AP ICET 2nd May 2018 Shift-2

Numbers divisible by eachof 4, 5 and 6 = Numbers divisible by LCM of (4,5,6) = 60

Number of numbers between 100 and 1000 divisible by 60 = 15

For the result to be prime, the expression must firstly yield a whole number. 
The expression can be broken up as =  3*k + 4 + (12/k)

Hence, k has to be a whole number factor of 12.
Probable values of k = 1,2,3,4,6,12 
Of these, the values of k = 1,3,4,12 yield prime numbers for the expression. 

The given information means that all the following numbers must be divisible by n
411 - 8 = 403
752 - 8 = 744
1031 - 8 = 103 

403 = 13 * 31 
744 = 24 * 31
1023 = 33 * 31
From this, we can say that the only common factor of all three is 31 and hence, n = 31

We are given that LCM = 12*GCD and also LCM + GCD = 403

Combining the two, we get GCD = 31 and hence, LCM = 12*31

Now, we know that 124*Other number = 31*(12*31)
Hence, the other number = 93 

$$5+\frac{1}{6+\frac{1}{8+\frac{1}{10}}}=5+\frac{1}{6+\frac{1}{\frac{81}{10}}}$$

$$=5+\frac{1}{6+\frac{10}{81}}$$

$$=5+\frac{1}{\frac{496}{81}}$$

$$=5+\frac{81}{496}$$

$$=\frac{2561}{496}$$

Hence, the correct answer is Option D

Recurring decimals can be expressed as fractions having 9 or multiples of 9 in some form.
0.6666.... can be expressed as 6/9
0.77777... can be expressed as 7/9
0.8888..... can be expressed as 8/9

Hence, 0.6666... + 0.77777.... + 0.8888.... = (6/9)+(7/9)+(8/9) = 21/9 = 7/3 

$$\frac{2}{7}=0.285$$

$$\frac{7}{15}=0.47$$

$$\frac{5}{8}=0.625$$

$$\frac{9}{23}=0.391$$

Decreasing order of the fractions is $$\frac{5}{8}$$, $$\frac{7}{15}$$, $$\frac{9}{23}$$, $$\frac{2}{7}$$

$$\Rightarrow$$ $$a_1=\frac{5}{8}$$ and $$a_4=\frac{2}{7}$$

$$\therefore\ $$ $$a_1-a_4=\frac{5}{8}-\frac{2}{7}=\frac{35-16}{56}=\frac{19}{56}$$

Hence, the correct answer is Option D

Given, $$\mid x-2\mid<5$$

$$\Rightarrow$$  $$-5<x-2<5$$

$$\Rightarrow$$  $$-3<x<7$$

The values of $$x$$ would range from -2 to +6 to satisfy the given condition.

$$\therefore\ $$The largest integer of the set = 6

Hence, the correct answer is Option A

This is a simple case of direct variation and we can say :

$$\frac{?}{3.52}=\frac{25}{16}$$
This brings us the ? value to be = 5.5 lakhs