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 Quantitative Aptitude - Arithmetic Ability Questions

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Q:

One of the roots of the equation x2 - 6x + k = 0 is x = 2. The other root is

 

A) x = -1 B) x = 4
C) x = -4 D) x = 1
 
Answer & Explanation Answer: B) x = 4

Explanation:
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Filed Under: Area
Exam Prep: Bank Exams

1 23712
Q:

Consider the following statements:

1) The perimeter of a triangle is greater than the sum of its three medinas.

2) In any triangle ABC, if D is any point on BC, then AB + BC + CA > 2AD.

Which of the above statements is/are correct?

A) 1 only B) 2 only
C) Both 1 and 2 D) Neither 1 nor 2
 
Answer & Explanation Answer: C) Both 1 and 2

Explanation:
Let ABC be the triangle and D. E and F are midpoints of BC, CA and AB respectively.
Recall that the sum of two sides of a triangle is greater than twice the median bisecting the third side,(Theorem to be remembered)
Hence in ΔABD, AD is a median
⇒
AB + AC > 2(AD)
Similarly, we get
BC + AC > 2CF
BC + AB > 2BE
On adding the above inequations, we get
(AB + AC) + (BC + AC) + (BC + AB )> 2AD + 2CD + 2BE
2(AB + BC + AC) > 2(AD + BE + CF)
∴
AB + BC + AC > AD + BE +CF
 
2.
To prove: AB + BC + CA > 2AD
Construction: AD is joined
Proof: In triangle ABD,
AB + BD > AD [because, the sum of any two sides of a triangle is always greater than the
third side]
----
1
In triangle ADC,
AC + DC > AD [because, the sum of any two
sides of a tri
angle is always greater than the
third side]
----
2
Adding 1 and 2 we get,
AB + BD + AC + DC > AD + AD
=> AB + (BD + DC) + AC > 2AD
=> AB + BC + AC > 2AD
Hence proved
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Filed Under: Volume and Surface Area
Exam Prep: Bank Exams

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Q:

The difference between the simple interest received from two different sources on Rs.1500 for 3 years is Rs.13.50. The difference between their rates of interest is

A) 0.1% B) 0.2%
C) 0.3% D) 0.4%
 
Answer & Explanation Answer: C) 0.3%

Explanation:

(1500 x R1 x 3)/100 

=> 4500 (R1-R2) = 1350 

=> (R1-R2)= 1350/4500 = 0.3 %

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Filed Under: Simple Interest
Exam Prep: GRE

48 23700
Q:

The cash difference between the selling prices of an article at a profit of 4% and 6% is Rs 3. The ratio of two selling prices is

A) 51:52 B) 52:53
C) 53:54 D) 54:55
 
Answer & Explanation Answer: B) 52:53

Explanation:

Let the Cost price of article is Rs. x

Required ratio = (104% of x) / (106% of x)

                            =104/106

                            =52/53 = 52:53                     

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Filed Under: Profit and Loss

39 23661
Q:

In what ratio should water and wine be mixed so that after selling the mixture at the cost price a profit of 33.33% is made?

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

Explanation:

33.33% profit means there is one part water and 3 part is pure wine. so the required ratio of water and wine in the mixture is 1:3

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Filed Under: Profit and Loss

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Q:

The tangent at any point of the circle is _________________ to the radius through the point of contact.

 

A) parallel B) intersecting
C) perpendicular D) equal
 
Answer & Explanation Answer: C) perpendicular

Explanation:
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Filed Under: Area
Exam Prep: Bank Exams

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Q:

In an examination, 34% of the students failed in Mathematics and 42% faiied in English. If 20% of the students failed in both the subjects, then the percentage of students who passed in both the subjects was :

A) 34 % B) 44 %
C) 54 % D) 64 %
 
Answer & Explanation Answer: B) 44 %

Explanation:

n (A) = 34, n (B) = 42, n (A  ∩ B) = 20.

 

So, n (A  U B) = n (A) + n(B) - n(A ∩B) = 34 + 42 - 20 = 56.

 

Percentage failed in either or both the subjects = 56.

 

Hence, percentage passed = (100 - 66)% = 44%.

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Filed Under: Percentage

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Q:

A cistern of capacity 8000 litres measures externally 3.3 m by 2.6 m by 1.1 m and its walls are 5 cm thick. The thickness of the bottom is:

A) 90 cm B) 1 dm
C) 1 m D) 1.1 cm
 
Answer & Explanation Answer: B) 1 dm

Explanation:

ke

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Filed Under: Volume and Surface Area

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