Aptitude and Reasoning Questions

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 

13513sin x + 1213cos x  -rcosx) ≥ -r 

513= cosA => sinA =1213

 

=> 13(sinx cosA + sinA cosx) ≥ -r

 

=> 13(sin(x + A)) ≥ -r

 

we know that , -1 ≤ sin (angle) ≤ 1

 

=> 13sin (x + A) ≥ -13 rmin =13 

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

8 6155
Q:

Choose the word which is least like the others word in a group?

A) Zinc B) Aluminium
C) Mercury D) Copper
 
Answer & Explanation Answer: C) Mercury

Explanation:

Mercury is the only liquid metal in the group.

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Filed Under: Classification

44 6149
Q:

The ratio between the perimeter and the breadth of a rectangle is 5 : 1. If the area of the rectangle is 216 sq. cm, what is the length of the rectangle?

A) 16cm B) 18cm
C) 24cm D) .Data inadequate
 
Answer & Explanation Answer: B) 18cm

Explanation:

2(l+b)/b = 5/1 

=> 2l + 2b = 5b  

=> 3b = 2l  

=> b =(2/3) x l

 Then, Area = 216 sq.cm 

 

l x b = 216  

=> l x [(2/3)x l] =216  

=> l x l = 324 

=> l = 18 cm.

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Q:

Consider the given arguments as true and decide which of the given assumptions is/are implicit.

Argument :
The best bus travels company has decided to increase its fare by 10%.

Conclusions :
1. Passengers may opt for other buses costing less than the best bus travels company.
2. The demand for the buses by passengers may remain unchanged even after the fare hike.

 

A) Both 1 & 2 are implicit B) Only assumption 1 is implicit
C) Only assumption 2 is implicit D) Neither 1 nor 2 is implicit
 
Answer & Explanation Answer: A) Both 1 & 2 are implicit

Explanation:
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Q:

Prasanna invested certain amount in three different schemes X, Y and Z with the rate of interest 10% p.a, 12% p.a and 15% p.a respectively. If the total interest accrued in one year was Rs. 3200 and the amount invested in Scheme Z was 150% of the amount invested in Scheme X and 240% of the amount invested in Scheme Y, what was the amount invested in Scheme Y by Prasanna ?

A) Rs.6000 B) Rs.4500
C) Rs.7500 D) Rs.5000
 
Answer & Explanation Answer: D) Rs.5000

Explanation:

Let a, b and c be the amounts invested in schemes X, Y and Z respectively. Then,

As we know:

Simple interest (S.I.) = PTR/100

(a × 10 × 1/100) + (b × 12 × 1/100) + (c × 15 × 1/100) = 3200

= 10a + 12b + 15c = 320000 .........(1)

Now, c = 240% of b = 12b/5 .........(2)

And, c = 150% of a = 3a/2 => a = 2/3 c = (2 × 12)b/(3 × 5) = 8b/5 .......(3)

From (1), (2) and (3), we have

16b + 12b + 36b = 320000 => 64b = 320000 => b = 5000

∴ Sum invested in Scheme Y = Rs.5000.

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Filed Under: Percentage
Exam Prep: AIEEE , Bank Exams , CAT , GATE
Job Role: Bank Clerk , Bank PO

9 6140
Q:

How many independent words can 'STAINLESS' be divided into without changing the order of the letters and using each letter only once ?

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

Explanation:

The words are STAIN and LESS 

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Filed Under: Alphabet Test

12 6138
Q:

Three fair coins are tossed simultaneously. Find the probability of getting more heads than the number of tails

A) 2 B) 7/8
C) 5/8 D) 1/2
 
Answer & Explanation Answer: D) 1/2

Explanation:

S = { HHH, HHT, HTH, HTT, THH, THT, TTH, TTT }

=> n(S) = 8

E = { HHH, HHT, HTH, THH }

=> n(E) = 4

P(E) = 4/8 = 1/2

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Filed Under: Probability

4 6137
Q:

From a deck of 52 cards, a 7 card hand is dealt.How many distinct hands are there if the hand must contain 2 spades and 3 diamonds ?

A) 7250100 B) 7690030
C) 7250000 D) 3454290
 
Answer & Explanation Answer: A) 7250100

Explanation:

There are 13 spades,we must include 2: 13C2

 

There are 13 diamonds,we must include 3: 13C3

 

Since we can't have more than 2 spades and 3 diamonds,the remaining 2 cards must be pulled out from the 26 remaining clubs and hearts : 26C2

 

Therefore,13C2*13C3*26C2 = 7250100

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