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Quantitative Aptitude Prep Tips for MBA

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Quantitative Aptitude Prep Tips for MBA Class 12th

Akbar sets off on his car from Delhi to Jaipur at a certain speed intending to reach Jaipur by 5pm. After covering a certain distance, he realises that he would be able to cover only five – eighth of the intended distance by 5pm. He therefore increases his speed by 75 percent and reaches Jaipur at 5pm. What fraction of the total distance did he cover at his initial speed?

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Payal Gupta

Contributor-Level 10

Let the distance between Delhi (D) and Jaipur (J) be 8x and Akbar's initial speed be 4a and final speed be 7a.

Let the point where he increased his speed at P and let Q be the point on DJ such that $D P = \frac{5}{8} (D J)$

$\frac{P Q}{P J} = \frac{4}{7}$

Let PQ = 4y,

PJ = 7y

QJ = 7y – 4y = 3x

3y = 3x

y= x

PQ = 4x and PJ =7x

Required ratio = $\frac{D P}{D J}$

= $\frac{x}{8 x}$ = 1/8

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Quantitative Aptitude Prep Tips for MBA Class 12th

In f (a) = a² – 2ax + y can be factorised as (a – x) (a – y) then find the value of f (4) where x and y are positive real numbers.

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Payal Gupta

Contributor-Level 10

f (a) = a² – 2ax + y

f (x) = x² – 2x² + y = 0

– x² + y =0

y = x² ………. (1)

f (y) = y² – 2xy + y = 0

y² – 2xy + x² = 0

(y – x)² = 0

y – x = 0

y = x

Put value of y in equation 1

We get

x = y = 1

So, f (4) = 4² – 2 (4*1) + 1

= 16 – 8 +1

= 9

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Quantitative Aptitude Prep Tips for MBA Class 12th

A vistara airline has a free luggage allowance up to a certain kg and if there is extra luggage, it charged at constant rate per kg. The total luggage charge paid by M and S is Rs. 1050. If both M and S has carried twice the luggage they actually did then charge would be Rs. 2400 and Rs. 900 respectively. Find the luggage charge paid by M (in Rs.).

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Payal Gupta

Contributor-Level 10

Let the airline has a free luggage allowance →'f' kg

Luggage by M →m kg

Luggage by S →s kg

Rate charger beyond f kg →'e'/kg

Extra luggage of m = (m – f) kg

Extra luggage of s = (s – f) kg

ATQ

e (2m – f) = 2400 ______equation 1

e (2s – f) = 900 ______equation 2

add 1 and 2

e (m + s –f ) = 1650

Also, e (m – f) + e (s – f) = 1050

e (m + s –f ) – ef = 1050

1650 – ef= 1050

ef = 600

Extra luggage from m = e (m – f)

= $\frac{e (2 m - 2 f)}{2} = \frac{e (2 m - f) - e f}{2}$

$= \frac{2400 - 600}{2}$

= Rs. 900

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Quantitative Aptitude Prep Tips for MBA Class 12th

If abcd = 100000000, then the value of $(\frac{1}{l o g_{a} 100} + \frac{1}{l o g_{b} 100} + \frac{1}{l o g_{c} 100} + \frac{1}{l o g_{d} 100})$ is.

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Payal Gupta

Contributor-Level 10

$\frac{1}{2 l o g_{a} 10} + \frac{1}{2 l o g_{b} 10} + \frac{1}{2 l o g_{c} 10} + \frac{1}{2 l o g_{d} 10}$

$= \frac{l o g_{10} a}{2} + \frac{l o g_{10} b}{2} + \frac{l o g_{10} c}{2} + \frac{l o g_{10} d}{2}$

$= \frac{l o g_{10} a + l o g_{10} b + l o g_{10} c + l o g_{10} d}{2}$

$= \frac{l o g_{10} a b c d}{2}$

$= \frac{l o g_{10} 1 0^{8}}{2}$

=8 * ½ = 4

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Quantitative Aptitude Prep Tips for MBA Class 12th

Which of the following values of 'x' satisfy the inequality x(x – 6) > 2x – 12?

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Payal Gupta

Contributor-Level 10

x (x – 6) > 2x – 12

x² – 6x > 2x – 12

x² – 8x > 12x > 0

(x – 2) (x – 6) > 0

x < 2 or x >6

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Quantitative Aptitude Prep Tips for MBA Class 12th

How many integers satisfy the inequality |x² – 25 | <5

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Payal Gupta

Contributor-Level 10

Given equation is

x² – 25 <5

–5 < x² – 25 < 5

20 < x² < 30

$\sqrt[]{20}$ < x < $\sqrt[]{30}$

Hence x = 5

x = 5

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Quantitative Aptitude Prep Tips for MBA Class 12th

For all even numbers 'n' f(n) is the sum of the squares of all even natural numbers less than or equal to 'n' If for some 'n' f(n) = 51 * n, what is the value of n?

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Payal Gupta

Contributor-Level 10

Sum of square of even natural number n = 2² + 4² + 6² + ……………. +n²

= 2² [1² + 2²+ 3²+ ……………+ (n/2)²]

$4 . \frac{(n / 2) (\frac{n}{2} + 1) (\frac{2 n}{2} + 1)}{6} = 51 * n$

(n+1) (n+2) = 51*6

n² + 3n +2 = 306

(n–16) (n+19) = 0

n=16

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Quantitative Aptitude Prep Tips for MBA Class 12th

A trader sells wheat at Rs. x/kg. A shopkeeper cons a trader into selling him 10 percent more wheat than what he is paying for. Later the shopkeeper uses faulty balance and gives a customer 10 percent less wheat what is paying for. If the shopkeeper also sells the wheat at Rs. x/kg what is the overall profit percentage of the shopkeeper in whole transactions?

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Payal Gupta

Contributor-Level 10

CP of wheat be Rs.100/kg So, when shopkeeper pays for 1kg wheat, he get 1.1kg of wheat.

CP of shopkeeper is Rs. $\frac{100}{1.1} p e r k g$

While selling, he sells 10% less

So, 5p = Rs. $\frac{100}{0.9 k g}$

Profit percent = $\frac{\frac{100}{0.9} - \frac{100}{1.1}}{\frac{100}{1.1}}$

=22.22percent

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Quantitative Aptitude Prep Tips for MBA Class 12th

A train covers half the distance with a speed of 150km/hr. The remaining part of the distance was covered with a speed of 80 km/hr for half of the time and with the speed of 120km/hr for the other half of the time. For the whole journey, calculate the average distance (in km) covered by the train in one hour.

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Payal Gupta

Contributor-Level 10

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Quantitative Aptitude Prep Tips for MBA Class 12th

Aman takes 40 hours to paint four walls and ceiling of a room of volume 2800 cubic feet. The ceiling height of the room is 28 feet. If Aman painted at a constant rate of 0.125sq. feet per minute, then how long it will take him to paint four walls.

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Payal Gupta

Contributor-Level 10

Total volume = 2800 cubic feet

Area of ceiling = 2800/28 = 100sqfeet

Total time taken = $\frac{100}{0.125}$ = 800min

= 13hr 20min

Time taken to paint four walls= 40 – 13* $\frac{1}{3}$ = 26hr 40min

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