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Which of the following could be the value of x + y, if both (x + 1/5)

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Which of the following could be the value of x + y, if both (x + 1/5)  [#permalink]

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New post 07 Jun 2019, 03:17
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

64% (02:32) correct 36% (02:36) wrong based on 58 sessions

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Re: Which of the following could be the value of x + y, if both (x + 1/5)  [#permalink]

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New post 07 Jun 2019, 03:26
Bunuel wrote:
Which of the following could be the value of x + y, if both (x + 1/5) and (y – 3/4) are positive integers?

(A) 13/5
(B) 51/20
(C) 31/20
(D) 21/20
(E) 13/20


Lowest positive integer is 1; so Comparing both x and y as equal to 1 results in x=1-1/5=4/5 and y=1+3/4=7/4

So x+y = 4/5+7/4 = 51/20 IMO Option B
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Re: Which of the following could be the value of x + y, if both (x + 1/5)  [#permalink]

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New post 07 Jun 2019, 03:34
1
(x + 1/5) is an integer
Hence x=4mod5
x=\(\frac{5a+4}{5}\)

(y – 3/4) is an positive integer
y=3(mod 4)
y=\(\frac{4b+3}{4}\)

x+y=\(\frac{5a+4}{5}\) + \(\frac{4b+3}{4}\)
x+y= (a+b) + 31/20
At b=0, (y – 3/4)=0. Hence minimum value of b we should take is 1

When a=0 and b=1
x+y= 51/20


Bunuel wrote:
Which of the following could be the value of x + y, if both (x + 1/5) and (y – 3/4) are positive integers?

(A) 13/5
(B) 51/20
(C) 31/20
(D) 21/20
(E) 13/20
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Re: Which of the following could be the value of x + y, if both (x + 1/5)  [#permalink]

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New post 07 Jun 2019, 05:05
According to the stem:
\((x+\frac{1}{5})\)\(+(y-\frac{3}{4})=Integer\)
\(x+y-\frac{11}{20}=integer\)

Only B and C satisfy, discard other choices
Now we have got
\(\frac{51}{20}-\frac{11}{20}=2\)
\(\frac{31}{20}-\frac{11}{20}\)=1

Then I was confused (several secs :) )
Checking back the stem I realized that
Positive integer+Positive integer=integer, which is >=2
As adding two positive integers cant yield 1

IMO
Ans: B
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Re: Which of the following could be the value of x + y, if both (x + 1/5)  [#permalink]

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New post 07 Jun 2019, 06:07
2
x+0.20 = positive integer
x = positive integer - 0.20
x = abc.80

Similarly,
y-0.75=positive interger
y=postive integer+0.75

Therefore, y is at least 1.75

Lets consider minimum value case where y=1.75 and x=0.80

x+y=2.55=255/100=51/20

Answer is (B)

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Re: Which of the following could be the value of x + y, if both (x + 1/5)   [#permalink] 07 Jun 2019, 06:07
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