MU-NLPC/Calc-aqua_rat huggingface dataset:
The inner circumference of a circular race track, 14 m wide, is 440 m. Find radius of the outer circle. Choose the correct choice from the following answers.
A) 84
B) 86
C) 82
D) 80
E) None of them

Solution: Let inner radius be r metres. Then, 2(22/7)r = 440 = r = (440 x (7/44))= 70 m.   Radius of outer circle = (70 + 14)= 
(70 + 14) = 84
84 m.   84nswer is 84
Answer: A
In how many different ways can the letters of the word 'LEADING' be arranged such that the vowels should always come together?
Choose the correct choice:	A) 650	B) 720	C) 420	D) 122	E) 450

Solution: Explanation:   The word 'LEADING' has 7 letters. It has the vowels 'E','A','I' in it and these 3 vowels should always come together. Hence these 3 vowels can be grouped and considered as a single letter. that is, LDNG(EAI).   Hence we can assume total letters as 5 and all these letters are different. Number of ways to arrange these letters   =5!=5Ã—4Ã—3Ã—2Ã—1=120=5!=5Ã—4Ã—3Ã—2Ã—1=120   In the 3 vowels (EAI), all the vowels are different. Number of ways to arrange these vowels among themselves   =3!=3Ã—2Ã—1=6=3!=3Ã—2Ã—1=6   Hence, required number of ways   =120Ã—6=720   ANSWER IS 720
Answer: B
If a and b is a positive integer, then 2^a + 2^(b + 1) =	Select the correct option:
A) cannot be determined B) 2^(a + b) C) 2a+b D) 2^(a + 1+b) E) none

Solution: If a and b is a positive integer, then 2^a + 2^(b + 1) =   2^a + 2^(b+ 1)   2^(1+a+b)   Answer:option 2^(a + 1+b)
Answer: D
By selling an article at Rs.600, a profit of 30% is made. Find its cost price?  Choose the correct choice from the following answers.
A) 400	B) 267	C) 287	D) 480	E) 811

Solution: SP = 600   CP = (SP)*[100/(100+P)]   = 600 * [100/(100+50)]   = 600 * [100/150] = Rs.400   400nswer: 400
Answer: A
In a certain sequence of 6 numbers, each number after the first is 1 more than the previous number. If the first number is −5, how many of the numbers in the sequence are positive?  Choose the correct answer
A) None	B) One	C) Two	D) Three	E) Four

Solution: Non - Negative ( zero to positive infinity )   Solution to the question :   -5,-4,-3,-2,-1,0   Hence ans is 0 ..option None
Answer: A
P says to Q "I am thrice as old as you were when i was as old as you are". If the sum of their present age is 100 years, then the present age of Q?  Choose the correct option:
A) 35.5	B) 36.5	C) 37.5	D) 38.5	E) 39.5

Solution: let the present age of q be x   the age of q years back(to be defined) is x/3   as the age of p will be x by then .   Years passed= x-x/3=2x/3(subtracting age of q)   so p acurrent age is x+2x/3   and q current age is x   adding them to 100   we get x =37.5   ANSWER:37.5
Answer: C
Excluding stoppages, the average speed of a bus is 60 km/hr and including stoppages, the average speed of the bus is 15 km/hr. For how many minutes does the bus stop per hour? Choose the correct answer:	A) 22	B) 88	C) 77	D) 20	E) 45

Solution: In 1hr, the bus covers 60 km without stoppages and 15 km with stoppages.   Stoppage time = time take to travel (60 - 15) km i.e 45 km at 60 km/hr.   stoppage time = 45/60 hrs = 45 min.   Answer: 45
Answer: E
The sum of the squares of two consecutive positive integers exceeds their product by 91. Find the integers?	Choose one:
A) 6,5	B) 5,8	C) 2,3	D) 9,8	E) 9,10

Solution: Explanation:   Let the two consecutive positive integers be x and x + 1   x2 + (x + 1)2 - x(x + 1) = 91   x2 + x - 90 = 0   (x + 10)(x - 9) = 0 => x = -10 or 9.   As x is positive x = 9   Hence the two consecutive positive integers are 9 and 10.   Answer 9,10
Answer: E
A student got 72% in math and 82% in history. To get an overall average of 75%, how much should the student get in the third subject?	Select the correct option:
A) 69%  B) 71%  C) 73%  D) 75%  E) 77%

Solution: 72 + 82 + x = 3*75   x = 71   The answer is 71%.
Answer: B
A 260 m long train running at the speed of 120 km/hr crosses another train running in opposite direction at the speed of 80 km/hr in 9 sec. What is the length of the other train? Choices: A) 230 B) 240 C) 267 D) 256 E) 298

Solution: Relative speed = 120 + 80= 
120 + 80 = 200
200 km/hr.= 200 * 5/18 = 500/9 m/sec.   Let the length of the other train be x m.   Then, (x + 260)/9 = 500/9 => x = 240.   Answer: 240
Answer: B
A technician makes a round-trip to and from a certain service center by the same route. If the technician completes the drive to the center and then completes 10 percent of the drive from the center, what percent of the round-trip has the technician completed? Choose the correct choice from the following.
A) 5%  B) 10%  C) 25%  D) 40%  E) 55%

Solution: Assuming that the technician makes a round-trip of 40 miles (each way is 20 miles), then the technician would have completed 20 miles + 2 miles (10% of the remaining 20 miles). Therefore, the total is 22 miles. 22miles/40 miles is 55% of the entire trip.   ANSW55%R:55%
Answer: E
A train consists of 12 boggies, each boggy 15 metres long. The train crosses a telegraph post in 9 seconds. Due to some problem, two boggies were detached. The train now crosses a telegraph post in Choose the correct choice from the following choices.
A) 18 sec B) 7.5 sec C) 15 sec D) 20 sec E) None of these

Solution: Length of train = 12 Ã— 15 = 180 m.   Then, speed of train = 180â„9 = 20 m/s   Now, length of train = 10 Ã— 15 = 150m   âˆ´ Required time = 150â„20 = 7.5 sec.   Answer 7.5 sec
Answer: B
There are 2 kinds of staff members in a certain company, PART TIME AND FULL TIME. 25 percent of the total members are PART TIME members others are FULL TIME members. The work time of part time members is 3/5 of the full time members. Wage per hour is same. What is the ratio of total wage of part time members to total wage of all members.	Pick one.
A) A.1/4
B) B.1/5
C) 1/6
D) 1/7
E) 1/8

Solution: Just plug in   Assuming there are 100 employees   25% are PT = 25   75% FT = 75   Assume that the total number of hrs FT employees have to work = 10   PT will work = 3/5*10= 
3/5*10 = 6
6   since the wages are same , there will no affect on ratios   total number of hrs FT employees work= 75*10= 
75*10 = 750
750   PT= 25*6= 
25*6 = 150
150   now the ratio is 150/900= 1/6 answer is 1/6
Answer: C
A cistern can be filled by a tap in 4 hours while it can be emptied by another tap in 9 hours. If both the taps are opened simultaneously, then after how much time will the cistern get filled?
Options
A) 7.3 hrs	B) 7.9 hrs	C) 7.1 hrs	D) 7.2 hrs	E) 7.8 hrs

Solution: Net part filled in 1 hour   = (1/4 - 1/9) = 5/36   The cistern will be filled in 36/5 hrs i.e., 7.2 hrs.   Answer:7.2 hrs
Answer: D
How long does a train 100 m long traveling at 72 kmph takes to cross a tunnel of 1400 m in length?	Answers:
A) 70 sec B) 60sec C) 82 sec D) 75 sec E) 62 sec

Solution: 75 sec = 1400+100= 
1400+100 = 1_500
1500 m   S= 72 * 5/18= 
72 * 5/18 = 20
20   T= 1500 * 1/20= 
1500 * 1/20 = 75
75 sec   ANSWER:75 sec
Answer: D
In a triangle ABC, AB = 6, BC = 8 and AC = 10. A perpendicular dropped from B, meets the side AC at D. A circle of radius BD (with centre B) is drawn. If the circle cuts AB and BC at P and Q respectively, then AP : QC is equal to  Choose the correct choice.
A) 1:1	B) 3:2	C) 4:1	D) 3:8	E) 2:5

Solution: Explanation :   Triangle ABC and Triangle A3:8B are similar,   AC/AB= BC/B3:8   10/6=8/r   r=24/5   BP=BQ=B3:8=r=24/5   AP=AB-r= 6-24/5 = 6/5   CQ=BC-r=8-24/5=16/5   AP:CQ= 6/16 = 3:8   Answer : 3:8
Answer: D
Maddie has 6 apples, if she give 3 to mike, how many does she have left?  Options.
A) 1	B) 2	C) 3	D) 4	E) 5

Solution: 6-3= 
6-3 = 3
3   C. 3
Answer: C
Three pipes, A, B, & C are attached to a tank. A & B can fill it in 20 & 30 minutes respectively while C can empty it in 20 minutes. If A, B & C are kept open successively for 1.5 minute each, how soon will the tank be filled?	Answers.
A) 2 hours B) 4 hours C) 5 hours D) 2 hours 15 min E) 3 hours

Solution: in three minute 1/20+1/30-1/20=2/60 = 1/30 part is filled   4.5 min--------1/30 parts   x min--------- 1 part(full)   x=135 min =2 hours 15 min   ANSWER:2 hours 15 min
Answer: D
If the time is currently 1:30 pm, what time will it be in exactly 644 hours?  Choose the correct choice from the following options.
A) 7:30 am	B) 8:30 am	C) 9:30 am	D) 10:30 am	E) 11:30 am

Solution: 644 = 26(24) + 20/24   The time will be 20 hours later than 1:30 pm which is 9:30 am.   The answer is 9:30 am.
Answer: C
A no.when divided by 220 gives a remainder 43, what remainder will be obtainedby dividingthe same no.17?
Select the correct option.
A) 5 B) 6 C) 9 D) 11 E) 15

Solution: 221 + 43= 
221 + 43 = 264
264/17= 9 (Remainder)   9
Answer: C
A river 5m deep and 35 m wide is flowing at the rate of 2 kmph, calculate the amount of water that runs into the sea per minute?	Choose the correct choice from the following answers.
A) 5832.75	B) 5839.75	C) 5837.75	D) 5222.75	E) 5835.75

Solution: Rate of water flow-2kmph--2000/60--33.33 m/min   depth of river--5m   width of river--35m   vol of water per min--33.33 *5*35---5832.75   5832.75nswer 5832.75
Answer: A
Dawson purchased a house for Rs.78000 and a site for Rs.12000 respectively, if he sold the house for Rs.79000 and the site for Rs.15000, then find the resultant percentage of gain?	Choose the correct choice from the following answers
A) 4.43%
B) 4.44%
C) 4.45%
D) 4.46%
E) 4.47%

Solution: Sol.   Total CP = 90000 & total SP = 94000 ⇒ gain = SP/CP = 94000/90000 = 1.0444 = 4.44%.   Answer 4.44%
Answer: B
Marketing executives for a certain chewing gum company projected a 25 percent increase in revenue this year over that of last year, but revenue this year actually decreased by 25%. What percent of the projected revenue was the actual revenue ?	Choose one
A) 53% B) 58% C) 60% D) 64% E) 75%

Solution: Last year revenue = 100 (assume);   This year revenue = 75;   Projected revenue = 125.   Actual/Projected*100=75/125*100= 
75/125*100 = 60
60%.   Answer: 60%.
Answer: C
A batsman makes a score of 87 runs in the 17th inning and thus increases his average by 3. Find his average after 17th inning?
Choose the correct choice from the following:
A) 38
B) 178
C) 39
D) 27
E) 11

Solution: Let the average after 7th inning = x   Then average after 16th inning = x - 3   16(x-3)+87 = 17x   x = 87 - 48= 
87 - 48 = 39
39   ANSWER:39
Answer: C
The average of first five multiples of 6 is?
Choose the correct option:
A) 6
B) 18
C) 9
D) 5
E) 7

Solution: Average = 6(1 + 2 + 3 + 4 + 5)/5   = 90/5= 
90/5 = 18
18.   Answer:18
Answer: B
The 19th of September 1987 was a Saturday. If 1988 was a leap-year, what day of the week was the 25th of September 1990? Choose the correct answer:
A) Monday	B) Tuesday	C) Wednesday	D) Thursday	E) Friday

Solution: 19th September   1987: Saturday   1988: Monday (due to leap year)   1989: Tuesday   1990: Wednesday   Hence 25th September was a Tuesday.   The answer is Tuesday.
Answer: B
The average marks obtained by 100 candidates in an examination is 50. Find how many candidates have passed in the examination, if the average marks of candidates who passed is 70 and that of failed candidates is 20.
Choose the correct option:	A) 90	B) 75	C) 60	D) 58	E) 65

Solution: Explanation:   Let the number of students who passed the examination be X   Number of students failed = (100 - X)   Total marks of students who have passed = 70X   Total marks of 100 students = 100 * 50= 
100 * 50 = 5_000
5000   Total marks of students who have failed= 20(100 – X)   20(100 – X) + 70X = 5000   2000 – 20 X + 70X = 5000   50 X = 3000   X = 60   ANSWER:60
Answer: C
What is the next number in this sequence:
1, 11, 21, 1211, 111221, 312211, 13112221, _________?
Choose the correct option.
A) 1113213211  B) 1113213244  C) 1113213233  D) 1113213222  E) 1113213255

Solution: A   1113213211   The next number in sequence is 1113213211.   EXPLANATION-   The sequence goes like   You need to spell the no of digits.   e.g. take the no 1,11,21   Take 1. it spells as one 1 so we get the no 11,   take 11 we spell it as two ones‘ and we get 21   .so take the last given no in the sequence 13112221 so we spell it as one 1 one 3 two 1 three 2’s one 1.   So   the next no in sequence is 1113213211.
Answer: A
Divide Rs. 1500 among A, B and C so that A receives 1/3 as much as B and C together and B receives 2/3 as A and C together. A's share is?
Choose the correct choice from the following options:	A) 297	B) 268	C) 375	D) 367	E) 363

Solution: A+B+375 = 1500   A = 1/3(B+375); B = 2/3(A+375)   A/(B+375) = 1/3   A = 1/4 * 1500= 
1/4 * 1500 = 375
> 375   Answer: 375
Answer: C
which one is odd?
4377
3954
9865
8454
9831	Choose the correct choice from the following options
A) 4377  B) 3954  C) 9865  D) 8454  E) None

Solution: 9865orrect Answer : 9865   sum of digit of all other number is 21, but sum of digit of 9865 is 28
Answer: C
Two trains of equal length, running with the speeds of 60 and 40 kmph, take 55 seconds to cross each other while they are running in the same direction. What time will they take to cross each other if they are running in opposite directions?
Pick one:
A) 10 sec  B) 16 sec  C) 13 sec  D) 67 sec  E) 11 sec

Solution: RS = 60 -40= 
60 -40 = 20
20 * 5/18= 100/18   T = 55   D = 55 * 100/18 = 2750/9   RS = 60 + 40= 
60 + 40 = 100
100 * 5/18   T= 2750/9 * 18/500= 
2750/9 * 18/500 = 11
11 sec   Answer: 11 sec
Answer: E
Mark bought a set of 6 flower pots of different sizes at a total cost of $8.25. Each pot cost 0.15 more than the next one below it in size. What was the cost, in dollars, of the largest pot?
Choose the correct answer.
A) $1.75	B) $1.85	C) $2.00	D) $2.15	E) $2.30

Solution: This question can be solved with a handful of different Algebra approaches (as has been shown in the various posts). Since the question asks for the price of the largest pot, and the answers are prices, we can TEST THE ANSWERS.   We're told that there are 6 pots and that each pot costs 25 cents MORE than the next. The total price of the pots is $8.25. We're asked for the price of the largest (most expensive) pot.   Since the total price is $8.25 (a 15-cent increment) and the the difference in sequential prices of the pots is 15 cents, the largest pot PROBABLY has a price that is a 15-cent increment. From the answer choices, I would then TEST Answer A first   IF....   The largest pot = $1.75   1   1.15   1.3   1.45   1.6   1.75   Total = $8.25   So this MUST be the answer.   $1.75
Answer: A
S is a set of 64 consecutive multiples of 4. If the smallest number in S is 68, then the greatest number in S is  Pick.
A) 198 B) 297 C) 320 D) 402 E) 405

Solution: last term =first term +(total no. of terms-1)consecutive difference   S is a set of 64 consecutive multiples of 4. If the smallest number in S is 68, then the greatest number in S is   first term = 68 ; total terms =64 ; difference = 4   68+(63)4 = 320   Ans 320
Answer: C
Ajay buys 6 dozen eggs for Rs 10.80, and 12 eggs are found rotten and the rest are sold at 5 eggs per rupee. Find his percentage gain or loss.	Select the correct option.
A) 11 1/9 % gain	B) 11 1/9 % loss	C) 9 1/11 % gain	D) 9 1/11 % loss	E) None of these

Solution: 6 dozen egg cost = Rs 10.80   Since one dozen is rotten , he sells 5 dozen at 5 eggs per rupee.   Hence, S.P = Rs 12   Thus, Gain % = [(12 - 10.8) / 10.8] x 100 = 11 1/9%   11 1/9 % gainNSWER:11 1/9 % gain
Answer: A
Given that there are 11 cricket players per team, how many ways can you select 3 cricket players from 4 teams if no more than one player can be selected from each team?
Choose the correct choice from the following choices.
A) 500	B) 484	C) 396	D) 656	E) 336

Solution: First select 3 group out of available 4 groups. This cane be done in 4C3 ways = 4 ways   Now from each group we have to select one person only: 11C1 * 11C1= 11 * 11= 
11 * 11 = 121
121   Total ways: 121 * 4= 
121 * 4 = 484
484 ways.   Answer is 484
Answer: B
|-5| (|-20|-|4|)= ??
Source: Preparation Material MBA Center
Pick:
A) 64
B) –60
C) 44
D) 75
E) 100

Solution: Absolute value will turn negatives into their positive 'equivalents', and will leave positives unchanged, so |-5| = 5, |-20| = 20, and |4| = 4. Getting rid of our absolute values we have:   |-5| (|-20|-|4|) = (5) (20 - 4) = 4*16= 
4*16 = 64
64
Answer: A
A train crosses a platform of 150 m in 15 sec, same train crosses another platform of length 250 m in 20 sec. then find the length of the train?	Choose the correct choice from the following options
A) 150metres B) 157m C) 750m D) 850m E) 350m

Solution: Length of the train be ‘X’   X + 150/15 = X + 250/20   4X + 600 = 3X + 750   X = 150m   150metresnswer:150metres:
Answer: A
The markup on a television set is 20 percent of the cost. The markup is what percent of the selling price?
(markup = selling price - cost)
Options:
A) 8%	B) 10%	C) 12 1/2%	D) 15%	E) 16 2/3%

Solution: SP = 1.2CP   markup/SP = 0.2CP/1.2CP = 1/6 * 100 = 50/3 = 16 2/3%   Answer - 16 2/3%
Answer: E
if (log5 5)(log4 9)(log3 2) is equal to  Choose the correct choice from the following choices
A) -1  B) 2  C) 3  D) 4  E) 1

Solution: =>1*log 9/log 4 * log 2/log 3   =>log 3^2/log 2^2 * log 2/log 3   =>2 log 3/2log 2*log 2/log 3=1   -1NSWER -1
Answer: A
A company pays 12.5% dividend to its investors. If an investor buys Rs.40 shares and gets 25% on investment, at what price did the investor buy the shares?  Choose the correct option:
A) 20  B) 66  C) 18  D) 19  E) 01

Solution: Explanation:   Dividend on 1 share = (12.5 * 40)/100 = Rs.5   Rs.25 is income on an investment of Rs.100   Rs.5 is income on an investment of Rs. (5 * 100)/25 = Rs.20   20NSWER: 20
Answer: A
If a and b are nonzero integers such that 6a = 15b, then each of the following must be true EXCEPT
Pick:	A) 0 < b/a < 1	B) ab is positive.	C) On the number line, b lies between 0 and a.	D) The ratio of a to b is equivalent to 10/4.	E) a – b is positive.

Solution: This question can be solved by TESTing VALUES. Based on its wording, you would likely need to do 2 TESTs to get to the correct answer though.   We're told that a and b are NONZERO INTEGERS and that 6a=15b or 2a = 5b. We're told that each of the answer is always true EXCEPT for one of them...   Before we get to the actual work, it's important to note a few details:   1) We are NOT told that a and b are positive - we're just told that they're NONZERO - that's interesting - it means that we have to consider the possibility that they're both NEGATIVE...   2) 4 of the answers will always be true, while one of them will EITHER be sometimes true OR never true. We'll have to keep working until we find 1 answer that is not true (for whatever reason) - that will be the solution to this question.   Since 2A = 5B, I'm going to run 2 pairs of TESTs at the same time...   A = 5   B = 2   AND   A = -5   B = -2   Answer A: 0 < B/A < 1   2/5 and -2/-5 both = 2/5. Answer A appears true.   Answer B: AB is positive   (2)(5) and (-2)(-5) both = +10. Answer B appears true.   Answer C: B is between 0 and A on the number line   0....2....5   -5....-2....0   Answer C appears true.   Answer D: A/B = 10/4   5/2 = -5/-2   10/4 = 5/2   Answer D appears true.   Answer E: A - B is positive     5 - 2= 
  5 - 2 = 3
3   -5 - (-2)= -3 *****This is NOT always true.   Final Answer:   a – b is positive.
Answer: E
Find the area of the quadrilateral of one of its diagonals is 30 cm and its off sets 9 cm and 6 cm? Options:
A) 188 cm2  B) 150 cm2  C) 168 cm2  D) 198 cm2  E) 225 cm2

Solution: 1/2 * 30(9 + 6)   = 220 cm2   Answer: 225 cm2
Answer: E
The simple interest on a sum of money is 4/9 of the principal. Find the rate percentage and time, if both are numerically equal. Choose the correct choice:	A) 6 1/3 % and 6 2/3 years	B) 6 2/3 % and 6 1/3 years	C) 6 2/3 % and 6 2/3 years	D) 6 1/3 % and 6 1/3 years	E) 6 % and 6 2/3 years

Solution: Let sum = Rs. x. Then, S.l. = Rs. 4x/9   Let rate = R% and time = R years.   Then, (x*R*R)/100=4x/9 or R^2 =400/9 or R = 20/3 = 6 2/3.   Rate = 6 2/3 % and   Time = 6 2/3 years = 6 years 8 months   Answer is 6 2/3 % and 6 2/3 years
Answer: C
A sum of 25 was paid for a work which A can do in 32 days, B in 20 days, B and C in 12 days and D in 24 days.How much did C receive if all the four work together ?	Select:
A) 14⁄3
B) 16⁄3
C) 15⁄3
D) 17⁄3
E) None of these

Solution: A's one day's work = 1⁄32   B's one day's work = 1⁄20   (B + C)'s one day's work = 1⁄12   ∴ C's one day's work = 1⁄12 - 1⁄20 = 1⁄30   D's one day's work = 1⁄24   ∴ (A + B + C + D)'s one day's work   1/32+1/20+1/30+1/24=75+120+80+100/2400   = 375⁄2400 = 15⁄96 = 5⁄32   ∴ Out of 5⁄32 of work done   1⁄30 of the work is done by C.   ⇒ Out of 25 paid for the work, C will receive   1/30 /5/32×25, i.e, 1⁄30 × 32⁄5 × 25, i.e, 16⁄3   Answer 16⁄3
Answer: B
A man can row at 6 kmph in still water. If the velocity of current is 2 kmph and it takes him 2 hour to row to a place and come back, how far is the place?
Choose one.
A) 5.33 km
B) 6.33 km
C) 5.63 km
D) 7.33 km
E) 5.93 km

Solution: Speed in still water = 6 kmph   Speed of the current = 2 kmph   Speed downstream = (6+2)= 
(6+2) = 8
8 kmph   Speed upstream= (6-2)= 
(6-2) = 4
4 kmph   Let the required distance be x km   Total time taken= 2 hour   x/8 +x/4 =2   x+2x/8 =2   3x/8=2   3x=16   x=5.33 km   5.33 kmNSWER:5.33 km
Answer: A
In a soccer bet,we play 4 teams.first team odd 1.30,second 5.23,third 3.25,fourth 2.05.we place the bet with 5.00 euros.
how much money we expect to win?	Choose the correct choice from the following choices:
A) 219.5  B) 226.49  C) 235.01  D) 266.74  E) 669.0

Solution: in the case we won the bet,we have:   1.30* 5.23* 3.25* 2.0*5.00=219.50   we will win 226.49   so correct answer is 226.49
Answer: B
Joe’s average (arithmetic mean) test score across 4 equally weighted tests was 70. He was allowed to drop his lowest score. After doing so, his average test score improved to 75. What is the lowest test score that was dropped? Choose the correct choice from the following options:
A) 20
B) 25
C) 55
D) 65
E) 80

Solution: The arithmetic mean of 4 equally weighted tests was 70. So what we can assume is that we have 4 test scores, each 70.   He dropped his lowest score and the avg went to 75. This means that the lowest score was not 70 and other three scores had given the lowest score 5 each to make it up to 70 too. When the lowest score was removed, the other 3 scores got their 5 back. So the lowest score was  3 *5= 
 3 *5 = 15
15 less than 70.   So the lowest score= 70 - 15= 
70 - 15 = 55
55   Answer (55)
Answer: C
In a series of consecutive numbers, 27 is the eighth smallest number and 20 is the tenth largest number. What is the range of the series?  Choose the correct choice from the following
A) 32
B) 30
C) 28
D) 16
E) 25

Solution: Imp:All are consecutive odd numbers.   27 is the 8th smallest ,there are 7 numbers smaller then 27 ,smallest number :  27-14= 
  27-14 = 13
13   20 is the 10th largest ,so there are 9 numbers larger then 20, largest number: 20+18= 
 20+18 = 38
38   Range:38-13= 
38-13 = 25
25   Ans : 25
Answer: E
The area of a triangle is with base 4m and height 5m?  Choose the correct choice from the following answers:  A) 88 m2  B) 10 m2  C) 66 m2  D) 77 m2  E) 31 m2

Solution: 1/2 * 4 * 5= 
1/2 * 4 * 5 = 10
10 m2   Answer: 10 m2
Answer: B
A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for Rs. 3200. With the help of C, they completed the work in 3 days. How much is to be paid to C? Choices
A) Rs. 375 B) Rs. 400 C) Rs. 600 D) Rs. 800 E) Rs. 850

Solution: C's 1 day's work = 1/3 - (1/6 + 1/8) = 1/3 - 7/24 = 1/24   A's wages : Rs. 400's wages : C's wages = 1/6 : 1/8 : 1/24 = 4: 3 : 1   C's share (for 3 days) = Rs.	(3 * 1/24 * 3200) =Rs.400   Answer = Rs. 400
Answer: B
If the height of an equilateral triangle GBC is equal in length to the hypotenuse of an isosceles right triangle DEF, a side of ΔGBC is how many times as long as a leg of the right triangle DEF?  Pick one
A) (√2)/(√3)
B) (√3)/(√2)
C) √2
D) (2√2)/(√3)
E) 2/(√3)

Solution: Side of the equilateral triangle GBC = 2m ----> height = m * sqtr(2)   Hipotenuse of the right triangle GBC = m * sqrt(3) ----> side = m * sqtr(3) / sqtr(2)   Question is 2m/m * sqtr(3) / sqtr(2) = 2*sqrt(2)/sqrt(3)=(2√2)/(√3)
Answer: D