Topic - Quant Mixed Bag

Solved ? - Yes

Source - ]]>

Topic - Quant Mixed Bag

Solved ? - Yes

Source - ]]>

f(2401) = 10/3

f(729) = 18

then f(343(root3)) = ?

(CAT 2013 question) ]]>

2401 = f(49 * 49)

4f(7)=10/3

f(7)=10/12

f(729) = 18

f(27 * 27) = 6f(3) = 18

f(sqrt3) = 3/2

f(343(root3)) = 10/4 + 3/2 = 4 ]]>

=> 2x + 2y = 2x² + 2y² - 2xy

=> (x - y)² + (x - 1)² + (y - 1)² = 2

So, two of these three terms have to be 1 and third one to be 0

Hence, only solutions are (0, 0), (2, 2), (1, 0), (1, 2), (0, 1), (2, 1)

(solved by Hemant Yadav sir) ]]>

solution by shashank srivastava

xy= x+y+15

Now take x and y to rhs we get xy-x-y=15

Add 1 to both lhs nd rhs for factorising we get xy-x-y+1=16

Or (x-1)(y-1)=16

Now it means (x-1) and (y-1) should be factors of 16 as their multiplication gives result as 16

no of factors of 16 is 4 + 1 = 5

but that is for positive only considering negatives we get another 5 so total sums upto 2 * 5 = 10.

answer will be smallest of √{a² + (b + c)²}, √{b² + (a + c)²} and √{c² + (a + b)²}

(solution by hemant yadav sir) ]]>

remaining numbers is 21 (1/3). What is the product of the two numbers that have been removed? ]]>

considrng 21 as middle number --> so n can be (39 + 2), (42 + 2), (45 + 2)....

when n = 41 --> sum = 832 + x + x + 1 = 833 + 2x

sum of first 41 natural numbers = 41 * 21 = 861

2x = 28

x = 14

two missd numbers 14 and 15

product = 14 * 15 = 210 ]]>

20/(4S/5) – 20/S = 12/60 = 1/5

100-80 = 4S/5

4S = 100

S = 25 KM/HR

Let the original distance is D

D-50/20 - D-50/25 = 3/4

5D-250-4D+200 = 75

D = 125 KM ]]>

2 orange 3 apple ----> 6c3

3 orange 2 apple ---> 6c2

4 orange 1 apple ---> 6c1

15 + 20 + 15 + 6 = 56 ]]>

The survey found:

15 had air conditioning

2 had air conditioning and power windows but no radios

12 had radio

6 had air conditioning and radio but no power windows

11 had power windows

4 had radio and power windows

3 had all three options.

What is the number of cars that had none of the options?

a. 4

b. 3

c. 1

d. 2

25 = 15 + 12 + 11 - 6 - 2 - 4 + 3 - car with no options

25 = 29 - car with no options

car with no options = 4 ]]>

M : G = 2 : 1

M : B : G = 2 : 4 : 1

daughter's share = 1/7 ]]>

a) 5%

b) 10%

c) 15%

d) 20%

e) None of the above ]]>

one of them can be 1 and other two any of (0,2,3....9) --> 3 * 9 = 27

total 27 + 1 = 28

similarly when first digit is 2,3,4...9 --> 9 * 28 = 252

]]>P(GnE) = 1/2 * 3/7 = 3/14

P(E) = 1/2

P(G/E) = 3 * 2/14 = 3/7 ]]>

a) 64 years

b) 48 years

c) 45 years

d) 40 years ]]>