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

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Math Expert
Joined: 02 Sep 2009
Posts: 56359
Which of the following could be the value of x + y, if both (x + 1/5)  [#permalink]

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07 Jun 2019, 03:17
00:00

Difficulty:

55% (hard)

Question Stats:

66% (02:27) correct 34% (02:32) wrong based on 52 sessions

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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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Joined: 22 Nov 2018
Posts: 491
Location: India
GMAT 1: 640 Q45 V35
GMAT 2: 660 Q48 V33
Re: Which of the following could be the value of x + y, if both (x + 1/5)  [#permalink]

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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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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
Senior Manager
Joined: 13 Feb 2018
Posts: 425
GMAT 1: 640 Q48 V28
Re: Which of the following could be the value of x + y, if both (x + 1/5)  [#permalink]

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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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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

Hit Kudos if this helped!

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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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