If n is even, which of the following cannot be odd?

Correct Answer: 21

Explanation:

A prime number is a whole number greater than 1 whose only factors are 1 and itself.

 

Factors of 5 are 1, 5

Factors of 11 are 1, 11

Factors of 21 are 1, 3, 7, 21

Factors of 37 are 1, 37.

 

Hence, according to the definition of a prime number, 21 is not a prime number as it has more than two factors.

Correct Answer: 320

Explanation:

1 to 300 = 300 numbers
squares btwn 1 to 300 = 1,4,9,16,25,36,49.....289 i.e, total 17
cubes = 1,8,27,64,125,216 i.e, 5
now 1 and 64 are common so total numbers that should be removed ( 17+5-2= 20 )
total 20 term removed so 300th term would be 320

Correct Answer: 6

Explanation:

Sum of decimal places = 7.

Since the last digit to the extreme right will be zero (since 4 x 5 = 20), so there will be 6 significant digits to the right of the decimal point.

Correct Answer: 11.5 kgs

Explanation:

Screws weight = 90x100 = 9000gms
bolts weight = 100 x 150 = 15000gms
weight = screws + bolts => 24000 gms =>24 kg
Given entire box weight = 35.5kg
empty box = entire box weight - weight => 35.5kg - 24kg => 11.5kg
so the empty box is 11.5kg.

Correct Answer: 9

Explanation:

Last digit for the power of 6 is 6 (always)

Power cycle of 7 is 7, 9, 3, 1.

Now 467/4 gives a remainder of 3

Then the last digit is 7 3 = 3

Last digit is 6 + 3 = 9.

Correct Answer: pq+27

Explanation:

A perfect cube will have prime factors that are in groups of 3; for example 125 has the prime factors 5 x 5 x 5 , and 64 x 125 will also be a cube because its factors will be 4 x 4 x 4 x 5 x 5 x 5

Consider the answer choices in turn.

8 is the cube of 2, and p is a cube, and so the product will also be a cube.

pq will also be a cube as shown above.

pq is a cube and so is 27, but their sum need not be a cube. Consider the case where p =1 and q = 8, the sum of pq and 27 will be 35 which has factors 5 x 7 and is not a cube.

-p will be a cube.

Since the difference between p and q is raised to the power of 6, this expression will be a cube (with cube root = difference squared).

Correct Answer: 7

Explanation:

   1 1
   8 A 9
+ 4 C 6
-  6 B 2
   7 2 3
We may represent the given sum, as shown below:

1 + A + C - B = 12
A + C - B = 11

Now,giving the maximum values to A and C, i.e.

A = 9 and C = 9, we get B = 7.

Correct Answer: 31

Explanation:

Given   6 5 × 35 9 × 11 3

? 2 × 3 5 × 5 × 7 9 × 11 3 

? 2 5 × 3 5 × 5 9 × 7 9 × 11 3

Thus, there are (5 + 5 + 9 + 9 + 3)= 31 prime numbers.

Correct Answer: 44 & 28

Explanation:

Let
x = peacocks
y = deers

2x + 4y = 200
x + y = 72
y = 72 - x
2x + 288 - 4x = 200
x = 44 peacocks
y = 28 deers

Correct Answer: 0

Explanation:

Let assume the value of a,b &c that will satisfy the equation.
so a=1,b=1,c= -1 or a=1,b= -1 &c=1 or a= -1,b=1,c=1
here all three cases satisfy the equation
assume any one a=1,b=1,c= -1

Hence (a+b)(b+c)(c+a)=(1+1)(1-1)(-1+1) = 0