Topic - Quant Mixed Bag

Solved ? : Yes

Source : CAT Prep Forums ]]>

Topic - Quant Mixed Bag

Solved ? : Yes

Source : CAT Prep Forums ]]>

7^(4k+1) --> 7

7^(4k+2) --> 9

7^(4k+3) --> 3

7^(4k) ---> 1

X^3 must end with 3, 1, 7 or 9

Case (i) 7^(4k+1) =>7

So we need

7 + 3 = 0

I.e x^3 ends with 3

And it is possible only when last digit is 7

here X should be of the form (4k+1)

So 17,37,57,77,97

5 possibilities

Case (ii)

9 + 1

=> 7^(4k+2) --> 9

X is even

And (even)^3 never ends with 1

Case(iii)

7^(4k+3) --> 3

And we need x^3 --> 7

Which is possible when last digit is 3

As 3^3 => 27

So we need to take x of the form (4k+3) whose last digit is 3

So, 3,23,43,63,83

5 possibilities

Case (iv)

7^(4k)--> 1

So we need x^3 --> 9

So X should end with 9

But it says X is of the form 4k

So can't be possible

So overall 10 possibilities

]]>We know PS and QT are two Medians and they are passing through a point and we know that point is called Centroid

Now best part of centroid : It divides Triangle into 6 equal parts

Now if some how I can calculate the area of PGT, I can calculate Area of whole triangle, just multiplying it by 6

For that additional information is given to us

that is PS is perpendicular to QT

I.e PGT is a right angled Triangle

So we just need base and height

I.e length of GT and PG

For that we know the property

centroid divides the median in the ratio 2:1

So GT => 1/3 of QT => 8

And PG => 2/3 of PS => 32/3

So area of Triangle PGT =>

1/2 * (32/3) * 8

=> 128/3

And area of whole Triangle

(128/3 ) * 6 = 256

Step 1: number of numbers will always be approx 2 * avg.

So number of numbers = 2 * 30 = near to 60

Avg= 877/29

Step 2: number of numbers(after forgetting) will always be multiple of denominator.

So 29 * 2 = 58 after forgetting.

And he forgot 1, means earlier there were 58 + 1=59 numbers.

Step 3:

Now sum of 59 numbers would be 1 + 2 + ... + 59 = 59 * 60/2 = 59 * 30 = 1770

Here sum for 58 numbers(after removing 1) 877 * 2= 1754

Final step:

One number removed = 1770 - 1754 = 16

Total solution --> 20c2 => 190

Now remove cases when two of them are equal

2a + b = 18

(0,..9)

10 cases

Which include one case (6, 6 * 6)

So overall cases 9

And these cases can be arranged in 3!/2! --> 3 ways

9 * 3 = 27 ways

Now (6,6,6) --> 1 case

So

total number of cases

(190 - 27 - 1 )/6

=> 27 + 9 ( cases when two are equal ) + 1 ( 6,6,6)

=> 37 ]]>

So possibile cases

1 * 40

2 * 20

4 * 10

5 * 8

Now case (I) can't be possible

I.e 1 diagonal can't be possible

Now we know

Number of diagonals is given by n(n-3)/2

n(n-3)/2 = 2

n = 4

n(n-3)/2 = 20

n(n-3) = 40

n = 8

Case (ii) is possible

Now case (iii)

n(n-3)/2 = 4

Not possible

Case (IV)

n(n-3)/2 = 5

n = 5

n(n-3)/2 = 8

Not possible

So only possibility

Case (ii)

I.e polygons of side 4 and 8

So 12 ]]>

2x + 3y < = 1000

atleast 1, so give 1,1 value

2x + 3y < = 1000 - 2 - 3

2x + 3y < = 995

Rhs represents amount.

Question is asking different possible values of amount. That can be anything 0 to 995 now.

x, y= 0. Amount = 0

x=1,y=0. Amount = 2

x=0,y=1. Amount = 3

x=2,y=0. Amount = 4

x=1,y=1. Amount = 5 and so on.

all amounts except amount 1 is possible

hence o to 995 => 996 values

Excluding 1, total 995 possible amount values. ]]>

Which of the following cannot be the ratio of methanol, phenyl and ethanol in beaker C?

(a) 10 : 23 : 15

(b) 7 : 15 : 16

(c) 6 : 13 : 13

(d) 9 : 20 : 18 ]]>

Phenyl --> (2x/6 + 5y/8) =>

(8x +15y)/24

Ethanol --> (3x/6 + y/8)

=> (12x + 3y)/24

Required ratio -->

(4x +6y) : (8x +15y) : (12x +3y)

Now let's check for the possibilities

Case (I)

X = Y = 1

10: 23: 15

Option (1) possible

Similarly

Case (ii)

X = (1/4) , Y = (1/15)

Option (2) is possible

Case (iii)

X = 1/2 and y = 1/6

Option (3) is possible

So option D ]]>

Case: e=6

We need a + b + c + d = 3k form

(1, 2, 4, 5) is a possibility.

Case: e = 8

Now a + b + c + d = 3k + 1 form

we need to choose 4 numbers from (1, 2, 3, 4, 5, 6, 7) which is of the form 3k + 1

Now 1, 4, 7 = 3k + 1

2, 5 => 3k + 2

3, 6 => 3k

3k + 1 can be made by two 3k + two 3k+2 => 1 way

one 3k + one 3k+2 + two 3k+1 => 2c1 * 2c1 * 3c2 = 12 ways

Total=14 ways

]]>Now he wants 20% profit means sp = 120% of cp

so sp should be doubled, means instead of selling 50 books for a rupee, he should sell them 50 books for 2 rupees means 25 books/rupee. ]]>

50% difference = 12 rupees

so 100%=cp=24 rupees

now 20% loss on cp = 20% of 24=4.8 rupees loss

If book was sold at 4.8 more this loss would be compensated and finally no loss no profit.

]]>When distance is constant time is inversely proportional to speed hence time ratio:3:5

So, BMW took 4 hrs to reach turning point. Hence, nano will take 4*(5/3)=20/3 hrs to reach that point. So it will reach at 9am + 20/3 hrs =3:40 pm ]]>