16^3-4. Sufficient

Statement 2: xy = 4; possible values are (2,2), (1,4), (4,1). Each gives different answers. So insufficient.

_________________

If you like my post, motivate me by giving kudos...

Intern
Joined: 25 Mar 2016
Posts: 40
Location: India
Concentration: Finance, General Management
WE: Other (Other)
Re: If x and y are integers, what is the value of 2x^(6y) - 4?  [#permalink]

### Show Tags

16 Nov 2017, 10:03
Bunuel wrote:
If x and y are integers, what is the value of $$2x^{(6y)} - 4$$?

(1) $$x^{(2y)} = 16$$

(2) $$xy = 4$$

given expression an be deduced to 2*x^(2y)^3 -4

From statement 1 we can find the value of x^(2y)

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6614
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: If x and y are integers, what is the value of 2x^(6y) - 4?  [#permalink]

### Show Tags

18 Nov 2017, 15:33
Bunuel wrote:
If x and y are integers, what is the value of $$2x^{(6y)} - 4$$?

(1) $$x^{(2y)} = 16$$

(2) $$xy = 4$$

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.
Since we have 2 variables and 0 equations, C is most likely to be the answer and so we should consider both conditions 1) & 2) together first.

By CMT(Common Mistake Type) 4(A), we need to consider A or B as an answer.

Condition 1)
Since $$x^2y = 16$$, $$x^6y = (x^2y)^3 = 16^3$$ and so $$2x^6y - 4 = 2\cdot16^3-4$$.
This is sufficient.

Condition 2)
$$xy = 4$$.
From $$xy = 4$$, we have $$(2,2)$$, $$(-2,-2)$$, $$(1,4)$$, $$(-1,-4)$$, $$(4,1)$$ and $$(-4,-1)$$ as pairs of $$(x,y)$$.
$$x^{6y} = 2^{12} = 2048$$ for $$x=2$$, $$y=2$$
$$x^{6y} = 1^{24} = 1$$ for $$x=1$$,$$y=4$$.
Since we don't have unique solutions, this is not sufficient.

Normally, in problems which require 2 or more additional equations, such as those in which the original conditions include 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, each of conditions 1) and 2) provide an additional equation. In these problems, the two key possibilities are that C is the answer (with probability 70%), and E is the answer (with probability 25%). Thus, there is only a 5% chance that A, B or D is the answer. This occurs in common mistake types 3 and 4. Since C (both conditions together are sufficient) is the most likely answer, we save time by first checking whether conditions 1) and 2) are sufficient, when taken together. Obviously, there may be cases in which the answer is A, B, D or E, but if conditions 1) and 2) are NOT sufficient when taken together, the answer must be E.
_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only \$99 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Re: If x and y are integers, what is the value of 2x^(6y) - 4? &nbs [#permalink] 18 Nov 2017, 15:33
Display posts from previous: Sort by