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- Question
If 1/a+1/b+1/c = 1/(a+b+c) where a+b+c not equals '0', abc not equals '0', What is the value of (a+b) (b+c) (a+c) ?
Options- A. 3
- B. 2
- C. 1
- D. 0
- Correct Answer
- 0
ExplanationLet 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= -1Hence (a+b)(b+c)(c+a)=(1+1)(1-1)(-1+1) = 0
- 1. There are several peacocks and deers in a cage (with no other types of animals). There are 72 heads and 200 feet inside the cage. How many peacocks are there, and how many deers ?
Options- A. 42 & 24
- B. 38 & 26
- C. 36 & 24
- D. 44 & 28 Discuss
- 2. How many prime numbers exist in 65×359×113 ?
Options- A. 29
- B. 31
- C. 33
- D. 27 Discuss
- 3. What should be the maximum value of B in the following equation? 8A9 ? 6B2 + 4C6 = 723
Options- A. 4
- B. 1
- C. 5
- D. 7 Discuss
- 4. A perfect cube is an integer whose cube root is an integer. For example, 27, 64 and 125 are perfect cubes. If p and q are perfect cubes, which of the following will not necessarily be a perfect cube?
Options- A. 8p
- B. pq
- C. pq+27
- D. -p Discuss
- 5. If n is even, which of the following cannot be odd?
Options- A. n+3
- B. 2n
- C. n+4
- D. 3n Discuss
- 6. Which of the following is a rational number?
Options- A. 0.241
- B. 1.732
- C. 4
- D. All of the above Discuss
- 7. Which of the following is the largest?
Options- A. 12/49
- B. 7/30
- C. 13/56
- D. 11/46 Discuss
- 8. If a2 = 12, then a4 =?
Options- A. 144
- B. 72
- C. 36
- D. 24 Discuss
- 9. A solid cube of side 6 is first painted pink and then cut into smaller cubes of side 2. How many of the smaller cubes have paint on exactly 2 sides?
Options- A. 30
- B. 24
- C. 12
- D. 8 Discuss
- 10. Which of the following can be used to illustrate that not all prime numbers are odd?
Options- A. 1
- B. 2
- C. 3
- D. 4 Discuss
Numbers problems
Search Results
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: 31
Explanation:
Given
Thus, there are (5 + 5 + 9 + 9 + 3)= 31 prime numbers.
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: 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: 2n
Explanation:
In case B, odd times even will give even
Correct Answer: 4
Explanation:
Any number which can be expressed as a fraction of two integers like P & Q as P/Q where Q is not equal to zero.
Every integer is a rational number since Q can be 1.
Hence, in the given options, 4 can be expressed as a simple fraction as 4/1. And all other options cannot be expressed as fractions.
Hence, 4 is a rational number in the given options.
Correct Answer: 12/49
Explanation:
In the given options,
12/49 can be written as 1/(49/12) = 1/4.083
7/30 can be written as 1/(30/7) = 1/4.285
13/56 can be written as 1/(56/13) = 1/4.307
11/46 can be written as 1/(46/11) = 1/4.1818
Here in the above,
1/4.083 has the smallest denominator and so 12/49 is the largest number or fraction.
Correct Answer: 144
Explanation:
Given a x a = 12
asked to find a x a x a x a = (a x a) x (a x a)
a4 = a2 x a2
= 12 x 12
= 144.
Correct Answer: 12
Explanation:
When the larger cube is cut into smaller cubes, the corner cubes will have paint on three sides. The cubes in the middle of the faces will have paint on only one side, but the cubes cut from the edges will have paint on two sides. In this case, there will be only one cube one each edge (excluding the corners), and since there are 12 edges, there will be 12 cubes with paint on two sides.
Correct Answer: 2
Explanation:
The only even numbers in the list are 2 and 4, but 4 is not a prime. So 2 can be used to illustrate the statement that all primes are not odd.
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