If x/y = 2/5, then which of the following must be true?
I. y + x = 7.
II. (x + y)/x = 7/2.
III. y^2/x^2 = 25/4.
(A) I only
(B) I and II only
(C) I and III only
(D) II and III only
(E) I, II and III
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x/y = 2/5
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sanju09
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limestone
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first, x/y = 2/5 it means y/x = 5/2
I. x + y = 7 just true only when x = 2, y =5, what if x =4, y = 10? or x = a*2, y = a*5 ( a is not 1) => not a "must-be"
II. (x+y)/x = x/x + y/x = 1 + 5/2 = 7/2, so this is a "must-be"
III. y/x = 5/2, hence (y/x)^2 = (5/2)^2, or y^2/x^2 = 5^2/2^2 = 25/4, another "must-be".
IMO, the answer is D.
Thanks sanju09 for this question.
I. x + y = 7 just true only when x = 2, y =5, what if x =4, y = 10? or x = a*2, y = a*5 ( a is not 1) => not a "must-be"
II. (x+y)/x = x/x + y/x = 1 + 5/2 = 7/2, so this is a "must-be"
III. y/x = 5/2, hence (y/x)^2 = (5/2)^2, or y^2/x^2 = 5^2/2^2 = 25/4, another "must-be".
IMO, the answer is D.
Thanks sanju09 for this question.
quick ans.
x/y = 2/5
here x can be 2 or 4 , y can be 5 or 10
now statement I
y + x = 7
as we see from the statement here ans can be both 7 or other figure,let's say 4+10.
that's why stament I don't have 1 answer.
eliminate I from ans choices , only D remains.
x/y = 2/5
here x can be 2 or 4 , y can be 5 or 10
now statement I
y + x = 7
as we see from the statement here ans can be both 7 or other figure,let's say 4+10.
that's why stament I don't have 1 answer.
eliminate I from ans choices , only D remains.
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Scott@TargetTestPrep
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We are given that x/y = 2/5, and need to determine what must be true.sanju09 wrote:If x/y = 2/5, then which of the following must be true?
I. y + x = 7.
II. (x + y)/x = 7/2.
III. y^2/x^2 = 25/4.
(A) I only
(B) I and II only
(C) I and III only
(D) II and III only
(E) I, II and III
I. y + x = 7
This is not true. If x = 2 and y = 5, then x + y = 7; however, if x = 4, and y = 10, then x + y does not equal 7.
(Notice that x and y do not have to equal 2 and 5, respectively; if they were to equal 4 and 10, respectively, the fraction x/y would would equal 4/10, which would reduce to 2/5.)
II. (x + y)/x = 7/2
This is true since:
(x + y)/x = x/x + y/x = 1 + 5/2 = 7/2
(Notice that if x/y = 2/5, then y/x = 5/2.)
III. y^2/x^2 = 25/4
This is true. Recall that in II, we've mentioned y/x = 5/2. Thus, y^2/x^2 = (y/x)^2 = (5/2)^2 = 25/4,
Answer: D
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