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The first six positive integers are used once to form two three-digit

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The first six positive integers are used once to form two three-digit [#permalink]

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New post 31 Jan 2018, 10:49
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Difficulty:

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Question Stats:

41% (01:17) correct 59% (01:34) wrong based on 43 sessions

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The first six positive integers are used once to form two three-digit numbers.
What is the minimum possible difference between the two numbers formed?

A. 87
B. 78
C. 69
D. 60
E. 47

Source: Experts Global
[Reveal] Spoiler: OA

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The first six positive integers are used once to form two three-digit [#permalink]

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New post 31 Jan 2018, 11:26
Difference of two numbers is minimum when they are close to each other as much as possible. So I think 234-165=69 (C)

To make sure that we have arrived the minimum difference, we can look through the answer choices. In our case we should only look at the options lower than 69: D)60 and E)47.

D) 60 - cannot be the answer, because in order units digit to be 0, the two three-digit numbers' units digit must be the same which is not allowed in this question or both of them must be 0, which is not included in this range (since we deal with only positive integers here, 0 is neither positive nor negative) as well. Hence, D is off.

E) 47- only case when the units digit of the difference of these two numbers is 7, is ab3-cd6. In all such cases the answer is more than 47. E is off as well.

So answer is C-69
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Re: The first six positive integers are used once to form two three-digit [#permalink]

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New post 31 Jan 2018, 11:42
pushpitkc wrote:
The first six positive integers are used once to form two three-digit numbers.
What is the minimum possible difference between the two numbers formed?

A. 87
B. 78
C. 69
D. 60
E. 47

Source: Experts Global


First six number are 1, 2, 3, 4, 5 & 6

Difference will be small when the numbers are as close as possible. One way to test the closeness is to fix the hundred's digit and then form two numbers. so we have

\(234-165=69\)

\(314-265=49\)

\(412-365=47\)......We Can stop here as this is the smallest number among the options

Option E
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Re: The first six positive integers are used once to form two three-digit [#permalink]

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New post 31 Jan 2018, 11:44
Mehemmed wrote:
Difference of two numbers is minimum when they are close to each other as much as possible. So I think 234-165=69 (C)

To make sure that we have arrived the minimum difference, we can look through the answer choices. In our case we should only look at the options lower than 69: D)60 and E)47.

D) 60 - cannot be the answer, because in order units digit to be 0, the two three-digit numbers' units digit must be the same which is not allowed in this question or both of them must be 0, which is not included in this range (since we deal with only positive integers here, 0 is neither positive nor negative) as well. Hence, D is off.

E) 47- only case when the units digit of the difference of these two numbers is 7, is ab3-cd6. In all such cases the answer is more than 47. E is off as well.

So answer is C-69


Hi Mehemmed

test with other combinations.
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Re: The first six positive integers are used once to form two three-digit [#permalink]

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New post 31 Jan 2018, 11:51
niks18 wrote:
Mehemmed wrote:
Difference of two numbers is minimum when they are close to each other as much as possible. So I think 234-165=69 (C)

To make sure that we have arrived the minimum difference, we can look through the answer choices. In our case we should only look at the options lower than 69: D)60 and E)47.

D) 60 - cannot be the answer, because in order units digit to be 0, the two three-digit numbers' units digit must be the same which is not allowed in this question or both of them must be 0, which is not included in this range (since we deal with only positive integers here, 0 is neither positive nor negative) as well. Hence, D is off.

E) 47- only case when the units digit of the difference of these two numbers is 7, is ab3-cd6. In all such cases the answer is more than 47. E is off as well.

So answer is C-69


Hi Mehemmed

test with other combinations.





niks18,

Yes, you are right. I forgot the other variations. Thank you for pointing out.
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The first six positive integers are used once to form two three-digit [#permalink]

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New post 31 Jan 2018, 13:46
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pushpitkc wrote:
The first six positive integers are used once to form two three-digit numbers.
What is the minimum possible difference between the two numbers formed?

A. 87
B. 78
C. 69
D. 60
E. 47

Source: Experts Global


higher number:
d1=digit just above median (4)
d2=lowest digit (1)
d3=next lowest digit (2)

lower number:
d1=digit just below median (3)
d2=highest digit (6)
d3=next highest digit (5)

412-365=47
E
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Re: The first six positive integers are used once to form two three-digit [#permalink]

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New post 31 Jan 2018, 19:15
pushpitkc wrote:
The first six positive integers are used once to form two three-digit numbers.
What is the minimum possible difference between the two numbers formed?

A. 87
B. 78
C. 69
D. 60
E. 47

Source: Experts Global


The questions asks for the minimum possible. So, try with the last two options... anything below \(60 (For Ex: 412 - 356, 512 - 463)\) will lead us to Option E. Otherwise, trying to find the correct combination is time consuming.
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Re: The first six positive integers are used once to form two three-digit   [#permalink] 31 Jan 2018, 19:15
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