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31 Dec 2020, 20:30
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
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Question Stats:
17% (02:52) correct
83%
(03:02)
wrong
based on 169
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Not Attempted Yet
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.
(A) Statement 1 alone is sufficient, but statement 2 alone is not.
(B) Statement 2 alone is sufficient, but statement 1 alone is not.
(C) Both statements together are sufficient, but neither alone is sufficient.
(D) Each statement alone is sufficient.
(E) Neither statement is sufficient, even when combined.
(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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(A) Statement 1 alone is sufficient, but statement 2 alone is not.
(B) Statement 2 alone is sufficient, but statement 1 alone is not.
(C) Both statements together are sufficient, but neither alone is sufficient.
(D) Each statement alone is sufficient.
(E) Neither statement is sufficient, even when combined.
02 Jan 2021, 10:22
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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.
(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.
01 Jun 2022, 05:41
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TarunKumar1234
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?
02 Jun 2022, 03:06
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Kushchokhani
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.
