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

Question

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

blueseas · Accepted Answer

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

nt2010 · Answer

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

Asifpirlo · Answer

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

Divyadisha · Answer

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.

Hero8888 · Answer

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.

Ze3rebz · Answer

This is how I visualised each solution algebraically. To increase a units digit by 1, we will add 1, and to increase a tens digit by 1, we will add 10. You will notice in each solution, we will find the original number again first, and the  change  in  bold  added to that. Then it becomes easy to compare and determine which change is the least.

A) 467*23*(15+ 10 ) = 467*15*23 +  467*10*23 
B) 467*15*(23+ 10 )= 467*15*23 +  467*10*15 
C) 15*23*(467+ 10 )= 467*15*23 +  15*10*23 
D) 15*23*(467+ 1 ) = 467*15*23 +  15*1*23 
E) 467*23*(15+ 1 ) = 467*15*23 +  467*1*23

You can also solve it much quicker if you know that  changing the biggest number/value will always have the least effect/change . So straight away, the answer will be either C or D. And increasing the units digit will always cause a smaller change than increasing the tens digit. So, final answer D.

When which digit in 4671523 is added 1

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