Elitmus
Exam
Numerical Ability
Algebra
if v,w,x,y,z are non negative integer, each less than 11,then how many distinct combinations(w,v,x,y,z) satisfy v(11^4)+w(11^3)+x(11^2)+y(11)+z=151001.
optn
a)0
b)1
c)2
d)3
Read Solution (Total 8)
-
- 151001 / 11^4 = 10 with remainder = 4591
4591 / 11^3 = 3 with remainder = 598
598 / 11^2 = 4 with remainder = 114
114 / 11^1 = 10 with remainder = 4
Therefore 151001=10(11^4)+3(11^3)+4(11^2)+10(11^1)+4
i.e., (v,w,x,y,z) is (10,3,4,10,4). These values satisfies given conditions and is one valid option.
Let's analyze if further option available satisfying the given condition. v,w,x,y,z should be less than 11 and greater than zero. The solution we got have v as 10. Suppose v=9. With this, the maximum value possible under the given constraints is
9(11^4)+10(11^3)+10(11^2)+10(11^1)+10=146409 - 9 years agoHelpfull: Yes(10) No(0)
- So Ans is B) = 1 Only.
- 9 years agoHelpfull: Yes(3) No(0)
- Remaining solution...
Let's analyze if further option available satisfying the given condition. v,w,x,y,z should be less than 11 and greater than zero. The solution we got have v as 10. Suppose v=9. With this, the maximum value possible under the given constraints is
9(11^4)+10(11^3)+10(11^2)+10(11^1)+10=146409 - 9 years agoHelpfull: Yes(1) No(0)
- ..
9(11^4)+10(11^3)+10(11^2)+10(11^1)+10=146409 - 9 years agoHelpfull: Yes(1) No(0)
- v(11^4)+w(11^3)+x(11^2)+y(11)+z=151001
151001/11 gives remainder 4.
v(11^4)+w(11^3)+x(11^2)+y(11) = 151001 - z
to make it divisible by 11, z should be 4..
as value of z cannot be any other number, we can form only on 1 distinct combination..
Answer is (B)-1 - 9 years agoHelpfull: Yes(1) No(0)
- ans is b only
- 9 years agoHelpfull: Yes(0) No(0)
- I am sorry to say that your question was wrong. Because there is no mention area, perimeter....
- 9 years agoHelpfull: Yes(0) No(1)
- v(11^4)+w(11^3)+x(11^2)+y(11)+z=151001=11*13727+4
therefore, z=4,next
11*v(11^3)+11*w(11^2)+11*x(11^1)+y(11)=11*13727
11*v(11^2)+11*w(11^1)+11*x+y=13727=11*1247+10
where,y=10,then
11*v(11^1)+11*w+x=1247=11*113+4
where,x=4,then
11*v+w=113=11*10+3
where,w=3,then
11*v=11*10
then,v=10
therefor,z=4,y=10,x=4,w=3,v=10,
ans is 3. - 9 years agoHelpfull: Yes(0) No(1)
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