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Question

A journalist is writing an article on the 100 members of the United States Senate. After researching her article, the journalist classifies the Senators into one of four categories: men who have earned at least one college degree, men who have not earned a college degree, women who have earned at least one college degree, and women who have not earned a college degree. How many Senators are men who have earned at least one college degree?

(1) The number of women who have not earned a college degree is 30 percent less than the number of men who have not earned a college degree, and the number of men who have not earned a college degree is 25 percent less than the number of women who have earned a college degree.

(2) The number of women who have not earned a college degree is 70 percent of the number of men who have not earned a college degree, and the number of men who have earned at least one college degree is 30 percent of the number of men who have not earned a college degree.

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Deepakjhamb · Answer

answer is a ) first statement alone is sufficient

for statement 1 : by matrix method we get

eq as 34x +35y = 100 which can have either 1 or 2 solutions by Diphantine equation analysis

we see that it can have only 1 solution that is x = 30 and y = 28 anything else will go into negative for other direction in trade -off method

so eq 1 is sufficient

statement 2 clearly insufficient

actually i would say there seems to be a subtle ambiguity in the question as statement 1 has language below :

the number of men who have not earned a college degree is 25 percent less than the number of women who have earned a college degree.

now the interpretation that it means exactly 1 college degree or at least 1 can actually change the solution for this question.
i took first interpretation as a college degree would definitely include people with atleast 1 college degree . but if we assume it be exactly 1 college degree the answer would turn out to be something else

ananya3 · Answer

IMO C

total = 100
find: MD= ??

(1) The number of women who have not earned a college degree is 30 percent less than the number of men who have not earned a college degree, and the number of men who have not earned a college degree is 25 percent less than the number of women who have earned a college degree.
MND = X
WND = 0.7 * X
WD = X/0.75
but the number of total men and total women are not given 
 Not Sufficient

(2) The number of women who have not earned a college degree is 70 percent of the number of men who have not earned a college degree, and the number of men who have earned at least one college degree is 30 percent of the number of men who have not earned a college degree.
MND = X
WND = 0.7 * X
MD = 0.3X
but the number of total men and total women are not given 
 Not Sufficient

combining 1 and 2
MND = X
WND = 0.7 * X
MD = 0.3X
WD = X/0.75

100 = 0.3X + x/0.75 +X + 0.7 X
100 = 2X + 4X/3
100 = 10X/3
X = 30 
0.3X = 9

Sufficient

rocky620 · Answer

Let,
Men with degree = md
Men without degree = mnd
Women with degree = wd
Women without degree = wnd

We are given =  md+mnd+wd+wnd = 100 ....... .eq1 
we have to find  md

(1) The number of women who have not earned a college degree is 30 percent less than the number of men who have not earned a college degree, and the number of men who have not earned a college degree is 25 percent less than the number of women who have earned a college degree.

wnd = .70mnd........ eq-2 
mnd = .75wd......... eq-3 
so, wnd = .70*.75wd

Putting these values in eq1, md+.75wd+wd+.70*.75wd = 100
2 variables 1 eq.

Insufficient

(2) The number of women who have not earned a college degree is 70 percent of the number of men who have not earned a college degree, and the number of men who have earned at least one college degree is 30 percent of the number of men who have not earned a college degree.

wnd=.70mnd
md=.30mnd

Putting these values in eq1

.30mnd+mnd+wd+.70mnd = 100
2mnd+wd = 100...... eq4

Insufficient

Combining 1&2
Putting value of mnd from eq3 in eq4

1.5wd+wd=100
2.5wd=100 =>  wd=40 
From eq3, mnd=.75wd => mnd=.75*40=30 
From eq2, wnd=.70mnd =>  wnd=.70*30=21

Putting all these values in eq1.

md=9 .

Sufficient

IMO Option C

Green2k1 · Answer

Correct Answer C

A journalist is writing an article on the 100 members of the United States Senate. After researching her article, the journalist classifies the Senators into one of four categories: men who have earned at least one college degree, men who have not earned a college degree, women who have earned at least one college degree, and women who have not earned a college degree. How many Senators are men who have earned at least one college degree?

Total: 100
 ------Men with >1 degree----------Men with no degree--------Women with >1 degree----------Women with no degree

(1) The number of women who have not earned a college degree is 30 percent less than the number of men who have not earned a college degree, and the number of men who have not earned a college degree is 25 percent less than the number of women who have earned a college degree.
 Total: 100
 ------Men with >1 degree----------Men with no degree--------Women with >1 degree----------Women with no degree
--------Z---------------------------------x or 0.75y---------------------------------y------------------------------0.7x
one equation z and x or y - unknown
- not sufficient

(2) The number of women who have not earned a college degree is 70 percent of the number of men who have not earned a college degree, and the number of men who have earned at least one college degree is 30 percent of the number of men who have not earned a college degree.

Total: 100
 ------Men with >1 degree----------Men with no degree--------Women with >1 degree----------Women with no degree
--------Z or 0.3x---------------------------------x -------------------------------------y------------------------------0.7x
one equation y and x or z - unknown
- not sufficient
 
 Together
Two equation 2 can be simplified in 2 variable terms
sufficient

TarunKumar1234 · Answer

Given, Total no. =100

(1) The number of women who have not earned a college degree is 30 percent less than the number of men who have not earned a college degree, and the number of men who have not earned a college degree is 25 percent less than the number of women who have earned a college degree.

Men without degree=x (say), So, women without degree=0.7*x, women with degree=4/3*x, men with degree=y (say)
So, y+x+0.7*x + 4/3*x = 100 or, 9.1*x +3*y= 300 or, 91*x+30*y=3000, now, (x,y)= (0,100) or (30,9). but atleast, there should be a value of x so, x=0 (not possible) Sufficient.

(2) The number of women who have not earned a college degree is 70 percent of the number of men who have not earned a college degree, and the number of men who have earned at least one college degree is 30 percent of the number of men who have not earned a college degree.

Men without degree=x (say), So, women without degree=0.7*x, men with degree=0.3*x, women with degree=y (say)
So, 0.3*x+x+y+0.7*x = 100 or, 2*x +y= 100; now, (x,y)= (0,100) or (1,98) or (2,96)....... Not sufficient.

So, I think A.

Kushchokhani · Answer

Deepakjhamb

Can you please elaborate your calculations? It is very hard to understand by just what you have stated here.

Kushchokhani · Answer

TarunKumar1234

How did you arrive at the values of (x,y)? Please let us know your approach. TIA.

Bunuel   chetan2u

Can you please help solving this ques?

chetan2u · Answer

91x+30y=3000 or 91x=3000-30y=30(100-y)

There are no shortcut methods but a bit of analysis of equation may help us.

1) x and y are integers as we are talking of number of men or women. 
2) 91 has no common factors with 30, so x has to be a multiple of 30, so 0, 30, 60… But as 91x<3000, x cannot be greater than 30
So x can be 0 or 30.
This means 91*0=30(100-y), that is y=100. (0,100)
Or, 91*30=30(100-y), that is y=9. (30,9)
No other possibilities

Also, 100-y has to be a multiple of 91. Thus y has to be 9, and we could find x accordingly.

Kushchokhani · Answer

A small correction- brackets should read (30,9) instead of (9,100)

Further, we can alternatively calculate as below:

Women with degree=x (say), So, men without degree=3/4*x, women without degree=3/4*7/10*x, men with degree=y (say)
So, y+x+3/4*x + 3/4*7/10*x = 100 or, 91/40*x + y= 100 or, 91*x+40*y=4000, so, (x,y)= (40,9).

In this alternative calculation, value of x is different from the quoted value.  chetan2u  Can you please check whether I have committed any error?

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