confused with this DS

Expert replies

gmatwarroom: Junior | Next Rank: 30 Posts; Posts: 12; Joined: Sat May 05, 2012 11:27 am; Thanked: 1 times

by gmatwarroom » Wed Sep 26, 2012 2:42 pm

Here is DS question:

If x is an integer and 4 power x < 100, what is x?

(1) 4 power (x + 1) - 4 power (x - 1) > 100
(2) 4 power (x + 1) + 4 power x > 100

My answer was E) but actual answer says each one is sufficient.

My approach:
from given that 4 power x < 100 ==> x < or = 3

1) derives finally that x > or = 3
2) derives finally that x > or = 3

Now, dont understand how each would suffice?? I know, it's given that x < or =3 but combined with 1), how can I infer that x =3 ???????

any help to explain it

Like this post

Source: Beat The GMAT — Data Sufficiency | Wed Sep 26, 2012 2:42 pm

anuprajan5: Master | Next Rank: 500 Posts; Posts: 279; Joined: Mon Jun 25, 2012 10:56 pmFollowed by: 10 members; Thanked: 60 times

by anuprajan5 » Wed Sep 26, 2012 10:24 pm

Hi,

Question states that 4 power x < 100 which means that x < = 3

Statement 1- 4 power (x + 1) - 4 power (x - 1) > 100

Simplifying,
4 power x * 15 > 400
4 power x > 80/3
or 4 power x > 26,6

and the only integer value of x which satisfies that and the condition in the question is 3.

Statement 2 - 4 power (x + 1) + 4 power x > 100

Simplifying
4 power x > 20

and the only integer value of x which satisfies that and the condition in the question is 3.

hence answer D

Regards
Anup

Like this post

neelgandham: Community Manager; Posts: 1060; Joined: Fri May 13, 2011 6:46 amFollowed by: 52 members; Location: Utrecht, The Netherlands; Thanked: 318 times

by neelgandham » Thu Sep 27, 2012 12:24 am

If x is an Integer and if (4^x)<100, what is x?

4^x < 100 < 4^4
x < 4.

The question can be rephrased to "If Integer x < 4, then what is the value of x ?"

(1) 4^(x + 1) - 4^(x - 1) > 100

4^(x + 1) - 4^(x - 1) > 100
[4^x * 4^1] - [4^x - 4^-1] > 100 > 64
4^x *[4-(1/4)] > 4^3
4^x * 15/4 > 4^3
4^x * 15 > 4^4
15 > 4^(4-x)
16 > 15 > 4^(4-x)
4^2 > 4^(4-x)
2 > 4-x
x > 2. We already know that x < 4 and x is an integer. So 3 is the only value of x between 2 and 4.
So statement I is sufficient to answer the question.

(2) 4^(x + 1) + 4^ x > 100

4^(x + 1) + 4^ x > 100 > 64
4^x [4+1] > 100
4^x > 20
4^x > 20 > 16
4^x > 16
4^x > 4^2
x > 2. We already know that x < 4 and x is an integer. So 3 is the only value of x between 2 and 4.
So statement II is sufficient to answer the question.

p.s: I tried to explain each step in detail for the benefit of the members who requested me to solve in detail.

Anil Gandham
Welcome to BEATtheGMAT | Photography | Getting Started | BTG Community rules | MBA Watch
Check out GMAT Prep Now's online course at https://www.gmatprepnow.com/

Like this post

LalaB: Master | Next Rank: 500 Posts; Posts: 425; Joined: Wed Dec 08, 2010 9:00 amFollowed by: 7 members; Thanked: 56 times; GMAT Score:690

by LalaB » Thu Sep 27, 2012 7:40 am

1)
4^(x+1)-4^(x-1)>100

4^(x+1)-4^x/4>100

(4^x)*4*4-4^x>400
4^x(16-1)>400
(4^x)*15> 400
26<4^x<100

x=3

2) 4^(x + 1) + 4^x > 100

4^x(4+1)>100
4^x>20

20<4^x<100
x=3
ans is D

Happy are those who dream dreams and are ready to pay the price to make them come true.(c)

In order to succeed, your desire for success should be greater than your fear of failure.(c)

Like this post

gmatwarroom: Junior | Next Rank: 30 Posts; Posts: 12; Joined: Sat May 05, 2012 11:27 am; Thanked: 1 times

by gmatwarroom » Sat Sep 29, 2012 10:53 am

thanks everyone for solving the equations.

However, my issue was not really "solving" each of the equations but solving the problem i.e. deriving the conclusion.

As I mentioned, I was able to derive
Given: x < or = 3 (i.e. 3,2,1....)
statement 1) derives finally that x > or = 3 (i.e. 3,4,5...)

what I was confused with (and unfortunately still is) that, how it would mean that I should take the common value (of "Given" and "Statement 1"), which is 3, as the answer -- ??
Seems I am missing something basic about DS problem

Like this post

anuprajan5: Master | Next Rank: 500 Posts; Posts: 279; Joined: Mon Jun 25, 2012 10:56 pmFollowed by: 10 members; Thanked: 60 times

by anuprajan5 » Sat Sep 29, 2012 12:27 pm

Hi,

Well the given condition and the statement give you the parameters that you have to work with. The statement is only sufficient if it along with the given information can conclusively answer the question.

Taking your statements:

Given: x < or = 3 (i.e. 3,2,1....) - a
statement 1) derives finally that x > or = 3 (i.e. 3,4,5...) - b

The only way both a and b are possible is if x = 3. (the commonality). Since we can conclude that we get only 1 value for x, this means that the condition in the question and the statement are sufficient to answer the question.

Regards
Anup

Like this post

gmatwarroom: Junior | Next Rank: 30 Posts; Posts: 12; Joined: Sat May 05, 2012 11:27 am; Thanked: 1 times

by gmatwarroom » Sat Sep 29, 2012 1:25 pm

The statement is only sufficient if it along with the given information can conclusively answer the question.

I think, I would rephrase it to make it more understandable --
The statement is only sufficient if it along with the given information can get UNIQUE value/answer to the question.

Also, I think I kind of understood my confusion -- I was confused with the fact that both "Given" and "Statement" separately was having multiple values of "x".

The point that I should look for is that, if "Given" and "Statement" together gives "UNIQUE" answer/value or not -- and that made me understand it.

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

560 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review