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- Question
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
- Correct Answer
- pq+27
ExplanationA 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).
- 1. All the boys are sitting together.
Options- A. 3/42
- B. 41/42
- C. 3/35
- D. 1/42 Discuss
- 2. Find the SP when CP is ? 40 and gain is 25%.
Options- A. ? 50
- B. ? 45
- C. ? 60
- D. ? 49 Discuss
- 3. The cost price of an article is C and the selling price of the same article is S, where Z is the profit or loss percentage. If the CP and SP both are increased by same amount then which of the following is true :
Options- A. Z increases
- B. Z decreases
- C. remains constant
- D. none of these Discuss
- 4. Which number is 60% less than 80?
Options- A. 48
- B. 42
- C. 32
- D. 12 Discuss
- 5. ?. ? 500x + ? 402 = 0
?. ? 360y + ( 200 ) 1/2 = 0
Options- A. 1
- B. 2
- C. 3
- D. 4 Discuss
- 6. A sum money becomes (8/5) of itself in 5 years at a certain rate of interest . The rate percent per annum is?
Options- A. 5%
- B. 8%
- C. 10%
- D. 12% Discuss
- 7. A certain sum of money at simple interest amounts to Rs. 1012 in 2 1/ 2 years and to Rs. 1067.20 in 4 years. The rate of interest per annum is?
Options- A. 2.5%
- B. 3%
- C. 4%
- D. 5% Discuss
- 8. In how many years will a sum of money double itself at 12% per annum?
Options- A. 6 years 9 months
- B. 8 years 4 months
- C. 7 years 6 months
- D. 8 years 6 months Discuss
- 9. The simple interest on a sum of money at 8% per annum for 6 years is half the sum. The sum is?
Options- A. Rs. 4800
- B. Rs. 6000
- C. Rs. 8000
- D. Data inadequate Discuss
- 10. 6888.009 - 487.999 - 87.989 =?
Options- A. 6000
- B. 6570
- C. 6430
- D. 6310 Discuss
More questions
Correct Answer: 1/42
Explanation:
Required probability = 6!5!/10! = 1/42
Correct Answer: ? 50
Explanation:
SP = 125% of CP [? SP = {(100 + Gain%)/100} x CP]
= {125/100} x 40
= (5/4) x 40 = 5 x 10 = ? 50
Correct Answer: Z decreases
Explanation:
The profit = SP - CP
If SP and CP both increase at same amount then the profit would be same.
As we know profit % (Z) = Actual profit / CP
So if CP increases the profit % (Z) will go down as there is no change in actual profit.
Correct Answer: 32
Explanation:
Required number = 80 - 60% of 80
= 80 - (60 x 80)/100
= 32
Correct Answer: 3
Explanation:
As per the given above equations , we can say that
?.
?500x + ?402 = 0
? ?500x = - ?402
? x = - ?( 402/500 ) = - ?( 400/500 ) = - 0.9
?. ?360y + ( 200 )1/2 = 0
? ?360y = - ?200
?
y = - ?( 200 / 360 ) = - 0.74
Clearly, we can see that x < y is required answer .
Correct Answer: 12%
Explanation:
Let sum = Rs. P.
Then amount = Rs. (8P/5)
? S.I = Rs. (8P/5 - P ) = Rs.(3P/5)
? Required rate = (100 x SI) / (P x T)
= [(100 x 3P/5) / (P x 5)]% = 12%
Correct Answer: 4%
Explanation:
? S.I. for 3/2 years = Rs. (1067.20 - 1012) = Rs. 55.20
? S.I. for 5/2 years = Rs. 55.20 x (2/3) x (5/2) = 92
? Sum = Rs. (1012 - 92) = Rs.920
Hence, Rate = (100 x SI)/(P x T) = (100 x 92) / (920 x 5/2 ) = 4%
Correct Answer: 8 years 4 months
Explanation:
Let principal = P.
Then, S.I = P,
Rate (R) = 12%
Time = (100 x SI) / (R x P) = (100 x P) / (P x 12) years
= 25/3 years
= 8 years 4 months
Correct Answer: Data inadequate
Explanation:
Let, Sum = P
Then S.I = P/2
Rate = 8%
and Time = 6 years
But P/2 = (P x 8 x 6) /100 (Not possible )
Thus, data is inadequate.
Correct Answer: 6310
Explanation:
? = 6888.009 - 487.999 - 87.989
? ? ? 6888 - 488 - 88
? ? ? 6888 - 576 ? ? ? 6312 ? 6310
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