1.

Four prime numbers are written in ascending order. The product of the first 3 numbers is 105. The product of the last 3 is 385. Find the second number

**Answer: Option 'C'**

**Let the numbers a, b, c and d.
abc = 105
bcd = 385
HCF(abc, bcd) = bc
Since a and d are prime.
105 = 3 × 5 × 7
385 = 5 × 7 × 11
HCF(105, 385) = 35 = 5 × 7
The second number is 5.**

2.

In a division sum, the remainder is 6 and the divisor is 5 times the quotient and is obtained by adding 2 to the thrice of the remainder. The dividend is:

**Answer: Option 'C'**

**Divisor = (6 × 3) + 2 = 20
5 × Quotient = 20
Quotient = 4.
Dividend = (Divisor × Quotient) + Remainder
Dividend = (20 × 4) + 6 = 86**

3.

If x and y are the two digits of the number 653xy such that this number is divisible by 80, then x + y = ?

**Answer: Option 'A'**

**80 = 2 x 5 x 8 Since 653xy is divisible by 2 and 5 both, so y = 0. Now, 653x is divisible by 8, so 13x should be divisible by 8. This happens when x = 6. x + y = (6 + 0) = 6.**

4.

217 x 217 + 183 x 183 = ?

**Answer: Option 'B'**

**(217) ^{2} + (183)^{2} = (200 + 17)^{2} + (200 - 17)^{2} = 2 x [(200)^{2} + (17)^{2}] [Ref: (a + b)^{2} + (a - b)^{2} = 2(a^{2} + b^{2})] = 2[40000 + 289] = 2 x 40289 = 80578.**

5.

How many numbers from 10 to 100 are exactly divisible by 10.

**Answer: Option 'D'**

**10/10 = 1 and 100/10 = 10
==> 10 - 1 = 9
==> 9 + 1 = 10 Numbers**

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