Data Sufficiency

DS001

If x is positive, is x>3?

a) (x-1)^2 > 4
b) (x-2)^2 > 9

A) a alone b not sufficient
B) b alone a not sufficient
C) both together but not alone sufficient
D) each alone sufficient
E) together not sufficient



Answers In 3 days of time

E.

First case leads to x > 3 or x > -1 => insufficient
Second case leads to x > 5 or x > -1 => insufficient

Both together is still inconclusive x could be a positive number greater or less or equal to 3.

Is it possible to go step by step in breaking down each condition

Im still a little fuzzy on this one.

thanks

Jeff,

Consider (x-1)^2 > 4
which will mean (x-1)^2-4>0
((x-1)+2)((x-1)-2)>0 [using the identity a^2-b^2 =(a+b)(a-b)]
Simplifying,
(x+1)(x-3)>0
now for a product of two terms {(x+1),(x+3)} to be positive
either both x+1 and x-3 to be postive which is possible only when x>3
or both x+1 and x-3 to be negative which is possible only when x<-1

so we can safely conclude that (x-1)^2 > 4 will mean x>3 or x<-1
moving on similar lines we can solve the other inequality also ...
Revert back to me if you have any doubts on this.

As promised, answers in 3 days of time

rajs.kumar wrote:E.

First case leads to x > 3 or x > -1 => insufficient
Second case leads to x > 5 or x > -1 => insufficient

Both together is still inconclusive x could be a positive number greater or less or equal to 3.

I think you have made a mistake there rajs.kumar,

is it x > -1 or x<-1 ?

DS002

What is the value of (2a+b)/(a+b)?

(1) 3a/(a+b) = 7
(2) a+b = 3

A) 1 alone b not sufficient
B) 2 alone a not sufficient
C) both together but not alone sufficient
D) each alone sufficient
E) together not sufficient



Answers In 3 days of time,

Hereafter, when you reply , either quote the question or reply with the question number as there can be overlap.
Thanks,
Ajith

ajith wrote:Jeff,

Consider (x-1)^2 > 4
which will mean (x-1)^2-4>0
((x-1)+2)((x-1)-2)>0 [using the identity a^2-b^2 =(a+b)(a-b)]
Simplifying,
(x+1)(x-3)>0
now for a product of two terms {(x+1),(x+3)} to be positive
either both x+1 and x-3 to be postive which is possible only when x>3
or both x+1 and x-3 to be negative which is possible only when x<-1

so we can safely conclude that (x-1)^2 > 4 will mean x>3 or x<-1
moving on similar lines we can solve the other inequality also ...
Revert back to me if you have any doubts on this.

As promised, answers in 3 days of time

Yes, i see it now. Thanks very much on the details

ajith wrote:DS001

If x is positive, is x>3?

a) (x-1)^2 > 4
b) (x-2)^2 > 9

A) a alone b not sufficient
B) b alone a not sufficient
C) both together but not alone sufficient
D) each alone sufficient
E) together not sufficient



Answers In 3 days of time

3 days are over!

When we solve a we get x>3 or x<-1(refer the above post for explanation)
since x is positive , x>3

So a is sufficient to answer

now conisdering b

(x-2)^2 > 9
=>(x-2+3)(x-2-3)>0
upon solving which we get x>5 or x<-1
since x is positive , x>5

So b is sufficient to answer

so the answer is D. Both alone are sufficient

DS003

How many people are in the second car in a line of three cars?

1. The total number of people in the three cars is one more than the total number of people in the first and third car.

2. There are a total of 7 people in the three cars.

A) 1 alone b not sufficient
B) 2 alone a not sufficient
C) both together but not alone sufficient
D) each alone sufficient
E) together not sufficient

:roll:

ajith wrote:

rajs.kumar wrote:E.

First case leads to x > 3 or x > -1 => insufficient
Second case leads to x > 5 or x > -1 => insufficient

Both together is still inconclusive x could be a positive number greater or less or equal to 3.

I think you have made a mistake there rajs.kumar,

is it x > -1 or x<-1 ?

I figured where I went wrong. thanks.

(x-1) ^ 2 > 4 => x-1 > 2 or x-1 < -2 and I missed the x is positive. Overlooked.

ajith wrote:DS002

What is the value of (2a+b)/(a+b)?

(1) 3a/(a+b) = 7
(2) a+b = 3

A) 1 alone b not sufficient
B) 2 alone a not sufficient
C) both together but not alone sufficient
D) each alone sufficient
E) together not sufficient



Answers In 3 days of time,

Hereafter, when you reply , either quote the question or reply with the question number as there can be overlap.
Thanks,
Ajith

x = a+b => (a + x)/x =

1. 3a/x = 7 => a = 7x/3

7x/3/x + 1 => suff

2. a+b = 3 = x

(a+3)/3 => insuff

Answer is A.

ajith wrote:DS003

How many people are in the second car in a line of three cars?

1. The total number of people in the three cars is one more than the total number of people in the first and third car.

2. There are a total of 7 people in the three cars.

A) 1 alone b not sufficient
B) 2 alone a not sufficient
C) both together but not alone sufficient
D) each alone sufficient
E) together not sufficient

:roll:

Answer is A.

A+B+C = A+C+1 => suff

ajith wrote:DS003

How many people are in the second car in a line of three cars?

1. The total number of people in the three cars is one more than the total number of people in the first and third car.

2. There are a total of 7 people in the three cars.

A) 1 alone b not sufficient
B) 2 alone a not sufficient
C) both together but not alone sufficient
D) each alone sufficient
E) together not sufficient

:roll:

A baby!

Im pretty sure I got this one

DS002

What is the value of (2a+b)/(a+b)?

(1) 3a/(a+b) = 7
(2) a+b = 3

A) 1 alone b not sufficient
B) 2 alone a not sufficient
C) both together but not alone sufficient
D) each alone sufficient
E) together not sufficient



Ans:
3a/(a+b)=7
=>a/a+b=7/3
=> 1+a/a+b=1+7/3
=>2a+b/a+b=10/7

so 1 is sufficient

it's evident that 2 is not by itself sufficient
so

A

DS004

is |x+y| = 5?

1) |x| = 3
2) |y| = 2