## Answer : A

### Solution :-

#### The first integer, after 60 which is divisible by 17 is 68

And the 1st integer, before 600 which is divisible by 17 is 595.

Therefore the sequence of integers between 60 and 600 which are divisible by 17 is

68, 85, 102,…,595

We have to find 68 + 85 + 102 + … + 595

#### It is an A.P with a = 68 and d = 17 and t(n) = 595

The formula to find nth term in A.P is, t(n) = a + (n – 1)d

Here, a +(n – 1)d = 595

68 + (n – 1)17 = 595

(n – 1)17 = 527

n – 1 = 31

n = 32

i.e., the 32-nd term of sequence is 595

#### We know that the sum of first n terms of the A.P series = s(n) = (n/2)[2a + (n – 1)d]

Here, s(32) = (32/2)[2(68) + (32 – 1)17]

16[136 + 31(17)]

16[136 + 527]

16[663] = 10608

Hence the required sum is 10608.

## Answer : C

### Solution :-

#### Average Points of juniors = 150

and the number of juniors = 20.

Total score obtained by juniors = 150 x 20

#### Average score of (juniors + seniors) = 152.

Total number of players = 32

Total score of (juniors + seniors) = 152 x 32

#### Total score of 12 seniors = 152 x 32 – 150 x 20

required average = (152 x 32 – 150 x 20)/12 = (152 x 8 – 150 x 5)/3 = (1216 – 750)/3 = 466/3 = 155.3.

Hence, the answer is 155.3 points.

**Answer : B**

**Solution :**

#### Let, 5 pens + 7 pencils + 4 erasers = x rupees

so 10 pens + 14 pencils + 8 erasers = 2*x rupees

also mentioned, 6 pens + 14 pencils + 8 erasers = 1.5*x rupees

so (10-6) = 4 pens = (2-1.5)x rupees

so 4 pens = 0.5x rupees => 8 pens = x rupees

so 5 pens = 5x/8 rupees = 5/8 of total (note x rupees is total amt paid by

amal) i.e 5/8 = 500/8% = 62.5% is the answer

**Answer : A**

**Solution :**

#### Let the speed of upstream be X km/hr.

#### Then, speed in downstream = 2X km/hr (since boat takes twice as much as time to cover up than as to cover down the same distance in running water).

#### Speed in still water = (2X+X)/2 km/hr. (formula 3)

= 3X/2 km/hr.

#### Given that, boat covers 10 1/3 km in 1 hour in still water.

#### Therefore, 3X/2 = 10 1/3

X = 62/9

#### So, speed in upstream = 62/9 km/hr.

And, speed in downstream = 2 x 62/9 = 124/9 km/hr

#### Hence, speed of the current = [(124/9 – 62/9)]/2 km/hr

= 62/9×2 = 34/9 = 3 4/9 km/hr.

**Answer : B**

**Solution :**

#### We know the property that, the unit’s digit of a perfect square cannot be 2, 3, 7 or 8.

#### Since, the numbers 1324802, 344578 and 868623 are ending with 2, 8 and 3. So, we can discard them.

#### Hence, the perfect square of given numbers is 127449.

**Answer : C**

**Solution :**

#### Time taken to rectify 0.128 errors is 1 second.

Time taken to rectify 25 errors,

#### Errors Time

#### 0.128 1

#### 25 ?

#### Here the number of errors has been increased, so time also increases. Hence error is directly proportional to time.

#### ? = (25 / 0.128)1

? = 25 x 1000 / 128

? = 195.31

#### Therefore, time taken to rectify 25 errors is 195 sec approximately.

**Answer : C**

**Solution :**

#### Given that, pq=28 and p, q are integers.

#### The factors of 28 are 1, 2, 4, 7, 14 and 28.

#### Then the possibilities of pq = 28 are (p,q) = (1, 28), (2, 14), (4, 7), (7,4), (14, 2) and (28,1)

#### We would have p > q since the given options are positive.

#### (That is, if p < q then (p^{2} – q^{2}) will be negative).

#### Therefore, the possibilities of (p, q) reduced to (7,4), (14, 2) and (28,1).

#### If (p,q) = (28,1) then (p^{2} – q^{2}) = 28^{2} – 1^{2} = 784 – 1 = 783.

If (p,q) = (14, 2) then (p^{2} – q^{2}) = 14^{2} – 2^{2} = 196 – 4 = 192

If (p,q) = (7,4) = (p^{2} – q^{2}) = 7^{2} – 4^{2} = 49 – 16 = 33

#### From the given options, required answer is option c.

**Answer : C**

**Solution :**

#### Total number of outcomes in the simultaneous throw of 2 dice is 6 x 6 = 36.

That is, n(S) = 36.

Let E be the event that 1st is a divisor of 2nd.

Then E = { (1,1),(1,2),(1,3),(1,4),(1,5),(1,6),(2,4),(2,2),(2,6),(3,3),(3,6),(4,4),(5,5),(6,6)}

N(E) = 14.

Required probability = p(E) = N(E) / n(S) = 14/36 = 7/18.

**Answer : D**

**Solution :**

#### Ravi went to hospital on Monday.

Then, three days before Monday is Friday and the two days after Friday is Sunday.

And the next day of Sunday is Monday and the day after tomorrow of Monday is Wednesday.

So, Ravi will go to hospital on Wednesday.

**Answer : B**

**Solution :**

#### For calendar to repeat exactly, the dates and days have to match perfectly.

Consider 2014 :

Any date on 2014 will correspond to same date on 2013 advanced by one day. (same logic used in first question.) For example if Jan 1 is Tuesday on 2013, then Jan 1 will be Wednesday on 2014.

#### Year 2014 2015 2016 (leap year) 2017 2018 2019

#### Advanced days 1 1 2 1 1 1

#### In 2019 the total number of advancements will be 1 + 1 + 1 + 2 + 1 + 1 = 7 . Any week has seven days. Hence advancement of 7 days also means the days are going to be the same for any dates. That is if 1^{st} Jan on 2013 is Tuesday, then 1^{st} Jan on 2019 will also be Tuesday.

Hence the calendar for the year 2013 and 2019 is the same.

**Answer : C**

**Solution :**

#### Inspecting the encoding of AEGI :

Pairing two-two letters we have AE GI.

The middle letter between A and E is C and the middle letter between G and I is H.

#### Similarly applying the same logic to ACDF we get

Pairing two-two letters, we have CE DH

The middle letter between C and E is D while the middle letter between D and H is F

Hence the answer is DF.

**Answer : D**

**Solution :**

#### From the question, we can infer that the triangle would be a scalene triangle.

#### From the above diagram, we have to find AD and CD.

By applying the Pythagoras theorem for the triangle BAD,

BD^{2} + AD^{2} = AB^{2}

AD^{2} = 13^{2} – 12^{2}

AD = 5

Similarly for triangle BDC,

BD^{2} + CD^{2} = BC^{2}

12^{2} + CD^{2} = 37^{2}

CD^{2} = 1369 – 144 = 1225 = 35^{2}

CD = 35

Or alternately, CD = AC – AD = 40 – 5 = 35

Now, the required ratio is AD : CD = 5 : 35 = 1 : 7

Hence, the answer is 1:7

**Answer : A**

**Solution :**

### Louis Pasteur started from his place and went 20 km towards north. Then he turned left and walked 40 km. At this stage he turned left and walked 20 km. Finally he moved 20 km after turning left. It may be seen that his present position is 20 km from the starting point. The starting point is to his right side now.

**Answer : A**

**Solution :**

#### General form is add the given two numbers and divide the results by 2, 3, 4 and 5 respectively, to get the answer.

#### That is,

#### 51 + 23 = 74 = 74 / 2 = 37

62 + 34 = 96 = 96 / 3 = 32

59 + 49 = 108 = 108 / 4 = 27

And, 84 + 56 = 140 = 140 / 5 = 28.

Hence, the required answer is 28.

**Answer : A**

**Solution :**

#### S is the tallest of all, is the correct answer. The second option is not true because S is taller than Q who in turn is taller than R.

**Answer : C**

**Solution :**

#### A takes 5 hours to complete 1/8 of work.

He will take 5 x 8 = 40 hours to complete whole work.

#### B takes 3 1/3 days to complete 80% of the work;

i.e., he takes 10/3 days = 10/3 x 24 hours = 80 hours to complete 80% work.

Therefore, whole work will be done by B in 100 hours.

#### C takes 1 1/12 days = 13/12 days to complete 2/3 of work.

i.e., he takes 13/12 x 24 hours = 26 hours for 2/3 of work.

#### Therefore, whole work will be done by C in (26 x 3/2) = 39 hours.

And he takes minimum time to do the work.

Hence, C will complete the work first.

**Answer : B**

**Solution :**

#### Total number of outcomes in the simultaneous throw of 3 dice is 6 x 6 x 6 = 216.

That is, n(S) = 216.

Let E be the event that sum of the three is greater than 12.

Then E = {(6,1,6), (6,2,6), (6,3,6), (6,4,6), (6,5,6),(6,6,6), (5,2,6), (5,3,6), (5,4,6), (5,5,6),(5,6,6), (4,3,6), (4,4,6), (4,5,6),(4,6,6), (3,4,6), (3,5,6), (3,6,6), (2,5,6), (2,6,6), (1,6,6)}

Therefore n(E) = 6 + 5 + 4 + 3 + 2 + 1 = 21

Hence p(E) = 21 / 216 = 7 / 72.

**Answer : C**

**Solution :**

#### From statement I, Total customers to three showrooms = (15 x 3) = 45.

#### From statement II, Given that A = C + 2 and A = B + 1

#### By sub. A = B + 1 in A = C + 2 we get,

#### B + 1 = C + 2

#### B = C + 1

#### Total Number of Customers = 45

#### i.e., A + B + C = 45

#### Sub. values for A and B,

#### C + 2 + C + 1 + C = 45

#### 3C = 42

#### C = 14

#### Hence, I and II together gives the answer.

main()

{

int x=10,y=5,p,q;

p=x>9;

q=x>3&&y!=3;

printf(“p=%d q=%d”,p,q);

}

{

int x=10,y=5,p,q;

p=x>9;

q=x>3&&y!=3;

printf(“p=%d q=%d”,p,q);

}

**Answer : 1 , 1 **

main()

{

int i=+1;

while(~i)

printf(“vicious circles”)

}

{

int i=+1;

while(~i)

printf(“vicious circles”)

}