The multiplication of a 3 digit number xy5 with digit z yields x215.What is x+y+z
Answers
Answer:
Step-by-step explanation:
The multiplication of a three-digit number XY5with digit Z yields X215.What is X+Y+Zequal to?
A) 13
B) 15
C) 17
D) 18
Correct Answer:
A) 13
Answer:
13
Step-by-step explanation:
here z has to be odd as it has to end with 5
therefore z can be 1,3,5,7,9
I) 1 is not possible as xy5 × 1 = xy5 not x215
2) if z is 3 then 5×3=15 5 in unit place and carry one
3y+1 must result in unit place 1 but there's no number that would do the same
3) if z is 5 then 5×5=25 2 carry, 5y+2 must result 1 but this is not possible as 5y+2 results only 2 or 7
ex: 5×1=5+2=7
5×2=10+2=12
5×3=15+2=17
4) if z is 7 then 5×7=35 3 carry, 7y+3 has to end in 1 , there is possibility i.e, 7×4+3=31 ,carry 3 , then
7X+3=X2 ,only possibility 7×7+3=52 , both x must be same but here 7 not equal to 5. So this doesn't work
5) last one left is 9, then 5×9=45 ,carry 4 then 9y+4 has to end in 1, 9×3+4=31, carry 3 , then 9X+3 has to end in 2 and start with X i.e, 9×1+3=12, So X=1 , y=3 and Z=9
135×9=1215
sum of x+y+z=1+3+9=13