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Question Detail
Which among following is not a prime number ?
- 97
- 33
- 45
- 72
Answer: Option A
1. Three times the first of three consecutive odd integers is 3 more than twice the third. The third integer is
- 12
- 13
- 15
- 17
Answer: Option C
Explanation:
Let the three integers be x, x+2 and x+4.
Then, 3x = 2(x+4)+3,
x= 11
Therefore, third integer x+4 = 15
2. Sum of two numbers is 25 and their difference is 13. Find their product.
- 104
- 108
- 114
- 124
Answer: Option C
Explanation:
Friends, this sort of question is quite important in competitive exams, whenever any question come which have relation between sum, product and difference, this formula do the magic:
\begin{aligned}
=> (x+y)^2 = (x-y)^2 + 4xy
\end{aligned}
\begin{aligned}
<=> (25)^2 = (13)^2 + 4xy
\end{aligned}
\begin{aligned}
<=> 4xy = (25)^2 - (13)^2
\end{aligned}
\begin{aligned}
<=> xy = \frac{456}{4} = 114
\end{aligned}
3. if the sum of \begin{aligned} \frac{1}{2} \end{aligned} and \begin{aligned} \frac{1}{5} \end{aligned} of a number exceeds \begin{aligned} \frac{1}{3} \end{aligned} of the number by \begin{aligned} 7\frac {1}{3} \end{aligned}, then number is
- 15
- 20
- 25
- 30
Answer: Option B
Explanation:
Seems a bit complicated, isnt'it, but trust me if we think on this question with a cool mind then it is quite simple...
Let the number is x,
then, \begin{aligned} (\frac{1}{2}x + \frac{1}{5}x) - \frac{1}{3}x = \frac{22}{3} \end{aligned}
\begin{aligned}
=> \frac{11x}{30} = \frac{22}{3}
\end{aligned}
\begin{aligned}
=> x = 20
\end{aligned}
4. The product of two numbers is 120 and the sum of their squares is 289. The sum of the number is
- 20
- 23
- 27
- 150
Answer: Option B
Explanation:
We know
\begin{aligned}
(x + y)^2 = x^2 + y^2 + 2xy
\end{aligned}
\begin{aligned}
=> (x + y)^2 = 289 + 2(120)
\end{aligned}
\begin{aligned}
=> (x + y) = \sqrt{529} = 23
\end{aligned}
5. find the number, If 50 is subtracted from two-third of number, the result is equal to sum of 40 and one-fourth of that number.
- 214
- 216
- 114
- 116
Answer: Option B
Explanation:
Let the number is x,
\begin{aligned}
=> \frac{2}{3}x-50 = \frac{1}{4}x + 40
\end{aligned}
\begin{aligned}
<=> \frac{2}{3}x-\frac{1}{4}x = 90
\end{aligned}
\begin{aligned}
<=> \frac{5x}{12} = 90
\end{aligned}
\begin{aligned}
<=> x = 216
\end{aligned}
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