Please provide solutions for these set of DS questions.

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snakedoc: Junior | Next Rank: 30 Posts; Posts: 13; Joined: Fri Nov 19, 2010 5:56 pm; Thanked: 4 times

by snakedoc » Thu Dec 15, 2011 10:55 pm

1) What is GCD of positive integers m and n?
a. m is a prime number
b. 2n = 7m

2) Each employee of company Z is employed in either Division X or Division Y, but not both. If each division has some part time employees, is the ratio of the number of full-time employees to number of part-time employees greater for Division X than for Company Z?
a. Ratio of number of full time employees to part-time employees is less for division Y than for company Z
b. More than Â½ of full-time employees of company Z are employees of div X, and more than Â½ of part-time employees of company Z are employees of div Y

3) Is m + z > 0
a. m - 3z > 0
b. 4z - m > 0

4) When 1000 kids were inoculated, some got inflammation, others got fever. How many developed inflammation but not fever.
a. 880 developed neither inflammation nor fever
b. 20 children developed fever

5) Linda put money in two investments A and B which paid simple interest. If annual interest rate of investment B is 1Â½ times that of A, what amount did Linda put into A?
a. Interest for 1 year is $50 for A and %150 for B
b. Linda put twice the amount of A into B

6) How many odd integers are greater than integer x and less than integer y?
a. There are 12 even integers greater than x and less than y
b. There are 24 integers greater than x and less than y

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Source: Beat The GMAT — Data Sufficiency | Thu Dec 15, 2011 10:55 pm

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by Anurag@Gurome » Thu Dec 15, 2011 11:36 pm

snakedoc wrote: 2) Each employee of company Z is employed in either Division X or Division Y, but not both. If each division has some part time employees, is the ratio of the number of full-time employees to number of part-time employees greater for Division X than for Company Z?
a. Ratio of number of full time employees to part-time employees is less for division Y than for company Z
b. More than Â½ of full-time employees of company Z are employees of div X, and more than Â½ of part-time employees of company Z are employees of div Y

Let us assume number of full-time employees for division X = Xf
Number of part-time employees for division X = Xp
Number of full-time employees for division Y = Yf
Number of part-time employees for division Y = Yp

Then question is: Is Xf/Xp > (Xf + Yf)/(Xp + Yp)? or is XfXp + XfYp > XpXf + XpYf? or is XfYp > XpYf?

(1) (Xf + Yf)/(Xp + Yp) > Yf/Yp
XfYp + YfYp > XpYf + YpYf
XfYp > XpYf, which answers the required question; SUFFICIENT.

(2) (Xf + Yf)/2 < Xf and (Xp + Yp)/2 < Yp
Yf < Xf and Xp < Yp, which implies XpYf < XfYp, which again answers the required question; SUFFICIENT.

The correct answer is D.

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by Anurag@Gurome » Thu Dec 15, 2011 11:37 pm

snakedoc wrote: 3) Is m + z > 0
a. m - 3z > 0
b. 4z - m > 0

(1) m - 3z > 0 implies m > 3z. But this is NOT SUFFICIENT to say whether m + z > 0.

(2) 4z - m > 0 implies m < 4z. Again this is NOT SUFFICIENT to say whether m + z > 0.

Combining (1) and (2), add both the inequalities, z > 0
Since m > 3z so m is also > 0
Therefore, m + z > 0.
SUFFICIENT.

The correct answer is C.

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by Anurag@Gurome » Thu Dec 15, 2011 11:46 pm

snakedoc wrote:1) What is GCD of positive integers m and n?
a. m is a prime number
b. 2n = 7m

(1) m is a prime number implies that it has 2 divisors, 1 and m, so GCD of m and n is either 1 or m.
No definite answer; NOT sufficient.

(2) 2n = 7m implies n = 7m/2
If m = 5, then n = 35/2
If m = 3, then n = 21/2
So, when m is odd, n will not be an integer.
This means m has to be an even integer for n to be an integer.

If m = 2, then n = 7; here GCD of m and n = 1
If m = 4, then n = 14; here GCD of m and n = 2
No definite answer; NOT sufficient.

Combining (1) and (2), we know that m is an even prime, and 2 is the only prime number that is even, so m = 2 and n = 7.
Hence GCD of 2 and 7 = 1; SUFFICIENT.

The correct answer is C.

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by Anurag@Gurome » Thu Dec 15, 2011 11:55 pm

snakedoc wrote:4) When 1000 kids were inoculated, some got inflammation, others got fever. How many developed inflammation but not fever.
a. 880 developed neither inflammation nor fever
b. 20 children developed fever

Let the no. of kids who got inflammation = I
and the no. of kids who got fever = F
We have to find the no. of kids who got only I but not F, only the blue region.

(1) 880 developed neither inflammation nor fever does not give us the relevant info; NOT sufficient.

(2) 20 children had fever but this statement alone is NOT sufficient.

Combining (1) and (2), 1000 = 880 + 20 + I - (both I + F)
100 = I - (both I + F), which means 100 kids had only inflammation but not fever; SUFFICIENT.

The correct answer is C.

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karthikpandian19: Legendary Member; Posts: 1665; Joined: Thu Nov 03, 2011 7:04 pmFollowed by: 70 members; Thanked: 165 times

by karthikpandian19 » Fri Dec 16, 2011 12:31 am

@anurag,

When combining both the statements, why cant this be possible?
m>3z from 1st one
4z>m from 2nd one
So, -4z<m>3z
Which again doesnot gives any solution and "E"can be the answer?????

Can you clarify?

Anurag@Gurome wrote:
snakedoc wrote: 3) Is m + z > 0
a. m - 3z > 0
b. 4z - m > 0

(1) m - 3z > 0 implies m > 3z. But this is NOT SUFFICIENT to say whether m + z > 0.

(2) 4z - m > 0 implies m < 4z. Again this is NOT SUFFICIENT to say whether m + z > 0.

Combining (1) and (2), add both the inequalities, z > 0
Since m > 3z so m is also > 0
Therefore, m + z > 0.
SUFFICIENT.

The correct answer is C.

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rijul007: Legendary Member; Posts: 588; Joined: Sun Oct 16, 2011 9:42 amFollowed by: 9 members; Location: New Delhi, India; Thanked: 130 times; GMAT Score:720

by rijul007 » Fri Dec 16, 2011 1:57 am

karthikpandian19 wrote:@anurag,

When combining both the statements, why cant this be possible?
m>3z from 1st one
4z>m from 2nd one
So, -4z<m>3z
Which again doesnot gives any solution and "E"can be the answer?????

Can you clarify?

Anurag@Gurome wrote:
snakedoc wrote: 3) Is m + z > 0
a. m - 3z > 0
b. 4z - m > 0

(1) m - 3z > 0 implies m > 3z. But this is NOT SUFFICIENT to say whether m + z > 0.

(2) 4z - m > 0 implies m < 4z. Again this is NOT SUFFICIENT to say whether m + z > 0.

Combining (1) and (2), add both the inequalities, z > 0
Since m > 3z so m is also > 0
Therefore, m + z > 0.
SUFFICIENT.

The correct answer is C.

combining the two statements we get
m>3z
m<4z

3z<m<4z
It can be represented in the no line like this

If z less than 0
3z < 4z wont be true

so z has to be +ve
because m lies b/w two positive nos, it too is +ve

hence,
m+z > 0
Sufficient

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rijul007: Legendary Member; Posts: 588; Joined: Sun Oct 16, 2011 9:42 amFollowed by: 9 members; Location: New Delhi, India; Thanked: 130 times; GMAT Score:720

by rijul007 » Fri Dec 16, 2011 2:08 am

snakedoc wrote:6) How many odd integers are greater than integer x and less than integer y?
a. There are 12 even integers greater than x and less than y
b. There are 24 integers greater than x and less than y

a. There are 12 even integers greater than x and less than y

lets say
x= 1 and y= 26
no of even integers > x and <y = 12
no of odd integers >x and <y = 12

another possible case
x = 1 and y = 25
no of even integers > x and <y = 12
no of odd integers >x and <y = 11

Insufficient

b. There are 24 integers greater than x and less than y

x = 1, y= 25

no of even integers > x and <y = 12
no of odd integers >x and <y = 11

x=2, y = 26

no of even integers > x and <y = 11
no of odd integers >x and <y = 12

combining the two statements

x = 1, y= 25

no of even integers > x and <y = 12
no of odd integers >x and <y = 11

all similar cases will have 11 odd nos

Option C

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