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The LCM of two numbers is 520 and their HCF is 4. If one of the number is 52, then the other number is

A.

42

B.

32

C.

50

D.

40

Answer with explanation

Answer: Option DExplanation

First number * second number = LCM * HCF

52*Second number = 520 * 4

Second number = (520*4)/52

= 40

Then the other number is 40.

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What is the number nearest to 10000 which is exactly divisible by 3, 4, 5, 6, 7, and 8?

A.

9956

B.

10080

C.

10096

D.

9240

Answer with explanation

Answer: Option BExplanation

Take LCM of 3, 4, 5, 6, 7, and 8. It will be = 840.

Now, 10000/840 = 760 (remainder).

840 – 760 = 80. If we add 80 in the given number, the number is exactly divisible by 840.

So, the required number is 10080.

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If LCM of two number is 693, HCF of two numbers is 11 and one number is 99, then find other

A.

34

B.

45

C.

77

D.

12

Answer with explanation

Answer: Option CExplanation

For any this type of question, remember

Product of two numbers = Product of their HCF and LCM

So Other number = 693×11/99 = 77

Workspace

The least number which when divided by 5, 6 , 7 and 8 leaves a remainder 3, but when divided by 9 leaves no remainder, is:

A.

1677

B.

1683

C.

2523

D.

3363

Answer with explanation

Answer: Option BExplanation

L.C.M. of 5, 6, 7, 8 = 840.

Required number is of the form 840*k + 3*

Least value of *k* for which (840*k* + 3) is divisible by 9 is *k* = 2.

Required number = (840 x 2 + 3) = 1683.

Workspace

The greatest number which on dividing 1657 and 2037 leaves remainders 6 and 5 respectively, is:

A.

135

B.

127

C.

235

D.

307

Answer with explanation

Answer: Option BExplanation

Required number = H.C.F. of (1657 – 6) and (2037 – 5)

= H.C.F. of 1651 and 2032 = 127.

Workspace

The LCM of two numbers is 30 and their HCF is 5. One of the numbers is 10. The other is

A.

20

B.

15

C.

32

D.

23

Answer with explanation

Answer: Option BExplanation

First number * Second number = LCM * HCF

Let the second number be x.

10x = 30*5

x = 150/10 = 15

Workspace

Which is the greatest three-digit number which when divided by 6, 9 and 12 leaves a remainder of 3 in each case?

A.

975

B.

996

C.

939

D.

903

Answer with explanation

Answer: Option AExplanation

Greatest three digit number = 999

LCM of 6, 9 and 12

LCM = 2 x 2 x 3 x 3 = 36

On dividing 999 by 36,

Remainder = 27.

∴ The greatest three digit number divisible by 6, 9, and 12

= (999 – 27) = 972

As per the question, the required number is (972 + 3) = 975.

Workspace

The least multiple of 7, which leaves a remainder of 4, when divided by 6, 9, 15 and 18 is:

A.

253

B.

356

C.

384

D.

364

Answer with explanation

Answer: Option DExplanation

L.C.M. of 6, 9, 15 and 18 is 90.

Let required number be 90*k* + 4, which is multiple of 7.

Least value of *k* for which (90*k* + 4) is divisible by 7 is *k* = 4.

Required number = (90 x 4) + 4 = 364.

Workspace

Find the probability of getting a numbered card when a card is drawn from the pack of 52 cards.

A.

9/13

B.

2/13

C.

4/13

D.

5/13

Answer with explanation

Answer: Option AExplanation

Total Cards = 52. Numbered Cards = (2, 3, 4, 5, 6, 7, 8, 9, 10) 9 from each suit 4 × 9 = 36

P (E) = 36/52 = 9/13

Or

If you count an ace as a number card there are 40 in a pack so p(get a number card) = 40/52 = 10/13.

If aces don’t count then there are 9 x 4 = 36 in a pack so p(get a number card) = 36/52 = 9/13.

Workspace

A.

35

B.

36

C.

37

D.

38

Answer with explanation

Answer: Option CExplanation

If we want to pack the drinks in the least number of cans possible, then each can should contain the maximum numbers of liters possible.As each can contains the same number liters of a drink, the number of liters in each can is a comman factor for 80,144 and 368; and it is also the highest such factor, as we need to store the maximum number of liters in each can.

So, the number of liters in each can = HCF of 80,144 and 368 = 16 liters.

Now, number of cans of Maaza = 80/16 = 5

Number of cans of Pepsi = 144/16 = 9

Number of cans of Sprite = 368/16 = 23

Thus, the total number of cans required = 5 + 9 + 23 = 37

Workspace

A room is 6 meters 24 centimeters in length and 4 meters 32 centimeters in Width. Find the least number of square tiles of equal size required to cover the entire floor of the room.

A.

107

B.

117

C.

127

D.

137

Answer with explanation

Answer: Option BExplanation

Let us calculate both the length and width of the room in centimeters.

Length = 6 meters and 24 centimeters = 624 cm

width = 4 meters and 32 centimeters = 432 cm

As we want the least number of square tiles required, it means the length of each square tile should be as large as possible.Further,the length of each square tile should be a factor of both the length and width of the room.

Hence, the length of each square tile will be equal to the HCF of the length and width of the room = HCF of 624 and 432 = 48

Thus, the number of square tiles required = (624 x 432 ) / (48 x 48) = 13 x 9 = 117

Workspace

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