Hemavathi cut a cake into two halves and cuts one half into smaller pieces of equal size. Each of the small pieces is fifteen grams in weight. If she has nine pieces of the cake in all with her, how heavy was the original cake ?

Correct Answer: Any one pair of A and B, B and C or C and A is sufficient

Explanation:

From the given data,

Let the two gits of a number be x & y

A) x + y = 15

 

B)  x 2 - y 2 = 45

(x+y) (x - y) = 45

 

C) x - y = 3

From any 2 of the given 3 statements, we can find that 2 digit number as 

2x = 18 => x = 9

=> y = 6

Hence, 2 digit number is 96.

 

Any one pair of A and B, B and C or C and A is sufficient to find.

Correct Answer: 5.008 x 10^3 kms

Explanation:

We know that, any decimal number when multiplied by the multiples of 10, the decimal point moves to right the number of zeroes in the multiplying number.

 

For example :: 

0.0410 x 100 = 4.10 (Number of zeros in 100 are 2. So, the decimal point in 0.0410 moves two places to the right and becomes 4.10.)

 

Similarly, here in the option C) 5.008 x 10^3 kms it makes 5008 kms as the number of zeros in 10^3  i.e,  1000 are 3 and 5.008 becomes 5008.

Correct Answer: 2015736

Explanation:

Divisibility rule for 24 is the number should be divisible by 3 and 8. As we know that 24 = 3 x 8

Now, 

Divisibility rule for 3 :

If the sum of the digits of a number is divisible by 3, then the number is divisible by 3.

 

Divisibility rule for 8 :

The last three digits of a number should be divisible by 8.

Hence, check for the given options,

A) 37804 => 804 is not divible by 8.

C) 36718 => 718 is not divible by 8.

D) 53810 => 810 is not divible by 8.

B) 2015736 => 736 is divisble by 8 and sum 2 + 0 + 1 + 5 + 7 + 3 + 6 = 24 which is divisible by 3.

 

Hence, 2015736 is divisible by 24.

Correct Answer: 9

Explanation:

Perimeter = 36

? 2 ( l + w ) = 36

? l + w = 18

Since length and width are positive integers in centimeters.

Therefore, possible dimensions are :

( 1, 17 )cm , ( 2, 16 ) cm , ( 3, 15 ) cm, (4 , 14) cm, ( 5,13) cm, ( 6, 12) cm , ( 7, 11) cm, ( 8, 10 ) cm, ( 9, 9) cm.

Hence, there are 9 rectangles.

Correct Answer: 31

Explanation:

We all know about BODMAS rule, by using that

3x3x3+3+3/3

= 3x3x3+3+1

= 27+3+1

= 27 + 4

= 31

 

Hence,  3x3x3+3+3/3 = 31.

Correct Answer: 11 days

Explanation:

Let 'n' number of days it take to complete.

 

we know that sum of n number= n/2[2a+(n-1)d]
where a=20,d=1;
n/2[2x20+(n-1)1]=275
n[n+39]=550
n 2 + 39n - 550 = 0
  n 2+ 50n - 11n - 550 = 0
(n-11) (n-50) = 0
n-11 = 0;
n = 11(Days).

Correct Answer: 54

Explanation:

Let R, G and B represent the number of balls in red, green and blue boxes respectively.

Then, .

R + G + B = 108 ...(i),

G + R = 2B ...(ii)

B = 2R ...(iii)

From (ii) and (iii), we have G + R = 2x 2R = 4R or G = 3R.

Putting G = 3R and B = 2R in (i), we get:

R + 3R + 2R = 108 6R = 108 R = 18.

Therefore Number of balls in green box = G = 3R = (3 x 18) = 54.

Correct Answer: 50

Explanation:

15 girls are absent => b = 2(g-15)...... eqn...(1)

45 boys are absent => g - 15 = 5(b-45).....eqn...(2)

=> g = 5(b-45) + 15

=> b = 2((5(b-45)+15)-15)

=> b = 2(5b - 225 + 15 - 15)

=> b = 2(5b-225)

=> b = 10b - 450

=> 9b = 450

=> b = 50

so from equation(2)

g - 15 = 5(b - 45)

=> g - 15 = 5(50-45)

=> g - 15 = 5(5)

=> g = 25 + 15

=> g = 40

Therefore, the number of boys = 50 and girls = 40

Correct Answer: is described generally, not using a formal definition

Explanation:

In geometry, we can define plane as a flat surface with no thickness.

The surface extends with no ends.

A plane does not have any edges even if we draw it on paper with edges, it does't mean it has edges.

 

Hence, A plane is an undefined term because it is described generally, not using a formal definition.

Correct Answer: 1

Explanation:

The product of a number and its reciprocal is always equals to 1.

 

For Example : Let the number be 4.

Now, its reciprocal is 1/4

Hence, required product = 4 x 1/4 = 1.

 

Now, take the number as -15.

Then its reciprocal is -1/15

Required product = -15 x -1/15 = 1.

 

Hence, the product of a number and its reciprocal is 1.