If 6^x + 7^y = ....4, where x and y are integers from 0 to 9. Then sum of all possible values of

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31 Mar 2010 Possible value of Y?

If 6^x + 7^y = ....4, where x and y are integers from 0 to 9.
Then sum of all possible values of y is?

OPtion

1) 13
2) 11
3) 10
4) 9
5) 6
6) 8
7) 4
8) 15
9) 14
10) 16

Solution

The only possible cases are
6^0 + 7^3 = ....4
6^0 + 7^7 = ....4
Sum of possible values of y = 3 + 7 = 10

Correct Option: 3 Best Solution (9)

Dr.Dipin Singh   14 years AGO

when x=0, 6^x=1....for other values of x, last digit will be 6...

for diff values of y, 7^1=7; 7^2=49, 7^3 = 343, 7^4= 2401

last digit of 6^x + 7^y will be 4 when x=0 and y = 3 or 7.

Then sum of possible values of y = 3+7=10

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HARMEET KAUR   14 years AGO

6^x + 7^y = ....4, is possible only when x=0 and y = 3 or 7.
Hence
sum of all possible values of y is 3+7=10.

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Shikha   14 years AGO

Y can hv values 3 and 7 when x=0.

Then sum of possible values of y = 3+7=10.

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Jeevan   14 years AGO

3+7=10

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ASHOK ROY   14 years AGO

The only power 6^0=1and only7^3 and 7^7 will have unit place=4 the sum of powers (y) will 10 to give the desired result with unit place 4

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Neha Bhatia   14 years AGO

6^0+7^3=...4 and 6^0+7^7=...4

so 3+7=10

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sanjib biswas   14 years AGO

last digit of all 6^x is 6 or 1 and last digit of all 7^y may be 1,7,9,3 like that i.e. multiplication of both = ...4 only possible when 6^x last digit 1 and 7^y last digit 3 i.e valu of y is 3 and 7 then sum of all possible value of y is 10.

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hitesh gakhar   14 years AGO

this condition only satisfies when x=0...
if x=0, to get ...4 , we need 7^y to be...3, which is possible if y=3,, y=7...
sum of all y's is 10...

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shailender   14 years AGO

6^0+7^3=244
6^0+7^7=...4
hence (3+7)=10

Like? Yes (1) | No