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If x = y, x + y = ? (1) x  y = 4 (2) x/y = 1
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12 Jul 2019, 07:00
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61% (01:28) correct 39% (01:26) wrong based on 325 sessions
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If \(x = y\), \(x + y = ?\) (1) \(x  y = 4\) (2) \(\frac{x}{y} = 1\)
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If x = y, x + y = ? (1) x  y = 4 (2) x/y = 1
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Updated on: 13 Jul 2019, 08:30
Given: x=y Question: x+y=?
Statement 1: x−y=4 Since x=y => x = y or x=y xy=4 x<>y => x=y x=2 & y=2 x+y=0 SUFFICIENT
Statement 2: x/y=−1 x=y x+y=0 SUFFICIENT
IMO D
Originally posted by Kinshook on 12 Jul 2019, 07:16.
Last edited by Kinshook on 13 Jul 2019, 08:30, edited 1 time in total.




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If x = y, x + y = ? (1) x  y = 4 (2) x/y = 1
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Updated on: 13 Jul 2019, 04:33
If x=y, x+y=? Since x and y are equal (note: their absolute values are so), let's pick some easy numbers to work with. ST1 x−y=4 Say x and y are 2 each. 22=0 (NO, must be 4). Does not work Say x and y are (2) each. (2)(2)=0 (NO, must be 4). Does not work Say x is (2) and y is (2). (2)2=4 (NO, must be 4). Does not work Say x is 2 and y is (2). 2(2)=4, yes it works. So 2+(2)= 0. We have an answer. Sufficient.ST2 xy=−1 Let's do similar testing. Say x and y are 2 each. 2/2=1(NO, must be (1)). Does not work Say x and y are (2) each. (2)/(2)=1 (NO, must be (1)). Does not work Say x is (2) and y is (2). (2)/2=1, yes it works. So, we have 2+2=0. We have an answer. Say x is 2 and y is (2). 2/(2)=1, yes it works. So 2+(2)=0. Again, we have an answer. (Although two different sets of value works, both yield the same answer) SufficientHence D
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Originally posted by JonShukhrat on 12 Jul 2019, 08:00.
Last edited by JonShukhrat on 13 Jul 2019, 04:33, edited 2 times in total.



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Re: If x = y, x + y = ? (1) x  y = 4 (2) x/y = 1
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12 Jul 2019, 08:19
Given : x=y Find: x+y? (single value should be available) Analysis: if x=y then, values are required if x= y then, x+y = 0 if x = y then, x+y =0 (1)Statement 1:xy=4 x=y+4 => x not equal to y we know x=y thus, we can have values like x(2), y(2), implying that x+y = 0 Hence, sufficient (ii) Statement 2:x/y = 1 x=y thus, x+y =0 Hence, Sufficient Final Answer D
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Re: If x = y, x + y = ? (1) x  y = 4 (2) x/y = 1
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12 Jul 2019, 08:22
Quote: If x=y, x+y=?
(1) x−y=4
(2) x/y=−1 It is given that x=y. Hence, either x = y or x =  y. We need to find out what is x + y? If x = y, then x + y is 2x or 2y. If x = y, then x + y = 0.Let us analyze the statements separately first and see if it is required to analyze them together. Statement 1:x  y = 4. From this statement we can conclude that x = y + 4, and x is not equal to y. From what we found in the beginning, it means that x = y. In this case, we can substitute y by x and write an equation as x + y = x  x = 0. Statement is sufficient. Statement 2: x/y = 1. From this stament, it can be calculated that x = 1 * y = y. Here, we can solve it in the same way as we did above in analysis of the first statement. Statement 2 is sufficient. As we have both statements sufficient to solve the question, the Answer is D.



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If x = y, x + y = ? (1) x  y = 4 (2) x/y = 1
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12 Jul 2019, 09:11
x=y > x^2 = y^2 > x^2  y^2 = 0 > (xy)(x+y)=0
QUESTION: x+y=?
(1) x−y=4 If (x−y)(x+y)=0 and (x−y)=4, then (x+y) must be 0 (1) is SUFFICIENT
(2) x/y=−1 x/y=−1 > x = −y > x+y = 0 (2) is SUFFICIENT
Correct answer is (D)



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If x = y, x + y = ? (1) x  y = 4 (2) x/y = 1
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12 Jul 2019, 12:24
Given: x=y
Question : x+y=0
St 1: xy = 4 ==> x = 2, y = 2 ==> 2+(2)=0 ===> sufficient since we can't find any other set of numbers that satisfies St 1 and x=y. St 2: \(\frac{x}{y}\)=1 ==> x=y ==> x+y=0 ==> sufficient
Therefore, the answer is D.



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Re: If x = y, x + y = ? (1) x  y = 4 (2) x/y = 1
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12 Jul 2019, 17:26
Statement 1 x=y and xy=4 It implies that x and y gas opposite signs Hence x+y=0 Sufficient
Statement 2 x=y and xy=1 Again we get that x and y are equal in magnitude, but have opposite signs x+y=0 sufficient
IMO D



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Re: If x = y, x + y = ? (1) x  y = 4 (2) x/y = 1
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12 Jul 2019, 19:22
x=y > x = ± y > x = y (or) x = y
(1) x − y = 4 > x & y can have ONLY opposite sign; x is positive & y is negative > x = y y  y = 4 > 2y = 4 > y = 2 > x = (2) = 2
x + y = 2  2 = 0
Sufficient
(2) x/y=−1 > x & y are of same value, BUT opposite sign > x = y
x + y = y + y = 0
Sufficient
IMO Option D
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Re: If x = y, x + y = ? (1) x  y = 4 (2) x/y = 1
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12 Jul 2019, 22:22
If x=y, x+y=? (1) x−y=4, from this we can get that x and y are opposite signs. If they both were negative, zero: 22=2+2=0. If they both were positive aslo xy=0. So we infer that both of them need to be opposite signs and x need to be positive. eg: 22=2+2=4 We have definite answer, sufficient. (2) x/y=−1 from this we get x and y different signs, hence x+y=0, sufficient. D is the answer.
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If x = y, x + y = ? (1) x  y = 4 (2) x/y = 1
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12 Jul 2019, 22:42
If x=y , x+y=?
\(x^2\) = \(y^2\) (squaring both sides) \(x^2\) = \(y^2\) (\(x^2\)\(y^2\)) = 0 (xy)(x+y) = 0 (xy)=0 or (x+y) = 0
STATEMENT (1) x−y=4 this statement tells us that (xy) ≠ 0 then definitely (x+y) = 0 SUFFICIENT
STATEMENT (2) \(\frac{x}{y}\)=−1 \(\frac{x}{y}\)+1 = 0 \(\frac{(x+y)}{y}\)=0 (x+y)=0 (since y cant be equal to zero) SUFFICIENT
D is the answer



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Re: If x = y, x + y = ? (1) x  y = 4 (2) x/y = 1
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13 Jul 2019, 00:12
If x=y, then x=y or x=y What is x+y?
1. xy=6 The condition is that x=y or x=y. So xy=6 The values of x and y that satisfy this condition are x=3 and y=3 and this satisfies the condition x=y 3(3)=6. Hence we can say that x+y=0 Statement 1 alone is sufficient.
Statement 2: x/y=1 We know that both x and y can be both positive or they both negative or one can be positive while the other is negative. So we mutiply both sides by y^2 to ensure the signs don’t change. y^2+xy=0 y(y+x)=0 either y=0, which makes x=0, or y+x=0 which means that x=y And this is true for any pairs of x=y, such as {1,1; 2,2; 3,3; 4,4} Hence we can say that x+y=0 Statement 2 is therefore sufficient. Answer imo is D
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Re: If x = y, x + y = ? (1) x  y = 4 (2) x/y = 1
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13 Jul 2019, 03:22
If x=y, x+y=? Possibilities: x and y can be pos and neg: '+' + '+' = 2x or 2y '' + '' = 2x or 2y '+' + '' = 0 '' + '+' = 0
(1) x−y=4 if x and y: '+' '+' = no sence, coz x=y '' '' = no sence, coz x=y '+' '' = can be x = 2 y = 2 '' '+' = no sense, coz result need to be negative SUFFICIENT: '+' + '' = 0
(2) xy=−1 if x and y: '+' '+' = no sence, multiple must be positive '' '' = no sence, multiple must be positive '+' '' = can be '' '+' = can be SUFFICIENT: '+' + '' = 0 '' + '+' = 0
Answ D




Re: If x = y, x + y = ? (1) x  y = 4 (2) x/y = 1
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13 Jul 2019, 03:22






