TestFunda Answers - Algebra

[sravanthia]

TFAnswers >> Quantitative Ability >> Algebra

Question # 12919

After the typist writes 12 letters and addresses 12 envelopes, she inserts the letters randomly into the envelopes (1 letter per envelope). What is the probability that exactly 1 letter is inserted in an improper envelope? After the typist writes 12 letters and addresses 12 envelopes, she inserts the letters randomly into theenvelopes (1 letter per envelope). What is the probability that exactly 1 letter is inserted in an improper envelope?

Options

1)  0 2)  12/212 3)  11/12 4)  1/12

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[vimbloid]

TFAnswers >> Quantitative Ability >> Algebra

Solution to Question # 12919

Not possible

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[vimbloid]

TFAnswers >> Quantitative Ability >> Algebra

Solution to Question # 12919

It is not possible

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[vimbloid]

TFAnswers >> Quantitative Ability >> Algebra

Solution to Question # 12917

Maximum handshakes are 9 as :
Suppose  1 shakes hands with 2
      2 with 3
.....7 with 8
Now let 8 shake hands with 10
and 10 shake hands with 9
Thus we get 9 handshakes and no cycle of hand shakes  

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[vimbloid]

TFAnswers >> Quantitative Ability >> Algebra

Solution to Question # 12916

Take a2 in the set now a1 and a3 have shaken hands with him.a4 has not so we take a5 in the set thus a4 and a6 have shaken hands with the set but a7 has not so we take a8...thus we leave a gap of two people and select the third person in the set. So answer is 36/3 = 12 

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[vimbloid]

TFAnswers >> Quantitative Ability >> Algebra

Solution to Question # 12915

We can see that
3 comes in the units place 64 times
tens place 64 times
hundreds placfe 64 times
Thus total no. of times 3 used is 192 

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[vimbloid]

TFAnswers >> Quantitative Ability >> Algebra

Solution to Question # 12912

Here the data about the distance is of no use.
For radius of 1 m if dart is inside the circle of 1/2 m radius the dart is closer to center than periphery
so area of 1/2 m circle is pie/4
area of board is pie
So probability = 0.25 

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[ajay_h]

TFAnswers >> Quantitative Ability >> Algebra

Solution to Question # 12892

option 2, 2.5%
Assuming x as tax rate.
3990 - 2790 * x = 4020 - 4020 * x + 0.75
1230 * x = 30.75 

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[sravanthia]

TFAnswers >> Quantitative Ability >> Algebra

Question # 12923

A hare and a tortoise have a race along a circle of 100 yards diameter. The tortoise goes in one direction and the hare in the other. The hare starts after the tortoise has covered 1/5 of its distance and that too leisurely. The hare and tortoise meet when the hare has covered only 1/8 of the distance. By what factor should the hare increase its speed so as to tie the race? A hare and a tortoise have a race along a circle of 100 yards diameter. The tortoise goes in one directionand the hare in the other. The hare starts after the tortoise has covered 1/5 of its distance and that too leisurely.The hare and tortoise meet when the hare has covered only 1/8 of the distance. By what factor should the hareincrease its speed so as to tie the race?

Options

1)  40 2)  37.80 3)  8 4)  5

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[sravanthia]

TFAnswers >> Quantitative Ability >> Algebra

Question # 12924

There are two boxes, one containing 10 red balls and the other containing 10 green balls. You are allowed to move the balls between the boxes so that when you choose a box at random and a ball at random from the chosen box, the probability of getting a red ball is maximized. This maximum probability is There are two boxes, one containing 10 red balls and the other containing 10 green balls. You are allowedto move the balls between the boxes so that when you choose a box at random and a ball at random from thechosen box, the probability of getting a red ball is maximized. This maximum probability is

Options

1)  3/4 2)  14/19 3)  37/38 4)  1/2

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[sravanthia]

TFAnswers >> Quantitative Ability >> Algebra

Question # 12925

A hollow cube of size 5 cm is taken, with a thickness of 1 cm. It is made of smaller cubes of size 1 cm. If 4 faces of the outer surface of the cube are painted, totally how many faces of the smaller cubes remain unpainted? A hollow cube of size 5 cm is taken, with a thickness of 1 cm. It is made of smaller cubes of size 1 cm. If 4faces of the outer surface of the cube are painted, totally how many faces of the smaller cubes remain unpainted?

Options

1)  900 2)  488 3)  500 4)  800

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[sravanthia]

TFAnswers >> Quantitative Ability >> Algebra

Question # 12927

Given a collection of points P in the plane, a 1-set is a point in P that can be separated from the rest by a line; i.e. the point lies on one side of the line while the others lie on the other side. The number of 1-sets of P is denoted by n1(P). The maximum value of n1(P) over all configurations P of 19 points in the plane is Given a collection of points P in the plane, a 1-set is a point in P that can be separated from the rest by aline; i.e. the point lies on one side of the line while the others lie on the other side. The number of 1-sets of P isdenoted by n1(P). The maximum value of n1(P) over all configurations P of 19 points in the plane is

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[sravanthia]

TFAnswers >> Quantitative Ability >> Algebra

Question # 12928

Alok and Bhanu play the following min-max game. Given the expression N = 38 + X*(Y – Z) where X, Y and Z are variables representing single digits (0 to 9), Alok would like to maximize N while Bhanu would like to minimize it. Towards this end, Alok chooses a single digit number and Bhanu substitutes this for a variable of her choice (X, Y or Z). Alok then chooses the next value and Bhanu, the variable to substitute the value. Finally Alok proposes the value for the remaining variable. Assuming both play to their optimal strategies, the value of N at the end of the game would be Alok and Bhanu play the following min-max game. Given the expressionN = 38 + X*(Y – Z)where X, Y and Z are variables representing single digits (0 to 9), Alok would like to maximize N while Bhanuwould like to minimize it. Towards this end, Alok chooses a single digit number and Bhanu substitutes this for avariable of her choice (X, Y or Z). Alok then chooses the next value and Bhanu, the variable to substitute thevalue. Finally Alok proposes the value for the remaining variable. Assuming both play to their optimalstrategies, the value of N at the end of the game would be

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[vimbloid]

TFAnswers >> Quantitative Ability >> Algebra

Solution to Question # 12927

Maximum value will be 19 it will occur when all points are aligned in a circle

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[vimbloid]

TFAnswers >> Quantitative Ability >> Algebra

Solution to Question # 12924

Any which way u arrange the probability will be 1/2
for 10 red in 1st box and 10 green in 2nd box
probability of picking red = 1/2 * 1 + 1/2 * 0 = 1/2
you can try for all combinations 

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[vimbloid]

TFAnswers >> Quantitative Ability >> Algebra

Solution to Question # 12923

After tortoise covers 1/5th distance hare starts the race
When hare covers 1/8th of distance tortoise meets hare
So distance covered by tortoise = 1-(1/5 + 1/8)
       = 27/40
Time taken by both is same
time = dist/speed
So (dist/ speed) of tortoise = (dist / speed) of hare
let speed of tortoise be t and of hare be h
27/40t = 1/8h
h = (40/(8*27) )* t = 5/27 * t  
Now for the next part hare has to cover 7/8 th distance when tortoise covers 1/8 th distance
so we get
1/8t = 7/8h
h = 7t
so the factor by which h's speed increases =  7t/ (5/27 * t)
which we get as 37.8 

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[sanjuds]

TFAnswers >> Quantitative Ability >> Algebra

Question # 12929

Fermat's Last Theorem is a statement in number theory which states that it is impossible  to separate any  power higher than the second into two like powers , or, more  precisely - If an integer n is greater than 2 then equation a^n b^n=c^n has no solutions in non zero intergers a,b,c Now  if the different of any two numbers is 9 then their product is 17 . what is the sum of squares ?

Options

1)  43 2)  45 3)  98 4)  115

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[sumit2goody]

TFAnswers >> Quantitative Ability >> Algebra

Solution to Question # 12929

We have x = y = 9
and xy = 17

=> y = 17/x

putting it in the above equation we have

x - 17/x = 9

=> x^2 - 9x - 17 = 0

solving we have  x = 10.6

and y = 1.6

now sum of squares = 115

hence option 4 

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[sanjuds]

TFAnswers >> Quantitative Ability >> Algebra

Question # 12930

A sheet of paper has statements numbered from 1 to 40. For all values of n from 1 to 40, statement n says:" Exactly n of the statements of this sheet are false ". which statements are true and which statments are false ?

Options

1)  The even numbered statements are true and the odd numbered statements are false 2)  The 39th statement is true and the rest are false 3)  The odd numbered statements are true and the even numbered statements are false 4)  All the statements are false.

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[vimbloid]

TFAnswers >> Quantitative Ability >> Algebra

Solution to Question # 12925

From the given data we see that each face of the cube gives us 25 cubes
So 6 faces gives us 150 cubes
4 faces are painted so in 100 small cubes 1 face is painted 5 faces are not painted
500 faces are not painted
in remaining 50 cubes 6 faces are not painted = 300 faces not painted
So total 800 faces are not painted 

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