MU-NLPC/Calc-aqua_rat huggingface dataset:
There are 16 teams divided in 4 groups. Every team from each group will play with each other once. The top 2 teams will go to the next round and so on the top two teams will play the final match. Minimum how many matches will be played in that tournament? Choose the correct choice from the following choices:
A) 43
B) 44
C) 45
D) 46
E) 47

Solution: In each group, total matches played = 4C24C2 = 6.   So total matches played in the first round = 6 × 4 = 24   Now top two teams from each group progress to the next round. Now these 8 teams are pooled into 2 groups. Total matches played in the second round = 6 × 2 = 12   Now 4 teams progress to the next round. Total matches played in the third round = 6   From this round, 2 teams progress to the next round. And final will be played between them.   Total matches = 24 + 12 + 6 + 1= 
24 + 12 + 6 + 1 = 43
43   43nswer:43
Answer: A
In a function they are distributing noble prize. In how many ways can 3 prizes be distributed among 4 boys when a boy gets any no. of prizes? Select the correct option
A) 48 B) 50 C) 64 D) 70 E) 80

Solution: Ans.(C)   Sol. In this case, repetitions are allowed, so all the three prizes can be given in 4 ways, i.e. (4 x 4 x 4) ways = 43 ways = 64 ways Or nr ways = 43 ways = 64 ways
Answer: C
There are 16 bees in the hive , then 8 more fly. How many bees are there in all?  Choose the correct choice from the following options.
A) 7
B) 33
C) 12
D) 24
E) 25

Solution: 16+8= 
16+8 = 24
24 . Answer is 24.
Answer: D
Two boys starts from the same place walking at the rate of 4 kmph and 5.5 kmph respectively in the same direction. What time will they take to be 10.5 km apart?  Choose one:
A) 8	B) 5	C) 7	D) 9	E) 6

Solution: Explanation:   Relative speed = 5.5 - 4= 
5.5 - 4 = 1.5
1.5 kmph (because they walk in the same direction)   distance= 10.5 km   time = distance / speed=10.5/1.5= 
10.5/1.5 = 7
7 hr   Answer :7
Answer: C
A cistern 5m long and 4 m wide contains water up to a depth of 1 m 25 cm. The total area of the wet surface is:  Choose the correct choice:
A) 49 m2  B) 42.5 m2  C) 53.5 m2  D) 55 m2  E) 57 m2

Solution: Area of the wet surface	= [2(lb + bh + lh) - lb]   = 2(bh + lh) + lb   = [2 (4 x 1.25 + 5 x 1.25) + 5 x 4] m2   = 42.5 m2.   Answer: Option 42.5 m2
Answer: B
The average of 10 numbers is 23. If each number is increased by 4, what will the new average be?
Choose the correct choice from the following
A) 22
B) 27
C) 88
D) 76
E) 16

Solution: Sum of the 10 numbers = 230   If each number is increased by 4, the total increase =   4 * 10= 
4 * 10 = 40
40   The new sum= 230 + 40= 
230 + 40 = 270
270 The new average= 270/10= 
270/10 = 27
27.   Answer: 27
Answer: B
If n is an integer, then the least possible value of |48 - 7n| is?  Pick:
A) 1	B) 0	C) 5	D) 4	E) 2

Solution: |48 - 7n| represents the distance between 48 and 7n on the number line. Now, the distance will be minimized when 7n, which is multiple of 7, is closest to 48. Multiple of 7 which is closest to 48 is 49 (for n = 7), so the least distance is 1: |48 - 49| = 1.   1nswer: 1.
Answer: A
If 24 lines are drawn in a plane such that no two of them are parallel and no three are concurrent, then in how many points do they intersect?	Choices
A) 276  B) 350  C) 425  D) 512  E) 648

Solution: If two lines are not parallel, then they will intersect in exactly one point. Lines can be extended infinitely on both ends so somewhere they will intersect with each other if they are not parallel. We are also given that no three lines are concurrent. This means that no three lines intersect at the same point. So every pair of two lines we select will have a unique point of intersection which they will not share with any third line.   The number of ways to select 2 lines from 24 lines is 24C2 = 276   The answer is 276.
Answer: A
A password for a computer uses eight digits from 0 to 9, inclusive. What is the probability that the digits of the password solely consist of prime numbers or zero?  Select the correct option
A) 1/32 B) 1/16 C) 1/8 D) 2/5 E) 1/256

Solution: To calculate all the possibilities, there are 10 choices for each digit. The number of possibilities for five digits is 10 × 10 × 10 × 10 × 10× 10 × 10 × 10 = 100,000,000 possible combinations.   Prime numbers constitute 2, 3, 5, 7, 11, 13 and 17. In addition to zero, this is 5 total possibility for each digit. So the number of satisfactory variants is 8 × 8 × 8 × 8 × 8 × 8 × 8 × 8 . So the probability is 1/2 × 1/2 × 1/2 × 1/2 × 1/2 × 1/2 × 1/2 × 1/2 = 1/256.   The right answer is choice (1/256).
Answer: E
Evaluate 100 / .25	Select
A) 400
B) 510
C) 500
D) None of these
E) 506

Solution: Explanation:   100/.25 = 10000/25= 
10000/25 = 400
400   Option 400
Answer: A
A start walking from a place at a uniform speed of 7 kmph in a particular direction. After half an hour, B starts from the same place and walks in the same direction as A at a uniform speed and overtakes A after 1 hour 48 minutes. Find the speed of B.  Select:	A) 4.7 kmph	B) 7.6 kmph	C) 4 kmph	D) 7 kmph	E) 5.3 kmph

Solution: Distance covered by A in 30 min = 1 Km   B covers extra 1km in 1 hour 48 minutes (9/5 hr)   i.e. Relative speed of 7.6 kmph over A = 1/(9/5) = 5/9   So the speed of 7.6 kmph = Speed of A + 5/9   = 7 + 5/9   = 7.55   Answer 7.6 kmph
Answer: B
In 1 hour, a boat goes 5 km along the stream and 5 km against the stream. The speed of the boat in still water (in km/hr) is : Choose the correct choice from the following
A) 3 km/hr.
B) 2 km/hr.
C) 6 km/hr.
D) 8 km/hr.
E) 5 km/hr.

Solution: Speed in still water = 1/2(5 + 5) km/hr   = 5 km/hr. ANSW5 km/hr.R :5 km/hr.
Answer: E
In 1950, Richard was 4 times as old as Robert. In 1955, Richard was 3 times as old as Robert. In which year was Richard 1.6 times as old as Robert? Choose the correct answer:
A) 1960
B) 1965
C) 1970
D) 1975
E) 1990

Solution: In 1950: Ri = 4 Ro -------------- eq1   In 1955: Ri +5 = 3(Ro+5)---------eq2   Thus in 1950, solving eq1 and eq2   1950 Ro= 10 , Ri =40   1990 Ro= 50 , Ri =80 =1.6 times   Thus Ans:1990
Answer: E
The distance between Delhi and Mathura is 110 kms. A starts from Delhi with a speed of 20 kmph at 7 a.m. for Mathura and B starts from Mathura with a speed of 25 kmph at 8 p.m. from Delhi. When will they meet? Choose the correct choice from the following answers
A) 19	B) 10	C) 14	D) 17	E) 15

Solution: D = 110 – 20 = 90   RS = 20 + 25= 
20 + 25 = 45
45   T= 90/45= 
90/45 = 2
2 hours   8 a.m. + 2= 10 a.m.   Answer: 10
Answer: B
Baseball's World Series matches 2 teams against each other in a best-of-seven series. The first team to win four games wins the series and no subsequent games are played. If you have no special information about either of the teams, what is the probability r that the World Series will consist of fewer than 7 games? Choose the correct choice from the following
A) 12.5% B) 25% C) 31.25% D) 68.75% E) 75%

Solution: In order to determine the probability r that the World Series will last less than 7 games, we can first determine the probability that the World Series WILL last exactly 7 games and then subtract this value from 1.   In order for the World Series to last exactly 7 games, the first 6 games of the series must results in 3 wins and 3 losses for each team.   Let's analyze one way this could happen for Team 1:   Game 1 Game 2 Game 3 Game 4 Game 5 Game 6   T1 Wins T1 Wins T1 Wins T1 Loses T1 Loses T1 Loses   There are many other ways this could happen for Team 1. Using the permutation formula, there are 6!/(3!)(3!) = 20 ways for Team 1 to win 3 games and lose 3 games in the first 6 games.   Logically, there are also 20 ways for Team 2 to win 3 games and lose 3 games in the first 6 games.   Thus, there are a total of 40 ways for the World Series to last the full 7 games.   The probability that any one of these 40 ways occurs can be calculated from the fact that the probability of a team winning a game equals the probability of a team losing a game = 1/2.   Given that 7 distinct events must happen in any 7 game series, and that each of these events has a probability of 1/2, the probability that any one particular 7 game series occurs is.   Since there are 40 possible different 7 game series, the probability that the World Series will last exactly 7 games is:   Thus the probability that the World Series will last less than 7 games is 100% - 31.25% = 68.75%.   The correct answer is 68.75%. 100  - 31.25= 
 100  - 31.25 = 68.75
68.75%.   The correct answer is 68.75%.
Answer: D
If A : B=4 : 3 and B : C = 1 : 2, then A : B : C is: Choose the correct choice:	A) 2:5:9	B) 4:6:3	C) 7:5:3	D) 4:3:6	E) 8:6:1

Solution: A:B=4:3, B:C=1:2, A:B:C=4Ã—1:1Ã—3:3Ã—2   â‡’ 4:3:6   Answer: 4:3:6.
Answer: D
If x and y are positive integers such that (3x + 7y) is a multiple of 11, then which of the followings are divisible by 11?
Choose the correct choice from the following answers:
A) 9x + 4y  B) x + y + 4  C) 4x - 9y  D) 4x + 6y  E) None of these

Solution: Explanation :   By hit and trial method, we get x=5 and y=1 such that 3x + 7y = 15 + 7= 
15 + 7 = 22
22 is a multiple of 11.   Then   (4x + 6y)= (4 × 5 + 6 × 1) = 26 which is not divisible by 11   (x + y + 4) = (5 + 1 + 4)= 
(5 + 1 + 4) = 10
10 which is not divisible by 11   (9x + 4y)= (9 × 5 + 4 × 1) = 49 which is not divisible by 11   (4x - 9y) = (4 × 5 - 9 × 1) = 20 - 9= 
20 - 9 = 11
11 which is divisible by 11. Answer : Option 4x - 9y
Answer: C
Set X consists of all the prime numbers between 10 and 25. What is the range of set X? Choose the correct answer.
A) 12  B) 13  C) 16.6  D) 17  E) 23

Solution: 12nswer of set X is 12=X
Answer: A
A and B complete a work in 4 days. A alone can do it in 8 days. If both together can do the work in how many days? Options:	A) 3.75 days	B) 3.99 days	C) 2.67 days	D) 2.98 days	E) 2.44 days

Solution: 1/4 + 1/8 = 3/8   8/3 = 2.67 days   Answer: 2.67 days
Answer: C
If four coins are tossed, the probability of getting two heads and two tails is -.	Choose the correct choice from the following choices:
A) 3/8
B) 4/5
C) 3/7
D) 2/9
E) 1/7

Solution: n(E) = six ways   p(E) = 6/2^4 = 3/8   3/8NSWER 3/8
Answer: A
A jar has 500 marbles. 46% are dark colors, and the remainder light colors. Green, blue, and purple marbles are considered dark colors, and yellow, orange, and red are considered light colors. Green and blue make up 60% of the dark marbles, and there are half as many red marbles as there are purple marbles. What percent of the light marbles are not red? Select the correct option.
A) 54.5%	B) 44.1%	C) 44.8%	D) 54.9%	E) 46.2%

Solution: 46% of 500 = 230 dark marbles   60% of 230 = 138 green and blue marbles     230-138= 
  230-138 = 92
92 purple marbles   50% of 92= 46 red marbles   500 total - 230 dark - 46 red = 224/500 = 44.8%   Answer is 44.8%
Answer: C
A lemonade stand sold only small and large cups of lemonade on Tuesday. 3/5 of the cups sold were small and the rest were large. If the large cups were sold for 7/12 as much as the small cups, what fraction of Tuesday's total revenue was from the sale of large cups?
Choose the correct answer
A) (a) 7/16
B) (b) 7/15
C) (c) 10/21
D) (d) 7/25
E) (e) 1/2

Solution: This problem is very good example how easy and quick plug-in method might be.   Let the total # of cups be 10.   # of small cups sold 3/5*10= 
3/5*10 = 6
6;   # of large cups sold  10-6= 
 10-6 = 4
4;   Let the price of small cup be $6, then the price of larges cup would be 7/12*6=$7/2;   Revenue from small cups: 6*$6=$36;   Revenue from large cups cups: 4*$7/2  6* 6= 
  6* 6 = 36
$36;   Revenue from large cups cups: 4*$7/2=$14;   Fraction of total revenue from large cups: 14/(36+14) 4* 7/2= 
 4* 7/2 = 14
$14;   Fraction of total revenue from large cups: 14/(36+14)=7/25.   Answer: (d) 7/25.
Answer: D
A sequence of odd integers begins at 61 and ends at 119. What is the sum of all numbers in this sequence?	Select.
A) 2610	B) 2700	C) 2790	D) 5400	E) 6000

Solution: Last Term = First Term + Common difference * (n-1)   119=61+2∗(n−1)   119=61+2n−2   58=2n−2   60=2n   n=30   Multiply 30 with the average from   (61+119)/2= 
  (61+119)/2 = 90
90=> 90*30= 
90*30 = 2_700
2700   ANSWER:2700
Answer: B
Lilly has 10 fishes, rosy has 7 fishes. Totally how many fishes they have in all?	Choose the most appropriate option.
A) 3 B) 10 C) 6 D) 17 E) 22

Solution: 10+7= 
10+7 = 17
17. Answer is 17.
Answer: D
Three unbased coins are tossed. the probability of getting at most two head is ?  Choose the correct choice from the following
A) 1/2	B) 7/8	C) 3/4	D) 1/5	E) 2/3

Solution: S={TTT,TTH,THT,HTT,THH,HTH,HHT,HHH}   E be the event of getting at least two head is {THH,HTH,HHT,TTT,TTH,THT,HTT}   P(E)=n(E)/n(S)=7/8   Answer(7/8)
Answer: B
Pipe A can fill a tank in 3 hours, pipe B in 4 hours, and pipe C in 6 hours. If all the pipes are open, in how many hours will the tank be filled?  Choose one.
A) 1  B) 1.3  C) 1.6  D) 1.9  E) 2.2

Solution: The part filled by A + B + C in 1 hour is 1/3 + 1/4 + 1/6 = 3/4   All the three pipes together will fill the tank in about 1.3 hours.   The answer is 1.3.
Answer: B
Dhoni spent 25 percent of his earning last month on rent and 10 percent less than what he spent on rent to purchase a new dishwasher. What percent of last month's earning did Dhoni have left over?	Select:
A) 50%	B) 55%	C) 60%	D) 62%	E) 52.5%

Solution: Say Dhoni's earning last month was $100.   Dhoni spent 30 percent of his earning last month on rent --> $25 on rent;   10 percent less than what he spent on rent to purchase a new dishwasher --> $25*0.9= 
25*0.9 = 22.5
$22.5 on the dishwasher.   Left over amount   100 - (25 + 22.5)= 
  100 - (25 + 22.5) = 52.5
$52.5   Answer: 52.5%
Answer: E
What profit percent is made by selling an article at a certain price, if by selling at 2/3rd of that price, there would be a loss of 20%?  Pick: A) 20% B) 80% C) 29% D) 90% E) 70%

Solution: SP2 = 2/3 SP1   CP = 100   SP2 = 80   2/3 SP1 = 80   SP1 = 120   100 --- 20 => 20%   20%nswer: 20%
Answer: A
The average score of a cricketer for ten matches is 38.9 runs. if the average for the first six matches is 42, then find the average for the last four matches.	Choose the correct choice from the following options:  A) 33.5  B) 33.5  C) 34.25  D) 35  E) None of these

Solution: Solution   Required average =(38.9x10)-(42x6)/4 =137/4= 
137/4 = 137/4 = around 34.25
34.25 Answer 34.25
Answer: C
The greatest number that divides 2928 and 3240 leaving remainders 5 and 1 respectively is:  Options:  A) 74  B) 78  C) 79  D) 81  E) 85

Solution: explanation:   2928-5= 
2928-5 = 2_923
2923 ,3240-1= 3239   Highest number that can divide 2923 and 3239 is HCF of numbers.   H79F of 2923 and 3239 = 79   Answer:79
Answer: C
What sum of money will produce Rs.70 as simple interest in 4 years at 3 1/2 percent? Choose the correct answer
A) 337
B) 500
C) 266
D) 288
E) 211

Solution: 70 = (P*4*7/2)/100   P = 500   Answer: 500
Answer: B
One used-car salesperson receives a commission of $ 200 plus 4 percent of $ 1,000 less than the car’s final sale price. Another car salesperson earns a straight commission of 4 percent of the car’s final sale price. What is the final sale price of a car if both salespeople would earn the same commission for selling it?	Pick
A) $ 5,000
B) $ 6,000
C) $ 8,000
D) $ 10,000
E) $ 12,000

Solution: This question can be solved by TESTing THE ANSWERS.   We're given the pay rate of two different salespeople who sell cars:   1) A commission of $ 200 plus 4 percent of $ 1,000 less than the car’s final sale price.   2) A straight commission of 6 percent of the car’s final sale price.   We're asked for the final sale price of a car if both salespeople would earn the SAME commission for selling it?   Let's TEST Answer B: $6,000   1st salesperson = $200 + .04(6,000 - 1,000) = $200 + .04(5,000) = $200 + $200 = $400   2nd salesperson 200 +  200= 
200 +  200 = 400
$400   2nd salesperson= .06(6,000) = $360   These totals are NOT the same, so we can eliminate B. Looking at the two pay 'formulas', we can see that the 2nd salesperson will make more money than the 1st when the price of the car increases to a significant level, so we need a price that is HIGHER than $6,000. Since the difference in pay is relatively small in Answer B, we're likely looking for a number that is fairly close to $6,000 though...   Let's TEST Answer C: $8,000   1st salesperson = $200 + .04(8,000 - 1,000) = $200 + .04(7,000) = $200 + $280 = $480   2nd salesperson 200 +  280= 
200 +  280 = 480
$480   2nd salesperson= .06(8,000) = $480   These totals are the SAME, so this must be the answer.   Final $ 5,000nswer:   $ 5,000
Answer: A
A first grade teacher uses ten flash cards, each numbered from 1 to10, to teach her students to order numbers correctly. She has students choose four flash cards randomly, then arrange the cards in ascending order. One day, she removes the cards '2' and '4' from the deck. On that day, how many different correct arrangements of four randomly selected cards are possible?	Choose the correct choice:
A) 70
B) 210
C) 336
D) 840
E) 1680

Solution: This is a combinations problem so you need to use the correct formula:   10-2= 
10-2 = 8
8 total cards. all possible permutations of 4 chosen from 8 cards are 8!/4!(8!-4!)= 8!/4!*4! =8*7*6*5*/4*3*2*1* 8 /4 *4= 
8 /4 *4 = 8
8*7*6*5*/4*3*2*1*=70   70NS:70
Answer: A
When positive integer n is divided by 5, the remainder is 1. When n is divided by 7, the remainder is 3. What is the smallest positive integer k such that k + n is a multiple of 70. Pick:  A) 3  B) 4  C) 12  D) 32  E) 35

Solution: First, let us say I have a number n which is divisible by 5 and by 7. We all agree that it will be divisible by 35, the LCM of 5 and 7.   Now, if I have a number n which when divided by 5 gives a remainder 1 and when divided by 7 gives a remainder 1, we can say the number is of the form   n = 5a + 1 e.g. 5 + 1, 10 + 1, 15 + 1, 20 + 1, 25 + 1, 30 + 1, 35 + 1 etc   and   n = 7b + 1 e.g. 7 + 1, 14 + 1, 21 + 1, 28 + 1, 35 + 1 etc   So when it is divided by the LCM, 35, it will give 1 as remainder (as is apparent above)   Next, if I have a number n which when divided by 5 gives a remainder 1 and when divided by 7 gives a remainder 3, we can say the number is of the form   n = 5a + 1   and   n = 7b + 3   Now, the only thing you should try to understand here is that when n is divided by 5 and if I say the remainder is 1, it is the same as saying the remainder is -4. e.g. When 6 is divided by 5, remainder is 1 because it is 1 more than a multiple of 5. I can also say it is 4 less than the next multiple of 5, can't I? 6 is one more than 5, but 4 less than 10.   Therefore, we can say n = 5x - 4 and n = 7y - 4 (A remainder of 3 when divided by 7 is the same as getting a remainder of -4)   Now this question is exactly like the question above. So when you divide n by 70, remainder will be -4 i.e. n will be 4 less than a multiple of 70. So you must add 4 to n to make it a multiple of 70   32
Answer: D
A professional athlete was offered a three-year contract to play with Team K that provided for an annual salary of $100,000 in the first year, an increase in annual salary of 30% over the previous year for the next two years, and a bonus of $50,000 on signing. Team L offered a three-year contract providing for an annual salary of $150,000 in the first year, an increase in annual salary of 10% over the previous year for the next two years, and no signing bonus. If he accepts the offer of Team L and fulfills the three-year contract terms, the athlete will receive how much more money by choosing Team L over Team K ?	Choose the correct choice from the following.
A) $32,500
B) $47,500
C) $82,500
D) $92,000
E) $100,000

Solution: Team K's contract = $100,000 + $100,000*1.3 + $100,000*1.3*1.3 + $50,000 = $449,000   Team L's contract = $150,000 + $150,000*1.1 + $150,000*1.1*1.1 = $496,500   The difference = $47,500.   Answer: $47,500.
Answer: B
40% of a 70% vinegar solution is replaced with water. From the resulting solution, again 10% is replaced with water. This step is repeated once more. What is the concentration of vinegar in the final solution obtained?  Choose the correct choice from the following answers:  A) 34%  B) 23%  C) 42%  D) 28%  E) 37%

Solution: A quick answer: (70)(0.6)(0.9)(0.9)   Imagine you have 100 ml of 70% vinegar solution.   In step 1, 40% of the vinegar solution is replaced with water. This means 60% of the original vinegar quantity remains. Hence the resultant concentration is (70)(0.6) = 42%   Next, 10% of this solution is replaced with water and the process is repeated. Both the times, 90% of the previous vinegar quantity remains. Thus, 42x0.9x0.9 = 34%   This gives the final concentration as 70x0.6x0.9x0.9 = 34%   34%nswer: 34%
Answer: A
How many integers between 362,855 and 852,755have tens digit 1 and units digit 3?	Choose the most appropriate option
A) 4,888 B) 4,898 C) 4,889 D) 4,869 E) 4,896

Solution: There is one number in hundred with 1 in the tens digit and 3 in the units digit: 13, 113, 213, 313, ...   The difference between 362,855 and 852,755 is 852,755-362,855=489,900 - one number per each hundred gives 133,900/100=4,889 numbers.   Answer: 4,889.
Answer: C
What is the decimal equivalent of (1/5)^2?	Options:
A) 0.0016
B) 0.04
C) 0.16
D) 0.25
E) 0.5

Solution: (1/5)² = (1/5)(1/5)=   1/25= 
  1/25 = 1/25 = around 0.04
0.04   0.04
Answer: B
A truck carrying cans of soup contains A stacks. Each stack contains B cases, and each case contains C cans. How many cans of soup are contained in 3 trucks? Pick
A) 3AB/C
B) 3AC/B
C) 3ABC
D) AB/3C
E) AC/3B

Solution: There are C cans in each case.   There are BC cans in each stack.   There are ABC cans in each truck.   There are 3ABC cans in 3 trucks.   The answer is 3ABC.
Answer: C
What is the present worth of Rs. 330 due in 2 years at 5% simple interest per annum?	Pick one:	A) 128	B) 277	C) 120	D) 300	E) 371

Solution: Let the present worth be Rs. x. Then,   S.I. = (330 - x)   (x * 5 * 2) / 100 = (330 - x)   10x = 33000 - 100x   110x = 33000 => x = 300.   Answer: 300
Answer: D
Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is: Answers.
A) 1:3  B) 3:1  C) 1:2  D) 3:2  E) 2:1

Solution: Let the speeds of the two trains be x m/sec and y m/sec respectively.   Then, length of the first train = 27x metres,   and length of the second train = 17y metres.   Therefore, 27x + 17y/(x+y)= 23   =27x + 17y = 23x + 23y   =4x = 6y   =x/y	= 3/2.   Answer is 3:2.
Answer: D
Rs.1500 is divided into two parts such that if one part is invested at 6% and the other at 5% the whole annual interest from both the sum is Rs.87. How much was lent at 5%?
Choose the correct choice from the following answers
A) 228  B) 299  C) 300  D) 500  E) 188

Solution: (x*5*1)/100 + [(1500 - x)*6*1]/100 = 87   5x/100 + 90 â€“ 6x/100 = 87   x/100 = 3   => x = 300   Answer:300
Answer: C
The average speed of a train is 87kmph. The train was scheduled to start at 9am in Bangalore, and as per schedule it has to reach a destination of 348km away from Bangalore at 1:45pm same day and a halt was scheduled onthe way. For how long was the halt scheduled?
Choose the correct choice
A) 45 minutes  B) 50 minutes  C) 55 minutes  D) 60 minutes  E) None of these

Solution: Speed of train = 87 kmph and distance it covers is 348 km.   Time taken to cover the distance= Distance/Speed   = 348/87= 
348/87 = 4
4 hours.   But total time taken by train to reach destination is= 1:45 pm – 9 a.m =4 hours 45 minutes.   Time of halt = Total time – take taken without halt   = 4 hours 45 minutes – 4 hours = 45 minutes 45 minutes)
Answer: A
A code is to be made by arranging 7 letters. Four of the letters used will be the letter A, one of the letters used will be the letter B, one of the letters used will be the letter C, and one of the letters used will be the letter D. If there is only one way to present each letter, how many different codes are possible?  Select the correct option:
A) 42
B) 210
C) 420
D) 840
E) 5,040

Solution: we have 7 letters out of which 3 are of one kind, 2 are of another kind..   so total ways = 7!/3!1!=840   ans 840
Answer: D