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When which digit in 467*15*23 is added 1

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When which digit in 467*15*23 is added 1  [#permalink]

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New post 06 Aug 2013, 20:32
13
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A
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D
E

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Question Stats:

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When which digit in 467*15*23 is added 1, the product changes by least value?
a. 1
b. 2
c. 6
d. 7
e. 5
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Re: When which digit in 467*15*23 is added 1  [#permalink]

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New post Updated on: 06 Aug 2013, 21:07
13
8
bsahil wrote:
When which digit in 467*15*23 is added 1, the product changes by least value?
a. 1
b. 2
c. 6
d. 7
e. 5


i will give one analogous example:

let volume of cuboid = 8*9*10 =720
which value(8/9/10) should be added 1 so the net result is least affected.

let add 1 to 8
vol= 9*9*10= 810 (change from original = 810-720 = 90)
let add 1 to 9
vol: 8*10*10 = 800 (change from original = 800-720 = 80)
let add 1 to 10
vol = 8*9*11 = 792 (change from original = 792-720 = 72)

so takeaway:
in order to have least effect always change the maximum value.

now in our example to have least effect on \(467*15*23\)
we need to keep 2 thing in mind
1)change the unit digit(Because if you change tens or hundred place then it will have larger effect thats common sense)
2)change the biggest number

so biggest number is 467 and unit digit of this 7.

hence D

hope this helps
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Originally posted by blueseas on 06 Aug 2013, 20:56.
Last edited by blueseas on 06 Aug 2013, 21:07, edited 1 time in total.
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Re: When which digit in 467*15*23 is added 1  [#permalink]

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New post 06 Aug 2013, 21:07
blueseas wrote:
bsahil wrote:
When which digit in 467*15*23 is added 1, the product changes by least value?
a. 1
b. 2
c. 6
d. 7
e. 5


i will give one analogous example:

let volume of cube = 8*9*10 =720
which value(8/9/10) should be added 1 so the net result is least affected.

let add 1 to 8
vol= 9*9*10= 810 (change from original = 810-720 = 90)
let add 1 to 9
vol: 8*10*10 = 800 (change from original = 800-720 = 80)
let add 1 to 10
vol = 8*9*11 = 792 (change from original = 792-720 = 72)

so takeaway:
in order to have least effect always change the maximum value.

now in our example to have least effect on \(467*15*23\)
we need to keep 2 thing in mind
1)change the unit digit(Because if you change tens or hundred place then it will have larger effect thats common sense)
2)change the biggest number

so biggest number is 467 and unit digit of this 7.

hence D

hope this helps



Thanks for the great explanation....it was very easy to understand...
:)
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Re: When which digit in 467*15*23 is added 1  [#permalink]

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New post 07 Aug 2013, 08:19
1
blueseas wrote:
bsahil wrote:
When which digit in 467*15*23 is added 1, the product changes by least value?
a. 1
b. 2
c. 6
d. 7
e. 5


i will give one analogous example:

let volume of cuboid = 8*9*10 =720
which value(8/9/10) should be added 1 so the net result is least affected.

let add 1 to 8
vol= 9*9*10= 810 (change from original = 810-720 = 90)
let add 1 to 9
vol: 8*10*10 = 800 (change from original = 800-720 = 80)
let add 1 to 10
vol = 8*9*11 = 792 (change from original = 792-720 = 72)

so takeaway:
in order to have least effect always change the maximum value.

now in our example to have least effect on \(467*15*23\)
we need to keep 2 thing in mind
1)change the unit digit(Because if you change tens or hundred place then it will have larger effect thats common sense)
2)change the biggest number

so biggest number is 467 and unit digit of this 7.

hence D

hope this helps

Good explanation. . explains clearly
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Re: When which digit in 467*15*23 is added 1  [#permalink]

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New post 07 Aug 2013, 08:35
2
Excellent explanation with an example from blueseas :-D

If interested the reason behind the noted effect is as follows

Any change that is smallest of each number would result in smaller overall change.

For E.g

changing 467 to 468 results in a net increase of 1/467 (if you change the tens digit instead of units, the net change will be 10/467, which is more than 1/467)
changing 15 to 16 results in a net increase of 1/15
changing 23 to 24 results in a net increase of 1/23

1/467 is the smallest number of 1/467, 1/23, 1/15. Hence 1 can be added to 467 (largest in the set) to result in smallest change.

Hope this helps
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Re: When which digit in 467*15*23 is added 1  [#permalink]

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New post 07 Aug 2013, 08:37
rrsnathan wrote:
blueseas wrote:
bsahil wrote:
When which digit in 467*15*23 is added 1, the product changes by least value?
a. 1
b. 2
c. 6
d. 7
e. 5


i will give one analogous example:

let volume of cuboid = 8*9*10 =720
which value(8/9/10) should be added 1 so the net result is least affected.

let add 1 to 8
vol= 9*9*10= 810 (change from original = 810-720 = 90)
let add 1 to 9
vol: 8*10*10 = 800 (change from original = 800-720 = 80)
let add 1 to 10
vol = 8*9*11 = 792 (change from original = 792-720 = 72)

so takeaway:
in order to have least effect always change the maximum value.

now in our example to have least effect on \(467*15*23\)
we need to keep 2 thing in mind
1)change the unit digit(Because if you change tens or hundred place then it will have larger effect thats common sense)
2)change the biggest number

so biggest number is 467 and unit digit of this 7.

hence D

hope this helps

Good explanation. . explains clearly




gist:
1)change the unit digit(Because if you change tens or hundred place then it will have larger effect thats common sense)
2)change the biggest number
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Re: When which digit in 467*15*23 is added 1  [#permalink]

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New post 21 Jun 2016, 09:20
1
bsahil wrote:
When which digit in 467*15*23 is added 1, the product changes by least value?
a. 1
b. 2
c. 6
d. 7
e. 5


I wrote the expression as :-

(400+60 +7) (10+5) (20+3)

Now in order to get the least value, we must add 1 to the digit that gives least value product with the other digits.

Say for instance if we add 1 to 1 in 15, the number will become (20 +5). And 20 will be multiplied by 467 and 23, giving us huge numbers

Similarly and digits from 15 and 23 when added 1 will be multiplied by 467 and give greater numbers.

However, When the last digit 7 in 467 is added 1, it will be multiplied by other smaller numbers in the expressions and will give least value.

Hence D is the answer.
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Re: When which digit in 467*15*23 is added 1  [#permalink]

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New post 22 Jun 2016, 03:29
great expalination blueseas...This is a different type of question...
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Re: When which digit in 467*15*23 is added 1  [#permalink]

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New post 26 Aug 2018, 10:33
When which digit in 467*15*23 is added 1, the product changes by least value?

My method: let the numbers 467, 15, and 23 be a,b, and c respectively

When we add +1, then we have 3 cases:

(a+1)*bc=abc+bc
(b+1)*ac=abc+ac
(c+1)*ab=abc+ab

Among them the least isfirst one as bc=15*23

Answer D.
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Re: When which digit in 467*15*23 is added 1 &nbs [#permalink] 26 Aug 2018, 10:33
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