Wells Fargo Divisibility Problems with Solutions Quiz-1

Solution
n divided by 5 yields a remainder equal to 3 is written as follows
n = 5 k + 3 , where k is an integer.
add 2 to both sides of the above equation to obtain
n + 2 = 5 k + 5 = 5(k + 1)
The above suggests that n + 2 divided by 5 yields a remainder equal to zero.

Video solution:

Solution
If n is divisible by 3, 5 and 12 it must a multiple of the lcm of 3, 5 and 12 which is 60.
n = 60 k
n + 60 is also divisible by 60 since
n + 60 = 60 k + 60 = 60(k + 1)
The answer is D.

Solution
It is the lcm of 5, 7 and 20 which is 140.
The answer is b.

Solution
When n is divided by 8, the remainder is 3 may be written as
n = 8 k + 3
multiply all terms by 6
6 n = 6(8 k + 3) = 8(6k) + 18
Write 18 as 16 + 2 since 16 = 8 * 2.
= 8(6k) + 16 + 2
Factor 8 out.
= 8(6k + 2) + 2
The above indicates that if 6n is divided by 8, the remainder is 2. The answer is C.

We first expand (2n + 2)²

(2n + 2)²= 4n² + 8n + 4

Factor 4 out.

= 4(n² + 2n + 1)

(2n + 2)² is divisible by 4 and the remainder is equal to 0.
The answer is A.

Solution -18- D
Let xy be the whole number with x and y the two digits that make up the number. The number is divisible by 3 may be written as follows
10 x + y = 3 k
The sum of x and y is equal to 9.
x + y = 9
Solve the above equation for y
y = 9 - x Substitute y = 9 - x in the equation 10 x + y = 3 k to obtain.
10 x + 9 - x = 3 k
Solve for x
x = (k - 3) / 3
x is a positive integer smaller than 10
Let k = 1, 2, 3, ... and select the first value that gives x as an integer. k = 6 gives x = 1
Find y using the equation y = 9 - x = 8
The number we are looking for is 18 and the answer is D. It is divisible by 3 and the sum of its digits is equal to 9 and it is the smallest and positive whole number with such properties.

Solution
One may answer this question using a calculator and test for divisibility by 3. However we can also test for divisibilty by adding the digits and if the result is divisible by3 then the number is divisible by 3.
3 + 3 + 9 = 15 , divisible by 3.
3 + 4 + 2 = 9 , divisible by 3.
5 + 5 + 2 = 12 , divisible by 3.
1 + 1 + 1 + 1 = 4 , not divisible by 3.
The number 1111 is not divisible by 3 the answer is D.

Answer:
98637 → 9863 – 7 = 9856 → 985 – 6 = 979 → 97 – 9 = 88, which is divisible by 11, so yes, 98637 is divisible by 11. Similarly we can check for other options also.

Answer:
212328 → 21232 + 2 × 8 = 21248 → 2124 + 2 × 8 = 2140 → 214 + 2 × 0 = 214 → 21 + 2 × 4 = 29, which is not divisible by 19, hence, 212328 is not divisible by 19.
180872 → 18087 + 2 × 2 = 18091 → 1809 + 2 × 1 = 1811 → 181 + 2 × 1 = 183 → 18 + 2 × 3 = 24, which is not divisible by 19, hence, 180872 is not divisible by 19.
133688 → 13368 + 2 × 8 = 13384 → 1338 + 2 × 4 = 1346 → 134 + 2 × 6 = 150 → 15 + 2 × 0 = 15, which is not divisible by 19, hence, 133688 is not divisible by 19.
149416 → 14941 + 2 × 6 = 14953 → 1495 + 2 × 3 = 1501 → 150 + 2 × 1 = 152 → 15 + 2 × 2 = 19, which is divisible by 19, so yes, 149416 is divisible by 19.

Solution
Answer:
We know that, 24 = 2 × 12, 4 × 6, 3 × 8
For the divisibility of 24, we will to check divisibility by 3 and 8 as these two are co primes.
Option 1 → 429572
Sum of digits = 4 + 2 + 9 + 5 + 7 + 2 = 29 (It is not divisible by 3, so it is not divisible by 24 also)
Option 2 → 427022
Sum of digits = 4 + 2 + 7 + 0 + 2 + 2 = 17 (It is not divisible by 3, so it is not divisible by 24 also)
Option 2 → 320724
Sum of digits = 3 + 2 + 0 + 7 + 2 + 4 = 18 (It is divisible by 3)
So we will check for divisibility by 8.
Last three digits i.e. 724
724/8 = 90.5 (Since, 724 is not divisible by 8 i.e. the number is not divisible by 24)
Option 4 → 237024
Sum of digits = 2 + 3 + 7 + 0 + 2 + 4 = 18 (It is divisible by 3)
So we will check for divisibility by 8.
Last three digits i.e. 024
Since, 024 is divisible by 8. Therefore the number is divisible by 24.