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# The sum of positive integers x and y is 77. What is value of

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Intern
Joined: 08 Nov 2006
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The sum of positive integers x and y is 77. What is value of  [#permalink]

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Updated on: 20 Aug 2013, 08:52
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Difficulty:

35% (medium)

Question Stats:

70% (00:46) correct 30% (00:41) wrong based on 926 sessions

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The sum of positive integers x and y is 77. What is value of xy?

(1) x = y + 1
(2) x and y have the same tens digit.

I answered that "statement 1 alone is sufficient, but statement 2 alone is not sufficient.

The test said that each statement alone is sufficient.

How can this be? If X = 32 and Y = 35, then XY = 1120 but if X= 33 and Y = 34, then XY = 1122. They have the same 10's digit in each case, but not the same product.

Am I missing something obvious or is the answer wrong in gmatprep?

Thanks,

Andrew

Originally posted by andrewnorway on 08 Nov 2006, 10:14.
Last edited by Bunuel on 20 Aug 2013, 08:52, edited 1 time in total.
Renamed the topic, edited the question, added the OA and moved to DS forum.
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Re: The sum of positive integers X and Y is 77. What is xy?  [#permalink]

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20 Aug 2013, 08:58
5
8
spjmanoli wrote:
The question says that X and Y are two positive integers but solving statement 1 you will get X and Y as fractions. If the statement refutes the question data then what is the answer?

Actually we don't get fractions.

The sum of positive integers x and y is 77. What is value of xy?

Given that $$x+y=77$$ find the value of $$xy$$.

(1) x = y + 1 --> $$(y+1)+y=77$$ --> $$y=38$$ and $$x=39$$ --> $$xy=39*38$$. Sufficient.

(2) x and y have the same tens digit. In order the sum to be 77 the tens digit of of x and y must be 3, thus $$x=38$$ and $$y=39$$ or vise-versa, in either case $$xy=39*38$$. Sufficient.

Hope this helps.
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Re: The sum of positive integers X and Y is 77. What is xy?  [#permalink]

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08 Nov 2006, 10:23
4
andrewnorway wrote:
Can someone explain this to me, its a data suff problem:

The sum of positive integers X and Y is 77. What is value of xy?

(1) X = Y+1

(2) X and Y have the same tens digit

I answered that "statement 1 alone is sufficient, but statement 2 alone is not sufficient.

The test said that each statement alone is sufficient.

How can this be? If X = 32 and Y = 35, then XY = 1120 but if X= 33 and Y = 34, then XY = 1122. They have the same 10's digit in each case, but not the same product.

Am I missing something obvious or is the answer wrong in gmatprep?

Thanks,

Andrew

32+35 is not equal to 77

There are only 2 numbers that add up to 77 and have the same 10 digits. They are 38 and 39. Therefore either statement is sufficient - D
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08 Nov 2006, 17:14
1
St1:
x = y+1
so y+1+y = 77 --> can solve for y, then can solve for x and finally xy. Sufficient.

st2:
x and y have the same tens digit. We can rule out the tens digit 1,2,4,5-9 because that would require the other integer to take either a bigger or smaller value. The only value that works is 38,39. Since it's multiplication, we don't care if x took 38 or x took 39. xy will be the same. Sufficient.

Ans D
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Re: The sum of positive integers X and Y is 77. What is xy?  [#permalink]

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20 Aug 2013, 08:48
The question says that X and Y are two positive integers but solving statement 1 you will get X and Y as fractions. If the statement refutes the question data then what is the answer?
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Status: Verbal Forum Moderator
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Re: The sum of positive integers X and Y is 77. What is xy?  [#permalink]

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24 Sep 2013, 01:46
Bunuel wrote:
spjmanoli wrote:
The question says that X and Y are two positive integers but solving statement 1 you will get X and Y as fractions. If the statement refutes the question data then what is the answer?

Actually we don't get fractions.

The sum of positive integers x and y is 77. What is value of xy?

Given that $$x+y=77$$ find the value of $$xy$$.

(1) x = y + 1 --> $$(y+1)+y=77$$ --> $$y=38$$ and $$x=39$$ --> $$xy=39*38$$. Sufficient.

(2) x and y have the same tens digit. In order the sum to be 77 the tens digit of of x and y must be 3, thus $$x=38$$ and $$y=39$$ or vise-versa, in either case $$xy=39*38$$. Sufficient.

Hope this helps.

Questions says 10's digit same, but isn't it assumption that it should be 3? Like this we can assume anything and solve the question.
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Re: The sum of positive integers X and Y is 77. What is xy?  [#permalink]

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24 Sep 2013, 01:52
1
honchos wrote:
Bunuel wrote:
spjmanoli wrote:
The question says that X and Y are two positive integers but solving statement 1 you will get X and Y as fractions. If the statement refutes the question data then what is the answer?

Actually we don't get fractions.

The sum of positive integers x and y is 77. What is value of xy?

Given that $$x+y=77$$ find the value of $$xy$$.

(1) x = y + 1 --> $$(y+1)+y=77$$ --> $$y=38$$ and $$x=39$$ --> $$xy=39*38$$. Sufficient.

(2) x and y have the same tens digit. In order the sum to be 77 the tens digit of of x and y must be 3, thus $$x=38$$ and $$y=39$$ or vise-versa, in either case $$xy=39*38$$. Sufficient.

Hope this helps.

Questions says 10's digit same, but isn't it assumption that it should be 3? Like this we can assume anything and solve the question.

No. The tens digit of x and y cannot be any digit but 3: if it's less than 3, then x+y<77 and if it's greater than 3 then x+y>77.

Does this make sense?
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Re: The sum of positive integers x and y is 77. What is value of  [#permalink]

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13 Feb 2014, 23:28
Nice question !

X+y=77

x=y+1

then x=39 and y=38 statement 1 is sufficient

statement 2---> same tens digit means both numbers are from 30 to 39 inclusive. so there is only two digits 38 and 39. sufficient

if it wud have been less 77.. for example 76 or 75..x+y=75 or x+y=76 then statement 2 wud have been insuffient. A trick is they have given 77..if we jump one number tens digit wud be 4.
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Re: The sum of positive integers x and y is 77. What is value of  [#permalink]

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03 Feb 2017, 05:13
Bunuel wrote:
spjmanoli wrote:
The question says that X and Y are two positive integers but solving statement 1 you will get X and Y as fractions. If the statement refutes the question data then what is the answer?

Actually we don't get fractions.

The sum of positive integers x and y is 77. What is value of xy?

Given that $$x+y=77$$ find the value of $$xy$$.

(1) x = y + 1 --> $$(y+1)+y=77$$ --> $$y=38$$ and $$x=39$$ --> $$xy=39*38$$. Sufficient.

(2) x and y have the same tens digit. In order the sum to be 77 the tens digit of of x and y must be 3, thus $$x=38$$ and $$y=39$$ or vise-versa, in either case $$xy=39*38$$. Sufficient.

Hope this helps.

In the statement 2, the restriction is given on the tenth digit. However, there was no restriction on unit digit. Hence, x and y can be 31, 32, 33, 34, 35, 36, 37, 38 and 39. If x = 35, y = 32, then X*Y = 1120. Again, if x= 33, y = 34, then X*Y = 1122.

I can't understand the explanation. Please elaborate the second statement in more details.

Thanks.

Regards
Jahid
Math Expert
Joined: 02 Sep 2009
Posts: 52296
Re: The sum of positive integers x and y is 77. What is value of  [#permalink]

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03 Feb 2017, 06:07
jahidhassan wrote:
Bunuel wrote:
spjmanoli wrote:
The question says that X and Y are two positive integers but solving statement 1 you will get X and Y as fractions. If the statement refutes the question data then what is the answer?

Actually we don't get fractions.

The sum of positive integers x and y is 77. What is value of xy?

Given that $$x+y=77$$ find the value of $$xy$$.

(1) x = y + 1 --> $$(y+1)+y=77$$ --> $$y=38$$ and $$x=39$$ --> $$xy=39*38$$. Sufficient.

(2) x and y have the same tens digit. In order the sum to be 77 the tens digit of of x and y must be 3, thus $$x=38$$ and $$y=39$$ or vise-versa, in either case $$xy=39*38$$. Sufficient.

Hope this helps.

In the statement 2, the restriction is given on the tenth digit. However, there was no restriction on unit digit. Hence, x and y can be 31, 32, 33, 34, 35, 36, 37, 38 and 39. If x = 35, y = 32, then X*Y = 1120. Again, if x= 33, y = 34, then X*Y = 1122.

I can't understand the explanation. Please elaborate the second statement in more details.

Thanks.

Regards
Jahid

The numbers you consider give the sum of 67 not 77: 35+32=67 and 33+34=67. The only numbers with the tens digit of 3 which give the sum of 77 are 38 and 39.

Hope it's clear.
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Re: The sum of positive integers x and y is 77. What is value of  [#permalink]

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21 Dec 2018, 21:04
x + y = 77 eq(1)
Statement 1. x = y + 1 eq(2)
Using eq(1) and eq(2), we get,
X = 39 and y = 38. So, xy = 1482. Hence, Sufficient.
Statement 2. X = 10a + b
Y = 10a + c
10a + b + 10a + c = 77
20a + b + c= 77( where a, b ,c are single digits)
This is possible only if (a, b, c) = (3, 8, 9) or (3, 9, 8)
So, the two no would be 36 and 37 in both the case.
Hence, xy = 38 x 39 = 1482. Hence, Sufficient.
Re: The sum of positive integers x and y is 77. What is value of &nbs [#permalink] 21 Dec 2018, 21:04
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