**Q1. A number N is a positive three-digit number. If x is in its hundred’s place and y is in its unit’s place, then the number N – 100x – y is always divisible by:**

**S1. Ans.(c)**

**Sol.**Let the number is xzy

**Q2. If a and b are odd numbers, then which of the following is even?**

**S2. Ans.(d)**

**Sol.**Odd number + odd number = even number

** Q4. Three difference containers contain different quantities of mixture of milk and water, whose measurements are 403 kg, 434 kg, and 465 kg. What biggest measure must be there to measure all the different quantities exactly? **

(a) 1 kg

(b) 7 kg

(c) 31 kg

(d) 41 kg

**S4. Ans.(c)**

**Sol.** Biggest measurements to measure 403 kg, 434 kg and 465 kg = HCF of (403, 434, 465)

= HCF of (13 × 31, 14 × 31, 15 × 31) = 31

Hence, required answer = 31 kg

**Q5. The greatest number that divides 43, 91 and 183 so as to leave the same remainder in each case is: **

(a) 9

(b) 8

(c) 4

(d) 3

**S5. Ans.(c)**

**Sol**. Let the greatest number be x

∴ 43 = nx + k

⇒ 91 = mx + k

⇒ 183 – 1x + k

⇒ 48 = (m – n) x

⇒ 92 = (l – m) x

⇒ 140 = (l – n) x

∴ x = H.C.F of 48, 92 and 104 = 4

Hence, 4 is a greatest number

**Q6. Multiply the difference between the two lowest numbers with the difference between the two highest numbers in the following sequences: **

**89, 7, 91, 72, 31, 25, 18, 89, 16, 58, 38, 42, 86 **

(a) 18

(b) 77

(c) 81

(d) 16

**S6. Ans.(a)**

**Sol.**Difference between two lowest numbers = 16 – 7 = 9