Q: Statements: Z % M, M * F, F δ D Conclusions: I. F % Z II. F δ Z III. D @ Z

Z = M ...(i) M ≤ F ...(ii) F > D ...(iii) From (i) and (ii) Z = M ≤ F or F ≥ Z ...(iv) Hence either F = Z (I is true) or F > Z (II follows) From (iii) and (iv) no relationship can be established between D and Z Hence III does not follow.

Q: Find the correct group of signs to solve the equation. 24 * 16 * 8 * 32

Solve by using all option one by one. Given equation is 24 * 16 * 8 * 32 Taking the sign of option (D), ⇒ 24 + 16 - 8 = 32 Apply the BODMAS Rule in equation. ⇒ 40 - 8 = 32 ⇒ 32 = 32 Hence, correct group of sign is option (b).

Q: If A + B = 2C and C + D = 2A, then

Given, A + B = 2C ----(i) C + D = 2A----(ii) Adding (i) and (ii) we get : A + B + C + D = 2C + 2A => B + D = A + C

Question 1

Statements: W © K, K δ R, R % N Conclusions: I. N @ K II. R @ W III. W δ N

Accepted Answer

W ≥ K ...(i) K > R ....(ii) R = N ...(iii) Combining these we get W ≥ K > R = N Hence N < K and I follows Again R < W and II follows. And, W > N III follows.

Question 2

Statements: H * W, W @ N, N % R Conclusions: I. R δ W II. N δ W III. H @ R

Accepted Answer

H ≤ W ..(i) W < N ...(ii) R = N ...(iii) Combining these we get H ≥ W < N = R Hence R > W and I follows Again N > W and II follows And, H < R III follows

Question 3

Statements: Z % M, M * F, F δ D Conclusions: I. F % Z II. F δ Z III. D @ Z

Accepted Answer

Z = M ...(i) M ≤ F ...(ii) F > D ...(iii) From (i) and (ii) Z = M ≤ F or F ≥ Z ...(iv) Hence either F = Z (I is true) or F > Z (II follows) From (iii) and (iv) no relationship can be established between D and Z Hence III does not follow.

Question 4

Statements: D @ K, K % F, F © B Conclusions: I. F δ D II. B @ K III. B % K

Accepted Answer

D < K ...(i) K = F ...(ii) F ≥ B ...(iii) From (i) and (ii) D < K = F or F > D Hence I is true From (ii) and (iii) K = F ≥ B or B ≤ K. Hence either II (B < K) or (B = K) is true

Question 5

Find the correct group of signs to solve the equation. 24 * 16 * 8 * 32

Accepted Answer

Solve by using all option one by one. Given equation is 24 * 16 * 8 * 32 Taking the sign of option (D), ⇒ 24 + 16 - 8 = 32 Apply the BODMAS Rule in equation. ⇒ 40 - 8 = 32 ⇒ 32 = 32 Hence, correct group of sign is option (b).

Question 6

If A + B = 2C and C + D = 2A, then

Accepted Answer

Given, A + B = 2C ----(i) C + D = 2A----(ii) Adding (i) and (ii) we get : A + B + C + D = 2C + 2A => B + D = A + C

Question 7

Find out the two signs to be interchanged for making following equation correct 5 + 3 x 8 - 12 / 4 =3

Accepted Answer

On interchanging - and /, we get the equation as 5 + 3 x 8 / 12 - 4 = 3 or 5 + 3 x (2/3) - 4 = 3 or 3 = 3, which is true.

Question 8

Given interchanges : Signs + and - , numbers 4 and 8.

Accepted Answer

On interchanging + and - and 4 and 8 in (b), we get the equation as 8 + 4 - 12 = 0 or 12 - 12 = 0 or 0 = 0, which is true.

Question 9

If × stands for 'addition', ÷ stands for 'subtraction', + stands for 'multiplication' and-stands for 'division', then 20 × 8 ÷ 8 - 4 + 2 = ?

Accepted Answer

By the Given data , We have the expression: 20 + 8 - 8 ÷ 4 × 2 = 20 + 8 - 2 × 2 = 20 + 8 - 4 = 24.

Question 10

Given intercharges : Signs + and x and numbers 4 and 5.

Accepted Answer

On interchanging + and x and 4 and 5 in (c), we get the equation as 4 + 5 x 20 = 104 or 104 = 104, which is true.

Question 11

Select the correct set of symbols which will fit in the given equation? 5 0 3 5 = 20

Accepted Answer

Clearly 5 - 0 + 3 X 5 = 20

Question 12

If × means ÷, - means ×, ÷ means + and + means- than (3 - 15 ÷ 19) × 8 + 6 = ?

Accepted Answer

By the given data, we have the expression : (3 × 15 + 19) ÷ 8 - 6 = (45 + 19) ÷ 8 - 6 = 64 ÷ 8 - 6 = 8 - 6 = 2

Question 13

12:30 :: 14: ?

Accepted Answer

Here 12 x 2.5 = 30 In the same way 14 x 2.5 = 35

Question 14

If Q means 'add to', J means 'multiply by', T means 'substract from' and K means 'divide by' then 30 K 2 Q 3 J 6 T 5 = ?

Accepted Answer

Using Correct Symbols , We have : Given expression = 30 / 2 + 3 x 6 - 5 = 15 + 18 - 5 = 28

Question 15

In a group of buffaloes and ducks the number of legs are 24 more than twice the number of heads. What is the number of buffaloes in the group ?

Accepted Answer

Let the number of buffaloes be x and number of ducks be y. Now, number of heads = x+y Number of legs = 4x+2y .......(1) But given that legs = 2(x+y)+24 ......(2) solving (1) & (2),we get 4x+2y=2x+2y+24 --> x=12. Therefore number of buffaloes =12

Question 16

In a cricket match, five batsmen P, Q, R, S and T scored an average of 36 runs. S Scored 5 more than T; T scored 8 fewer than P; Q scored as many as S and T combined; and Q and R scored 107 between them. How many runs did T score ?

Accepted Answer

Let the runs scored by P, Q, R, S and T be a, b, c, d and e From given data, a + b + c + d + e = 36 x 5 = 180 b + c = 107 Let a = x e = x-8 d = x-3 now 3x - 11 + 107 = 180 3x = 84 x = 28 e's score = 28-8 = 20

Question 17

The solution of 3(2u + v) = 7 uv and 3(u + 3v) = 11 uv is _____

Accepted Answer

Using Trial and error method, From the options u = 1, v = 3/2 satisfies both the equations.

Question 18

What approximate value will come in place of question mark (?) in the following question ? (49.001)2 = ?

Accepted Answer

Given (49.001)2 = ? => =~ 49 x 49 =~ 2401 =~ 2400

Question 19

What should come in place of the question mark(?) in the following questions ? 316 + 412 - 223 - 11112 = ?

Accepted Answer

? = (3 + 4 - 2 - 1) + ( 1/6 + 1/2 - 2/3 - 11/12) = 4 + [(2+6-8-11)/12] = 4 - (11/12 )= 31/12.

Question 20

A sum of Rs.1890 has to be used to give 9 prizes to the customers of a super market for their overall academic purchases. If each prize is Rs.30 less than its preceding price, what is the least value of the price ?

Accepted Answer

Let the least value of the prize = Rs. x Then the next value of the prize is x+30 , x+60, x+90, ....x+240. Given total amount of cash prizes = Rs.1890 --> x + (x+30) + (x+60) + (x+90) + ....+ (x+240) = 1890 --> 9x + (30 + 60 + 90 + 120 + 150 + 180 + 210 + 240) = 1890 --> 9x + 30(1 + 2 + 3 + 4....+ 8) = 1890 --> 9x + 30(36) = 1890 --> 9x = 810 --> x=90 Hence the least value of the prize x=90

Mathematical Operations Questions