Quantitative Aptitude - Arithmetic Ability Questions

Q:

The product of two numbers is 2028 and their H.C.F. is 13. The number of such pairs is:

A) 1 B) 2
C) 3 D) 4
 
Answer & Explanation Answer: B) 2

Explanation:

Let the numbers 13a and 13b.

Then, 13a x 13b = 2028

=>ab = 12.

Now, the co-primes with product 12 are (1, 12) and (3, 4).

[Note: Two integers a and b are said to be coprime or relatively prime if they have no common positive factor other than 1 or, equivalently, if their greatest common divisor is 1 ]

So, the required numbers are (13 x 1, 13 x 12) and (13 x 3, 13 x 4).

Clearly, there are 2 such pairs.

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Filed Under: HCF and LCM

231 68511
Q:

An air conditioner can cool the hall in 40 miutes while another takes 45 minutes to cool under similar conditions. If both air conditioners are switched on at same instance then how long will it take to cool the room approximately ?

A) 18 minutes B) 19 minutes
C) 22 minutes D) 24 minutes
 
Answer & Explanation Answer: C) 22 minutes

Explanation:

Let the two conditioners be A and B

 

'A' cools at 40min

 

'B' at 45min

 

Together = (a x b)/(a + b)

= (45 x 40)/(45 + 40)

= 45 x 40/85

= 21.1764

= 22 min (approx).

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Filed Under: Time and Work
Exam Prep: GRE , GATE , CAT , Bank Exams , AIEEE
Job Role: Bank PO , Bank Clerk

92 68191
Q:

A began a business with Rs. 85,000. He was joined afterwards by B with Ks. 42,500. For how much period does B join, if the profits at the end of the year are divided in the ratio of 3 : 1 ?

A) 4 months B) 5 months
C) 6 months D) 8 months
 
Answer & Explanation Answer: D) 8 months

Explanation:

Suppose B joined for x months . Then,  ( 85000 * 12 )/(42500 * x) = 3. or x = (85000 * 12) / (42500 * 3) = 8.

So, B joined for 8 months.

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Filed Under: Partnership

97 68189
Q:

A man's speed with the current is 15 km/hr and the speed of the current is 2.5 km/hr. The man's speed against the current is :

A) 9.5 km/hr B) 10 km/hr
C) 10.5 km/hr D) 11 km/hr
 
Answer & Explanation Answer: B) 10 km/hr

Explanation:

Man's rate in still water = (15 - 2.5) km/hr = 12.5 km/hr.

Therefore,  Man's rate against the current = (12.5 - 2.5) = 10 km/hr.

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

109 67774
Q:

Consider the following for real numbers α, β, γ and δ ?

1) sec α = 1/4

2) tan β = 20

3) cosec γ = 1/2

4) cos δ = 2

How many of the above statements are not possible?

 

A) one  B) two
C) three D) four
 
Answer & Explanation Answer: C) three

Explanation:
Sec of any number can never be less than 1
tan can take any value from -∞ to + ∞
cosec of any number can never be less than 1
cos of any number can never be greater than 1
so option 1,3,4 are not possible
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Filed Under: Simplification
Exam Prep: Bank Exams

1 67635
Q:

Find the wrong number in the given number series?

180, 90, 60, 40, 36

A) 36 B) 40
C) 60 D) 90
 
Answer & Explanation Answer: B) 40

Explanation:

The given number series is 180, 90, 60, 40, 36

It follows a pattern that,

180 x 1/2 = 90

90 x 2/3  = 60

60 x 3/4  = 45 (NOT 40)

45 x 4/5  = 36

 

Hence, the wrong number in the given series is 40.

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Filed Under: Odd Man Out
Exam Prep: AIEEE , Bank Exams , CAT , GATE
Job Role: Analyst , Bank Clerk , Bank PO

2 67486
Q:

In how many different ways can the letters of the word 'LEADING' be arranged in such a way that the vowels always come together?

A) 720 B) 520
C) 700 D) 750
 
Answer & Explanation Answer: A) 720

Explanation:

The word 'LEADING' has 7 different letters.

When the vowels EAI are always together, they can be supposed to form one letter.

Then, we have to arrange the letters LNDG (EAI).

Now, 5 (4 + 1) letters can be arranged in 5! = 120 ways.

The vowels (EAI) can be arranged among themselves in 3! = 6 ways.

Required number of ways = (120 x 6) = 720.

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84 67384
Q:

The average weight of a class of 24 students is 35 kg. If the weight of the teacher be included, the average rises by 400 g. The weight of the teacher is : 

A) 45 kg B) 46 kg
C) 47 kg D) 48 kg
 
Answer & Explanation Answer: A) 45 kg

Explanation:

Weight of the teacher = (35.4 x 25 - 35 x 24) kg = 45 kg.

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Filed Under: Average

233 67314