MU-NLPC/Calc-aqua_rat huggingface dataset:
Find the area of a rhombus whose side is 25 cm and one of the diagonals is 35 cm? Options.
A) 276 sq.cm B) 268 sq.cm C) 618 sq.cm D) 297 sq.cm E) 700 sq.cm

Solution: Consider the rhombus ABCD. Let the diagonals intersect at E. Since diagonals bisect at right angles in a rhombus.   BE2 + AE2 = AB2   252 = 152 + AE2 AE = √(625 - 225)= 
(625 - 225) = 400
√400= 20,   AC = 20 + 20= 
20 + 20 = 40
40 cm.   Area of a rhombus= 1/2 * d1d2   = 1/2 * 40 * 35= 
1/2 * 40 * 35 = 700
700 sq.cm.   Answer:700 sq.cm
Answer: E
In a mixture of 45 litres the ratio of milk to water is 4:1. Additional 3 litres of water is added to the mixture. Find the ratio of milk to water in the resulting mixture.	Pick one: A) 2/1 B) 4/1 C) 2/3 D) 3/4 E) 3/1

Solution: Given that Milk/Water=4x/x and 4x+x=45 --> x=9.   Thus Milk=4x=36 liters and Water=x=9 liters.   New ratio = 36/(9+3) = 36/12= 
36/12 = 3
3/1.   Answer: 3/1.
Answer: E
Tough and Tricky questions: Ratios
1/5 of a certain class left on a field trip. 1/3 of the students who stayed behind did not want to go on the field trip (all the others did want to go). When another vehicle was located, 1/2 of the students who did want to go on the field trip but had been left behind were able to join. What fraction of the class ended up going on the field trip?	Choose the correct choice:
A) 1/2  B) 2/3  C) 7/15  D) 23/30  E) 4/5

Solution: let total no. of students be 30   students left on a field trip = 1/5(30) =6   thus 24 students left behind   1/3(24)=8 students did not want to go. thus 16 students want to go on the trip   1/2(16)=8 were able to join the other students on the field trip.   thus total number of students that went on a field trip =6+8= 
6+8 = 14
14   thus required fraction= 14/30 =7/15   7/15
Answer: C
The proportion of copper and zinc in the brass is 13:7. How much zinc will there be in 100 kg of brass? Choose the most appropriate option
A) 37 kg	B) 35 kg	C) 85 kg	D) 45 kg	E) 25 kg

Solution: 7/20 * 100= 
7/20 * 100 = 35
35   Answer: 35 kg
Answer: B
The sum and the product of the roots of the quadratic equation x2 + 20x + 3 = 0 are?
Choose the correct choice from the following options.
A) 10, 3
B) -10, 3
C) 20,-3
D) -10,-3
E) None of these

Solution: Explanation:   Sum of the roots and the product of the roots are -20 and 3 respectively.   ANSWNone of theseR IS None of these
Answer: E
John want to buy a $100 Trouser at the store, but he think itâ€™s too expensive. Finally, it goes on sale for $55. What is the percent decrease?
Options
A) 20%	B) 30%	C) 40%	D) 50%	E) 45%

Solution: The is always the difference between our starting and ending points. In this case, itâ€™s 100 â€“ 55 = 45. The â€œoriginalâ€ is our starting point; in this case, itâ€™s 100. (45/100)*100 = (0.45)*100= 
(0.45)*100 = 45
45%.   45%
Answer: E
The triplicate ratio of 1:2 is?  Pick:
A) 1:7
B) 1:8
C) 1:3
D) 1:1
E) 1:2

Solution: 13: 23 = 1:8   Answer: 1:8
Answer: B
A certain gallery is hanging a series of 7 paintings. All the paintings will be exhibited in a row along a single wall. Exactly 3 of the paintings are on panel, the remainder are on canvas. In how many ways can the paintings be exhibited if the works on panel must be the second and sixth in the row?
OE	Choose one:
A) 240 B) 200 C) 144 D) 80 E) 16

Solution: We need to consider them separately because the question specifies:   1. Panel paintings have to be placed only at 2nd, 3nd and 6th place.   2. Implies that Canvas has to be placed 1,4,5,7th place.   So we have two separatebucketsto consider.   So panels can be ordered in 3!   144anvas can be ordered in 4!   since relative position of panels to canvas is fixed (Panels 2nd and 6th) the answer is 3! x 4! = 144   144
Answer: C
The average age of 28 students in a group is 11 years. When teacher’s age is included to it, the average increases by one. What is the teacher’s age in years? Pick.
A) 36
B) 38
C) 40
D) cannot be determined
E) None of these

Solution: Age of the teacher = (29 × 12 – 28 × 11) years   = 40 years.   Answer 40
Answer: C
Two cyclist start on a circular track from a given point but in opposite direction with speeds of 7m/s and 8m/s. If the circumference of the circle is 630meters, after what time will they meet at the starting point? Choices
A) 20sec
B) 15sec
C) 42sec
D) 50sec
E) 1min

Solution: They meet every 630/7+8 = 42sec   Answer is 42sec
Answer: C
Average between two sets of numbers is closer to the set withmore numbers?  Choose the correct choice from the following answers:
A) 60  B) 80  C) 98  D) 89  E) 91

Solution: If on a test three people answered 90% of the questions correctly and two people answered 80% correctly, then the average for the group is not 85% but rather 3×90+2×805=4305=86.3×90+2×805=4305=86.   Here, 90 has a weight of 3 => it occurs 3 times.   Whereas 80 has a weight of 2 => it occurs 2 times.   So the average is closer to 90 than to 80 as we have just calculated.   80
Answer: B
If an organization were to sell n tickets for a theater production, the total revenue from ticket sales would be 20 percent greater than the total costs of the production. If the organization actually sold all but 5 percent of the n tickets, the total revenue from ticket sales was what percent greater than the total costs of the production?
Answers.
A) 4%  B) 10%  C) 14%  D) 15%  E) 18%

Solution: Let 14%ost of PROD for 1 ticket = 1   So 14%OP for n tickets = n   So for selling n tickets, SP = 1.2 * n = 1.2n   So SP of 1 ticket = 1.2   SP of 95% tickets = 1.2 * 0.95n   So profit % = (1.2 * 0.95n - n)/n * 100   = 0.14 * 100= 
0.14 * 100 = 14
14%   Answer - 14%
Answer: C
How many possible ways are there to select 2 stocks at random from 7 stocks? Choose the correct choice:
A) 17
B) 19
C) 21
D) 23
E) 25

Solution: 7212 = 21   The answer is 21.
Answer: C
A 6% stock yields 8%. The market value of the stock is Choose one: A) 33 B) 75 C) 44 D) 27 E) 91

Solution: For an income of Rs. 8, investment = Rs. 100.   For an income of Rs. 6, investment = Rs. 100	x 6 = Rs. 75.   8   Market value of Rs. 100 stock = Rs. 75.   Answer: 75
Answer: B
Which of the following number is divisible by 24 ?  Pick one:
A) 35718 B) 63810 C) 537804 D) 3125736 E) 63811

Solution: 24 = 3 x8, where 3 and 8 co-prime.   Clearly, 35718 is not divisible by 8, as 718 is not divisible by 8.   Similarly, 63810 is not divisible by 8 and 537804 is not divisible by 8.   Consider option (D),   Sum of digits = (3 + 1 + 2 + 5 + 7 + 3 + 6)= 
(3 + 1 + 2 + 5 + 7 + 3 + 6) = 27
27, which is divisible by 3.   Also, 736 is divisible by 8.   3125736 is divisible by (3 x 8), i.e., 24.   Answer:3125736
Answer: D
Two trains of equal length are running on parallel lines in the same directions at 46km/hr. and 36km/hr. The faster trains pass the slower train in 54 seconds. The length of each train is:
Choose the correct answer
A) 82m  B) 50m  C) 75m  D) 80m  E) None of these

Solution: Explanation:   The relative speed of train is 46-36= 
46-36 = 10
10 Km/hr= (10 X 5) / 18 = 25/9 m/s10×518=259m/s   In 54 secs the total distance traveled is 54x25/9 = 150 m.   Therefore the length of each train is = 150/2= 
150/2 = 75
75 m.   Answer 75m
Answer: C
If the number 53,1n9, where n represents the tens digit, is a multiple of 3, then the value of n could be which of the following?
Choose the correct option:
A) 7 B) 5 C) 2 D) 1 E) 0

Solution: The sum of the digits 5 + 3 + 1 + n + 9 must be a multiple of 3   18 + n must be a multiple of 3   substituting the numbers n must = 0   Answer 0
Answer: E
A beauty pageant is being held with 50 competitors (one from each state in the USA). Each competitor has an equal chance of winning the competition. Four competitors will be chosen, and each will win either 1st, 2nd, 3rd, or 4th place. What is the probability California, Florida, and Hawaii will win three of the four places?	Select the correct option:
A) 3/100
B) 3/5
C) 1/100
D) 1/4,900
E) 1/5

Solution: Combination Formula: nCr = n!/(r!(n - r)!), where n is the population/set, and r is the sample/subset.   Total number possible = 50C4 - 50!/(4!(50 - 4)!) = 230,300   Number CA possible = 1C1 = 1   Number FL possible = 1C1 = 1   Number HI possible = 1C1 = 1   Number other possible = 47C1 = 47   Probability Formula: P(A) = (Number Favorable Outcomes)/(Total Number Possible Outcomes)   P(CA, FL, HI) = (1C1)(1C1)(1C1)(47C1)/50C4 = 47/230,300 = 1/4,900   Answer: 1/4,900
Answer: D
The mean of four integers E will not change if all the integers are multiplied by any constant. What is always true about this set of numbers?
I. The mean of the set is 0
II. The sum of the largest member and the smallest member of the set is 0
III. The set contains both positive and negative integers  Pick:
A) I only  B) II only  C) III only  D) I and II only  E) I, II, and III

Solution: If we consider a set {1,2,3,4}, when multiplied with a constant we take that constant as 1 and multiply resulting set will contain the same numbers as the original. so how can the answer be I only.....I only
Answer: A
Sheila works 8 hours per day on Monday, Wednesday and Friday, and 6 hours per day on Tuesday and Thursday. She does not work on Saturday and Sunday. She earns $324 per week. How much does she earn in dollars per hour?  Pick
A) 2 B) 8 C) 9 D) 1 E) 2

Solution: Explanation:   Total hours worked = 8 x 3 + 6 x 2 = 36   Total earned = 324. Hourly wage = 324 / 36= 
324 / 36 = 9
9   Answer: 9) 9
Answer: C
The number 4 is the smallest positive
integer that has exactly three factors:
1, 2, and 4. If k is the next-highest integer
that also has exactly three factors, what is
the sum of the three factors of k?  Answers:	A) 20	B) 18	C) 16	D) 14	E) 13

Solution: The greatest of the five possible answers is 20, so k is less than 20. Use trial and error to   find the value of k:   Factors of 5: 1 5   Factors of 6: 1 2 3 6   Factors of 7: 1 7   Factors of 8: 1 2 4 8   Factors of 9: 1 3 9   Thus, k = 9, and the sum of the factors of k is 1 + 3 + 9= 
1 + 3 + 9 = 13
13.   correct answer 13)13
Answer: E
John makes $60 a week from his job. He earns a raise andnow makes $70 a week. What is the % increase?  Choose the most appropriate option:
A) 16%  B) 16.66%  C) 16.98%  D) 17.23%  E) 18.3%

Solution: Increase = (10/60)*100 = (1/6)*100 = 16.66%.   16.66%
Answer: B
What is 0.01 percent of 15,356? Choose the most appropriate option.
A) 0.15356	B) 1.5356	C) 15.356	D) 0.015356	E) 0.0015356

Solution: Since, Percent=1/100, what=something(s), and is:=. We can write the question as s=0.01(1/100)15,356. The answer is 1.5356. Hence, the correct answer is 1.5356.
Answer: B
Two taps can separately fill a cistern 20 minutes and 30 minutes respectively and when the waste pipe is open, they can together fill it in 18 minutes. The waste pipe can empty the full cistern in?	Choose the correct option
A) 38
B) 37
C) 36
D) 39
E) 35

Solution: 1/20 + 1/30 - 1/x = 1/18   x = 36   Answer:36
Answer: C
The sum of two numbers is 16. The difference is 6. What are the two numbers? Choose the correct option.
A) 10-6  B) 8-8  C) 9-7  D) 11-5  E) 13-3

Solution: 11+5= 
11+5 = 16
16   11 - 5= 
11 - 5 = 6
6   The Answer is 11-5
Answer: D
Printer P can print one lakh books in 8 hours. Printer Q can print the same number of books in 10 hours while Printer R can print the same in 12 hours. All the Printers started printing at 9 A.M. Printer P is stopped at 11 A.M. and the remaining 2printers complete work. Approximately at what time will the printing of 1 lac books be completed?	Choose the most appropriate option:
A) 12 pm  B) 1 pm  C) 2 pm  D) 3 pm  E) 4 pm

Solution: Work done by P in 1 hour = 1/8   Work done by Q in 1 hour = 1/10   Work done by R in 1 hour = 1/12   Work done by P,Q and R in 1 hour = 1/8 + 1/10 + 1/12 = 37/120   Work done by Q and R in 1 hour = 1/10 + 1/12 = 22/120 = 11/60   From 9 am to 11 am, all the Printer were operating.   Ie, they all operated for 2 hours and work completed = 2 × (37/120) = 37/60   Pending work = 1- 37/60 = 23/60   Hours taken by Q an R to complete the pending work = (23/60) / (11/60) = 23/11   which is approximately equal to 2   Hence the work will be completed approximately 2 hours after 11 am ; ie around 1 pm   1 pm
Answer: B
Paul buys his co-workers donuts 24 glazed, 12 creme-filled and 6 with sprinkles. The glazed donuts cost $0.75 each, the creme-filled donuts cost $1.00 each, and the sprinkle covered donuts cost $0.50 each. What is the average cost Paul paid for each donut?  Choose the correct option:
A) 70 cents	B) 75 cents	C) 79 cents	D) 80 cents	E) 1 dollar

Solution: Explanation:   24 12 6   0.75 1.00 0.50   $18 + $12 + $3 = $33/42  18 +  12 +  3= 
 18 +  12 +  3 = 33
$33/42= $0.79   79 cents
Answer: C
How many positive integers less than 100 have a remainder of 6 when divided by 13?	Select:
A) 2 B) 7 C) 6 D) 9 E) 10

Solution: We have to include 6 also.As 13*0 + 6= 
13*0 + 6 = 6
6   If somebody says to divide 6 by 13 ,we will be telling we have 0 quotient and remainder as 6.   Answer is 6
Answer: C
If the price of a certain computer increased 30 percent from d dollars to 377 dollars, then 2d = Choose one:
A) 540	B) 570	C) 619	D) 649	E) 580

Solution: Before Price increase Price = d   After 30% Price increase Price = d+(30/100)*D = 1.3d = 377 (Given)   i.e. d = 377/1.3= 
377/1.3 = 290
$290   i.e. 2d= 2*290= 
2*290 = 580
580   Answer: option 580
Answer: E
For any number x, x* is defined as the greatest positive even integer less than or equal to x. What is the value of 5.2 – 5.2*?	Pick one:  A) 0.2  B) 1.2  C) 1.8  D) 2.2  E) 4.0

Solution: Since x* is defined as the greatest positive even integer less than or equal to x, then 5.2* = 4 (the greatest positive even integer less than or equal to 5.2 is 4).   Hence, 5.2 – 5.2* = 5.2 - 4= 
5.2 - 4 = 1.2
1.2   Answer: 1.2.
Answer: B
The compound ratio of 5:6, 3:2 and 4:5?
Choose the correct answer.
A) 1:8	B) 1:6	C) 1:2	D) 1:1	E) 1:7

Solution: 5/6 * 3/2 * 4/5= 
5/6 * 3/2 * 4/5 = 1
1/1   1:1   Answer: 1:1
Answer: D
The amount of water (in ml) that should be added to reduce 9 ml. Lotion, containing 50% alcohol, to a lotion containing 40% alcohol, is?	Choose one
A) 2.25 B) 4.25 C) 5.25 D) 6.25 E) 7.25

Solution: 4.5 4.5   40% 60%   40% ----- 4.5   60% ------? => 6.75 - 4.5= 
6.75 - 4.5 = 2.25
2.25 ml   2.25NSWER:2.25
Answer: A
The sum of five numbers is 655. The average of the first two numbers is 85 and the third number is 125. Find the average of the two numbers?  Choose the correct option.
A) 180  B) 128  C) 276  D) 297  E) 236

Solution: Let the five numbers be P, Q, R, S and T.   => P + Q + R + S + T = 655.   (P + Q)/2 = 85 and R = 125   P + Q = 170 and R = 125   P + Q + R = 295   S + T = 655 - (P + Q + R) = 360   Average of the last two numbers = (S + T)/2 = 180.   180nswer:180
Answer: A
When positive integer x is divided by positive integer y, the result is 59.32. What is the sum Q of all possible 2-digit remainders for x/y? Choose the correct choice from the following
A) 560  B) 616  C) 672  D) 728  E) 784

Solution: ans B 616...   remainders = .32=32/100=8/25=16/50 and so on..   so two digit remainders are 16+24+32+....+96..   Q=8(2+3+4....+12)=616
Answer: B
A trained covered x km at 40 kmph and another 2x km at 20 kmph. Find the average speed of the train in covering the entire 6x km.	Select:	A) 40kmph	B) 45kmph	C) 48kmph	D) 50kmph	E) 55kmph

Solution: Total time taken = x/40 + 2x/20 hours   = 5x/40 = x/8 hours   Average speed = 6x/(x/8)   = 48 kmph   Answer:48kmph
Answer: C
If a#b = ab – b + b^2, then 3#8 =	Choose the correct option:
A) 80
B) 8
C) 15
D) 21
E) 35

Solution: Solution -   Simply substitute 3 and 8 in equation in the place of a and b respectively.   3#8 = 3*8 - 8 + 8^2 = 24 - 8 + 64= 
24 - 8 + 64 = 80
80. 80NS 80
Answer: A
The sum of the two digits of a number is 10. If the number is subtracted from the number obtained by reversing its digits, the result is 54. Find the number? Choose the correct choice from the following options.
A) 76 B) 28 C) 26 D) 20 E) 27

Solution: Any two digit number can be written as (10P + Q), where P is the digit in the tens place and Q is the digit in the units place.   P + Q = 10 ----- (1)   (10Q + P) - (10P + Q) = 54   9(Q - P) = 54   (Q - P) = 6 ----- (2)   Solve (1) and (2) P = 2 and Q = 8   The required number is   = 28   Answer:28
Answer: B
A survey is conducted on 800 people from a city. It is found that 6 1% of people surveyed speakHindi, 54.5% people speak Bangla and 37.5% of them speak English. 16.5% people can speak only Hindi and Bangla, 14.5% people can speak only Hindi and English and 6% people can speak only Bangla and English. Answer the following questions based on this information.
How many people are there who can speak only Hindi ?	Choose the correct choice from the following options:
A) 172  B) 174  C) 176  D) 178  E) 179

Solution: Explanation :   x + y + z + k = 800 - (132 + 116 + 48)= 
800 - (132 + 116 + 48) = 504
504 .....(i)   x + k= 488 - (132 + 116)= 
488 - (132 + 116) = 240
240 .....(ii)   y + k= 436 - (132 + 48)= 
436 - (132 + 48) = 256
256 ......(iii)   z + k= 300 - (116 + 48)= 
300 - (116 + 48) = 136
136 .....(iv)   (eqn ll + lll + IV) - eqn (l) gives   2k= (240 + 256 + 136) - 504   2k = 632 - 504= 
632 - 504 = 128
128 ∴ k= 64   x = 240 - 64= 
240 - 64 = 176
176   y= 256 - 64= 
256 - 64 = 192
192   z= 136 - 64= 
136 - 64 = 72
72   Answer : Option 176
Answer: C
An engine moves at the speed of 60 kmph without any coaches attached to it.Speed of the train reduces at the rate that varies directly as the square root of the number of coaches attached.When 4 coaches are attached speed decreases to 48 kmph.What will be the speed of train when 36 coaches are attached.	Choices.
A) 24
B) 28
C) 20
D) 32
E) 40

Solution: 1.   No. of coaches =4   sqr root=2   speed decreases by 12   12=k*2   k=6   No. of coaches=36   swr root=6   decrease=6*6= 
6*6 = 36
36   New speed=60-36= 
60-36 = 24
24   24
Answer: A
Divide 5679 by 7 and find out remainder and quotient ? Choose the correct choice from the following answers:
A) 901, 5 B) 811, 2 C) 921, 7 D) 805, 4 E) 951, 20

Solution: dividend = divisor * quotient + remainder ===> 5679 = 7 * 811 + 2 ===> remainder = 2 and quot = 811 Ans - 811, 2
Answer: B
If a and b are different values and a – b = 3(√a - √b), then in terms of b, a equals:  Pick:	A) √b	B) b	C) b - 2√b + 1	D) b - 6√b + 9	E) b^2 – 2b√b + b

Solution: (√a)^2 - (√b)^2 = 3(√a - √b) -----> ( √a + √b) ( √a - √b) = 3(√a - √b) -------> √a + √b = 3, so   √a = 3 - √b, square both sides and solve.   Answer is b - 6√b + 9.
Answer: D
If a train, travelling at a speed of 90 kmph, crosses a pole in 5 sec, then the length of train is? Choose the correct choice from the following.
A) 119	B) 125	C) 772	D) 662	E) 812

Solution: D = 90 * 5/18 * 5= 
90 * 5/18 * 5 = 125
125 m   Answer:125
Answer: B
A train passes a station platform in 38 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?  Options:  A) 180 m  B) 200 m  C) 270 m  D) 320 m  E) None

Solution: Sol.   Speed = [54 * 5/18] m/sec = 15 m/sec.   Length of the train = (15 * 20)= 
(15 * 20) = 300
300 m.   Let the length of the platform be x metres.   Then, x + 300 / 38= 15 ⇔ x + 300 = 570 ⇔ x = 270 m.   Answer 270 m
Answer: C
The sum of four consecutive odd numbers is equal to the sum of 3 consecutive even numbers. Given that the middle term of the even numbers is greater than 101 and lesser than 220, how many such sequences can be formed? Options
A) 29 B) 17 C) 25 D) 33 E) 50

Solution: Four consecutive odd numbers: k-2, k, k+2, k+4   Three consecutive even numbers: n-2, n, n+2   k-2+k+k+2+k+4=n-2+n+n+2   4k+4=3n   4(k+1)=3n   k+1=(3/4)n   k=(3/4)n-1   All n's that's divisible by 4 will have an integral k. So, we need to find out how many such n's are available within given range:   We know,   101<n<220   104<=n<=216   Count=(216-104)/4+1=212/4+1=28+1= 
28+1 = 29
29   29ns: 29.
Answer: A
Look at this series: 36, 34, 30, 28, 24, ... What number should come next?  Choose the correct choice from the following choices
A) 20	B) 22	C) 25	D) 24	E) 26

Solution: This is an alternating number subtraction series. First, 2 is subtracted, then 4, then 2, and so on.   ANSWER 22
Answer: B
What is the sum of all the multiples of 10 between 0 and 75? Pick.
A) 500	B) 620	C) 450	D) 340	E) 280

Solution: The multiples of 10 between 0 and 99 are 10, 20, 30, 40, 50, 60, 70. If these are all added together, the result is 280.   Final Answer:   280
Answer: E
P,Q and R together earn Rs.1890 in 9 days. P and R can earn Rs.600 in 5 days. Q and R in 7 days can earn Rs.910. How much amount does R can earn per day?  Choose the correct option:
A) s.40
B) s.70
C) s.90
D) s.100
E) s.120

Solution: Explanation :   s.40mount Earned by P,Q and R in 1 day = 1890/9= 
1890/9 = 210
210 ---(1)   s.40mount Earned by P and R in 1 day= 600/5= 
600/5 = 120
120	---(2)   s.40mount Earned by Q and R in 1 day= 910/7= 
910/7 = 130
130	---(3)   (2)+(3)-(1)=> s.40mount Earned by P , Q and 2R in 1 day   - s.40mount Earned by P,Q and R in 1 day = 120+130-210= 
120+130-210 = 40
40=>s.40mount Earned by R in 1 day = 40   s.40nswer : Option s.40
Answer: A
A cricketer has a certain average for 10 innings. In the eleventh inning, he scored 108 runs, there by increasing his average by 4 runs. His new average is:	Choose one:
A) 64 runs  B) 66 runs  C) 68 runs  D) 70 runs  E) 72 runs

Solution: Let average for 10 innings be x. Then,   (10x + 108)/11 = x + 4   = 11x + 44 = 10x + 108   = x = 64.   New average = (x + 4) = 68 runs.   Answer:68 runs
Answer: C
During a recent track meet, Peter ran x meters of the 100 meter dash in 6 seconds; running at the same rate, how many seconds will it take Peter to run z meters of the 200 meter dash?  Choose the correct choice from the following options.
A) 6z/x
B) 6zx
C) 6x/z
D) 6/xz
E) xz/6

Solution: Speed of Peter = x/6 meters per second   Time needed to run z meters = DIST6z/xNCE/SPEED = z / (x/6) = 6z/x   Option 6z/x   The values 100m and 200m have no role to play here and are just given to confuse you.
Answer: A
If A, B and C together can finish a piece of work in 4 days. A alone in 36 days and B in 18 days, then C alone can do it in?	Choose the correct choice from the following options:
A) 1  B) 7  C) 8  D) 9  E) 6

Solution: C = 1/4 - 1/36 – 1/18 = 1/6 => 6 days'   Answer: 6
Answer: E
A man takes 5 hours 45 min in walking to a certain place and riding back. He would have gained 2 hours by riding both ways. The time he would take to walk both ways is
Select the correct option:	A) 11 hrs	B) 8 hrs 5 min	C) 7 hrs 45 min	D) 9 hrs 20 min	E) None of these

Solution: Explanation :   Given that time taken for riding both ways will be 2 hours lesser than   The time needed for waking one way and riding back   From this, we can understand that   Time needed for riding one way = time needed for waking one way - 2 hours   Given that time taken in walking one way and riding back = 5 hours 45 min   Hence The time he would take to walk both ways = 5 hours 45 min + 2 hours = 7 hours 45 min   Answer : 7 hrs 45 min
Answer: C
Which of the following is between 14/19 and 19/23?
Choose the correct option
A) 1/3  B) 3/8  C) 1/2  D) 5/8  E) 7/9

Solution: I see this as a POE (Process of Elimination) and Ballparking (Estimation) question. Not sure if this is the most efficient, but it worked:   1) I estimate 14/19 to be ~3/4+ (approximately slightly greater than 3/4)   2) I estimate 19/23 to be ~4/5+ (approximately slightly greater than 4/5)   3) So now I'm looking for an answer choice that is .75 < x < .80   It should be pretty easy to identify which answer choices are less than .75 (or 3/4) if you have had practice with fractions.   A) clearly wrong - it's less than 3/4   B) also clearly wrong - it's less than 3/4   C) also clearly wrong - it's less than 3/4   D) also clearly wrong - it's less than 3/4   I would just stop here and select E. But to verify:   7/9) 7/9 ~ .77 which is greater than .75 and less than .80
Answer: E
The diameter of a cylindrical tin is 8cm and height is 5 cm. Find the volume of the cylinder?	Choose the most appropriate option
A) 33  B) 45  C) 66  D) 80  E) 21

Solution: r = 4 h = 5   π * 4 * 4 * 5 = 80 π cc   Answer:80
Answer: D