Question

the number of 3 digit numbers which end in 7 and divisible by 11 is

A. 2
B. 4
C. 6
D. 8

Answer 1

When writing decimally, any positive integer which is divisible by 11 is in the form,

a/(a+b)/b

where, it's expanded form is,

100a + 10(a + b) + b

for any whole number a and for any positive one-digit integer b

Actually it is,

a/b × 11 = a/(a+b)/b

[Written decimally, means written the number by splitting the digits. Digits are not divided here.]

For getting no. of three digit multiples of 11 ending in 7, we have to take b = 7.

Thus the no. looks like:   a/(a+7)/7.

As we see earlier, the one-eleventh of this number is in the form of a/b.

[a/b × 11 = a/(a+b)/b   ;   a/b = a/(a+b)/b ÷ 11]

Thus, the one-eleventh of these three digit numbers also end in 7.

Hence the nos. are,

1.  17 × 11 = 187
2.  27 × 11 = 297
3.  37 × 11 = 407
4.  47 × 11 = 517
5.  57 × 11 = 627
6.  67 × 11 = 737
7.  77 × 11 = 847
8.  87 × 11 = 957

But, as 97 × 11 = 1067 is a 4-digit number, it won't include here.

Thus, the total no. of integers which end in 7 and divisible by 11 is 8.

Answer 2

Answer:

8

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