Of the following intergers, which is the closest ..

Hi,
Q1)(sqrt2 + sqrt5)^2 = 2+5+2sqrt(2*5) = 7+2*sqrt(10)
sqrt(10) is between 3.1 and 3.2
So, the value is between 7+2(3.1) and 7+2(3.2) i.e. 13.2 and 13.4
Hence, 3

Q2)450y= n^3 => 2*(3^2)*(5^2)y = n^3
For 2*(3^2)*(5^2)y to be a cube of integer, y should be of the form (2^2)*3*5*p^3, where p is an integer.
So, y/3x2^2x5 = p^3
We can certainly say that only I is an integer, II and III may or may not be
Hence, 2

Q3)y km/hr = y*1000 m/ (60*60)sec = 5y/18 m/sec
So, 5y/18 = x =>y =18x/5
Hence, 3
Can you check the OA for Q3.

1)

(root 2+ root5)^2

2+2root10+5

7 + 2 root 10

root 10 = ~3

7 + 2*3

= 13

if my answer is right, question 3 seemed fairly easy. the square root of 2 is 1.41 something and the square root of 5 has to be slightly higher than 2.2 maybe 2.3 since the square root of 4 is already 2. those 2 added together equals 3.6ish. since 3 squared already equals 9 and 4 squared equals 16, it has to be something in between. 10 or 13. since 3.6ish is closer to 4 I would go with 13


the 1st question, if I am not wrong, I would go with answer choice C. I'm not very sure with this one though...I made up the number 10 for x . so x=10m./s this is equal to 600m/min. (60s. in a min) this is equal to 36000m/hour. Since 1km=1000m, we have 36km/hour answer choice C offers us 18x/5. if we substitute x with 10 we have 180/5 and that equals to 36...with this one, I'm not very sure though...

3)

X meters/1 sec = Y Km/ 1 hr

x/1 = 1000y/3600

y= 3600x/1000

y= 18x/5

Great answers by everyone.

A little addition concerning question number 3:

Since Km/h and m/s are the two most common speed units, memorizing the conversion rate between the two is a great way to avoid lengthy calculations.

10 meters per second is equivalent to 36 Km/h, meaning that 'speed in Km/h' = 3.6 * 'speed in m/s'.

In this case:

y = 3.6*x = 36/10*x = 18x/5

Or using rates:

y/x = 36/10 ---> y = 36/10*x = 18x/5

Thank you everyone for your responses. They really help me a lot.