Question Detail

1307 * 1307 = ?

1608249
1508249
1408249
1708249

Answer: Option D

Explanation:

$\begin{aligned} (a + b)^{2} = (a^2 + b^2 + 2ab) \end{aligned}$
$\begin{aligned} 1307^{2} = (1300 + 7)^2 = (1690000 + 49 + 18200) \end{aligned}$

1. There are four prime numbers written in ascending order. The product of first three is 385 and that of last three is 1001. The last number is:

Answer: Option B

Explanation:

$\begin{aligned} \frac{abc}{bcd} = \frac{385}{1001} => \frac{a}{d} = \frac{5}{13} \end{aligned}$ So d = 13

2. 1939392 * 625

1212120010
1212120000
1212120011
1212121010

Answer: Option B

Explanation:

Trick: when multiplying with $\begin{aligned} 5^n \end{aligned}$ then put n zeros to the right of multiplicand and divide the number with $\begin{aligned} 2^n \end{aligned}$
So using this we can solve this question in much less
time.
$\begin{aligned} 1939392 \times 5^4 = \frac {19393920000}{16} = 1212120000 \end{aligned}$

3. 7589 - X = 3434

4155
2321
3155
None of above

Answer: Option A

4. A number when divided by 44, gives 432 as quotient and 0 as remainder. What will be the remainder when dividing the same number by 31

Answer: Option A

Explanation:

P ÷ 44 = 432

=> P = 432 * 44 = 19008

P / 31 = 19008 / 31 = 613, remainder = 5

5. Find the unit digit in $\begin{aligned} (544)^{102} + (544)^{103} \end{aligned}$

Answer: Option C

Explanation:

Required digit is = $\begin{aligned} (4)^{102} + (4)^{103} \end{aligned}$
as $\begin{aligned} (4)^2 \end{aligned}$ gives unit digit 6 so $\begin{aligned} (4)^{102} \end{aligned}$ unit digit is 6 and $\begin{aligned} (4)^{103} \end{aligned}$ unit digit is, unit digit of $\begin{aligned} 6 \times 4 \end{aligned}$ = 4, so answer will be unit digit of 6 + 4 = 0