**10. Sum of consecutive integers is 18. What is the smallest integer less 3?**

A) 2 B) 3 C) 4 D) 5 E) None

Sol: Let, the three consecutive integers be n, n+2. Hence

3n + 3 = 18 = 3n=15

= n = 5

**:.**5-3 = 2

Ans: (A)

**11. The sum of 3 consecutive even integers is equal to 4 times the smallest. What is the smallest of the integers?**

Sol: Let, the consecutive integers be

X, X+2, X+4

According to question,

X+X+2+X+X+4 = 4X

= 3X + 6 = 4X

= 4X- 3X = 6

= X = 6

**:.**The smallest integer is 6.

Ans: 6

**12. If the average of 9 consecutive integers is 0, what is the average of the last 4 of the integers ?**

Sol: -4,-3,-2,-1,0,1,2,3,4

**:.**1,2,3&4 Average = (1+2+3+4)/4

= 10/4

= 2.5

Ans: 2.5

**13. If the average of 5 consecutive integers is 12, what is the sum of the smallest and the largest of the 5 integers?**

Sol: Let, the numbers be

X,X+1, X+2, X+3, X+4,

:. X+X+1+ X+2+ X+3+ X+4 = 12x5

= 5X+10 = 60

= 5X = 60 -10 = 50

= X = 50/5 = 10

:. Sum of the smallest and the largest number

= X+X+4

= 2X+4

= 2x10+4

= 24 (Ans)

**14. The sum of the 3 consecutive odd numbers exceeds twice the largest number by 6, What is hte sum ob the 3 number?**

Sol: Let, the three consecutive odd numbers be X, X+2, X+4

So, according to the problem

X+(X+2)+(X+4) = 2(X+4)+6.

Observe that on the left side of the equation we have

odd + odd +odd

Since, three odd numbers added together is always odd, the L.H.S is odd.

On the T.H.S we have

2 x odd + even = even + even = even

So, the R.H.S is even

Hence, this equation is invalid. This problem has no answer.

Ans: (D)

**15. Sum of 15 consecutive odd numbers is 375. Which of the 15 odd numbers is the largest?**

A) 39 B) 37 C) 35 D) 41 E) None

Sol: Let, the first number in the series be

**n .**So, the others are n +2, n+4,......n+28.

So, their sum is

n+(n+2)+(n+4)+......+(n+28)

= 15n + 2(1+2+3+........+14)

= 15n+ 2. 14(14+1)/2 = 15(n + 14)

According to the problem,

15(n+14) = 375

or, n + 14 = 375/15 = 25

or, n = 25-14 = 11

The largest number is (n + 28) = 11 + 28 = 29

Ans: (A)

**16. The average of 15 consecutive integers is 15. What is the smallest of the 15 integers?**

A) 6 B) 7 C) 8 D) 9 E)

**15**

Sol: Let, X be the 1ts integer. So, (X+14) is the last one. Hence, we can write

{(X+(X+1)+(X+2)+.......+(X+14)}/15 = 15

or, {15X+(1+2+............+14)}/15 = 15

or, X + {14(14+1)}/2.15 = 5

or, X+7 = 15

or, X = 15-7 = 8

Ans: (C)

**17. Find the next number in the series:**

3,6,4,9,5,12,6,...

Sol: 3 6 4 9 5 12 6 15 7 18 8

Ans: 15

**18. In a triangular seating area, the seats are arranged in rows so that the 1th , 2th , 3rd, 4th, etc. Rows contain 1,2,3,4 etc. seats and so on. 70 students take seat starting from the first row & filling up the rows in incre3asing order. How many rows are completely filled?**

**A) 9 B) 10 C) 11 D) 12 E) None**

Sol: If 1 row is completely filled we have 1 student

Of 2 rows are " " " " 1+2 = 3 student

But going like this is not very efficient. So, let us assume that 11 rows are completely filled. So, let us assume that 11 rows are completely filled. So no. of students is

1+2+3+...............+11 = 11(11+1)/2 = 11x12/2

= 66

Since 66< 70, This means that 11 rows are completely filled & the last row contains 4 student.

Ans: (C)

**19. What is the next number in the series 1, 11, 27, 57,.......?**

A) 123 B) 113 C) 93 D) 63 E) None

Sol: The answer is (E) since there is no definite pattern among the given numbers.

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