5% Search

Q:

Find the unit digit of 4¹⁹⁸ + 6¹²³⁴⁵ + 348⁶⁶ + 24¹¹ + 1.

A) 3	B) 2
C) 1	D) 0

Answer & Explanation Answer: C) 1

Explanation:

Given that, $4^{198} + 6^{12345} + 348^{66} + 24^{11} + 1$

Now Power Cycle of

4 is 4, 6

6 is 6

8 is 8, 4, 2, 6

1 is 1

$4^{198}$ - 198 is even number , So the unit digit value is 6

$6^{12345}$ - It is always 6

$348^{66}$ - 66/4 the remainder is 2 , So the second value is 4

$24^{11}$ - 11 is odd number, So the unit digit value is 4

1 - It is always 1

Total = 21

Therefore, The unit digit is 1

Report Error

View Answer Report Error Discuss

Filed Under: Numbers
Exam Prep: CAT
Job Role: Bank PO

Q:

A man is riding a bike with front and back wheel circumference of 40 inches and 70 inches respectively. If the man rides the bike on a straight road without slippage, how many inches will the man have travelled when the front wheel has made 15 revolutions more than the back wheel?

A) 1100	B) 1300
C) 1400	D) 1200

Answer & Explanation Answer: C) 1400

Explanation:

Given the ratio of the circumference of front wheel is 40 inches and back wheel is 70 inches.

Distance covered = Circumference of the wheel × No. of Revolutions made by the wheel

If n is the number of revolutions made by back wheel, the number of revolutions made by front wheel is n+15

Distance covered by both the wheels is the same

i.e, 40*(n+15)=70n

n=20

Front wheel : Back Wheel

Circumference 40 : 70

Revolutions 35 : 20

Distance covered : 40×35 = 70×20 = 1400 inches.

Report Error

View Answer Report Error Discuss

Filed Under: Time and Distance
Exam Prep: CAT
Job Role: Bank PO

Q:

The ratio of Karthik’s and Kalyan’s ages is 4: 5. If the difference between the present age of Kalyan and the age of Karthik 5 years hence is 3 years, then what is the total of present ages of Karthik and Kalyan?

A) 56 years	B) 62 years
C) 69 years	D) 72 years

Answer & Explanation Answer: D) 72 years

Explanation:

Let us consider Karthik as K1 and Kalyan as K2.

Given $\frac{k 1}{8 + k 1}$ and K2 - (K1 + 5) = 3

K2 - K1 = 8

K2 = 8 + K1

Now,

$\frac{k 1}{8 + k 1} = \frac{4}{5}$

=> K1 = 32 years

Therefore K2 = 40 years.

K1 + K2 = 72 years.

Report Error

View Answer Report Error Discuss

Filed Under: Problems on Ages
Exam Prep: CAT
Job Role: Bank PO

Q:

How many prime numbers exist in $6^{5} \times 35^{9} \times 11^{3}$ ?

A) 29	B) 31
C) 33	D) 27

Answer & Explanation Answer: B) 31

Explanation:

Given $6^{5} \times 35^{9} \times 11^{3}$

$\Rightarrow {(2 \times 3)}^{5} \times {(5 \times 7)}^{9} \times 11^{3}$

$\Rightarrow 2^{5} \times 3^{5} \times 5^{9} \times 7^{9} \times 11^{3}$

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

Report Error

View Answer Report Error Discuss

Filed Under: Numbers
Exam Prep: CAT
Job Role: Bank PO

Q:

5 sin(x)+ 12 cos(x) + r is always greater than or equal to zero. What is the smallest value satisfied by 'r' ?

A) -13	B) 11
C) 13	D) -11

Answer & Explanation Answer: C) 13

Explanation:

Given,

5sinx + 12cosx ≥ -r

$\Rightarrow 13 (\frac{5}{13} \sin x + \frac{12}{13} \cos x) \geq - r$ cosx) ≥ -r

$\frac{5}{13}$ = cosA => sinA = $\frac{12}{13}$

=> 13(sinx cosA + sinA cosx) ≥ -r

=> 13(sin(x + A)) ≥ -r

we know that , -1 ≤ sin (angle) ≤ 1

=> 13sin (x + A) ≥ -13 $\Rightarrow r_{m i n} = 13$

Report Error

View Answer Report Error Discuss

Filed Under: Simplification
Exam Prep: CAT
Job Role: Bank PO

Q:

A container contains 50 litres of milk. From that 8 litres of milk was taken out and replaced by water. This process was repeated further two times. How much milk is now contained by the container ?

A) 24.52 litres	B) 29.63 litres
C) 28.21 litres	D) 25.14 litres

Answer & Explanation Answer: B) 29.63 litres

Explanation:

Given that container has 50 litres of milk.

After replacing 8 litres of milk with water for three times, milk contained in the container is:

$\Rightarrow [50 {(1 - \frac{8}{50})}^{3}]$

$\Rightarrow (50 \times \frac{42}{50} \times \frac{42}{50} \times \frac{42}{50})$ = 29.63 litres.

Report Error

View Answer Report Error Discuss

Filed Under: Alligation or Mixture
Exam Prep: CAT
Job Role: Bank PO

Q:

A person takes a loan of Rs. 200 at 5% simple interest. He returns Rs.100 at the end of one year. In order clear his dues at the end of 2 years, he would pay :

A) Rs. 100	B) Rs. 105
C) Rs. 115	D) Rs. 110

Answer & Explanation Answer: C) Rs. 115

Explanation:

Amount to be paid = $R s . [100 + \frac{200 \times 5 \times 1}{100} + \frac{100 \times 5 \times 1}{100}]$ = Rs. 115.

Report Error

View Answer Report Error Discuss

Filed Under: Simple Interest
Exam Prep: CAT
Job Role: Bank Clerk

Q:

3125 256 ? 4 1

Which number replaces the "?" in the question?

A) 27	B) 128
C) 32	D) 64

Answer & Explanation Answer: A) 27

Explanation:

In the given series numbers are arranged following the rule,

$5^{5}, 4^{4}, 3^{3}, 2^{2}, 1^{1}$

Therefore, the missing number is 27.

Report Error

View Answer Report Error Discuss

Filed Under: Odd Man Out
Exam Prep: CAT
Job Role: Bank PO

Searching for "5%"

Quick Links