MU-NLPC/Calc-aqua_rat huggingface dataset:
what is the least number by which 2,100 must be divided to get a number perfect square Choose the correct choice:
A) 21
B) 42
C) 24
D) 40
E) 45

Solution: 2,100/21=100   100=(10)^2   21ns-21   21NSWER:21
Answer: A
Rick deposited $750 to his bank account using $5 and $15 dollar bills only. If Rick came to the bank with 70 bills and left with 10 bills only, how many $15 dollar billsმ did he deposit? Choices
A) 5.
B) 45.
C) 50.
D) 55.
E) 65.

Solution: 5x+15y=750 --1   x+y=60 ---2   multiply eq 2 with 5 and subtract from eq 1   5x+15y=750   5x+5y=300   10y= 450   y=45 and x = 15   therefore $15 bills = 45   Answer 45.
Answer: B
Find large number from below question The difference of two numbers is 1390. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder Choose the correct choice from the following answers:	A) 1245	B) 1345	C) 1455	D) 1577	E) 1665

Solution: Let the smaller number be x. Then larger number = (x + 1390).   x + 1390 = 6x + 15   5x = 1375   x = 275   Large number = 275+1390= 
275+1390 = 1_665
1665   1665
Answer: E
10 litres of water are poured into an aquarium of dimensions 50cm length, 20cm breadth, and 40cm height. How high (in cm) will the water rise?
(1 litre = 1000cm³) Choose the most appropriate option:
A) 6
B) 8
C) 10
D) 20
E) 40

Solution: lXbXh= 10000   h= 10000/50*20= 10 cm   '10' is the answer.
Answer: C
The average marks obtained by 120 cndidates in a certainexaminationis 35.if the average marks of passed candidate is 39 and that of the failedcandidates is 15,what is the number of candidates who passed the examination Choose the most appropriate option:
A) 12 years 8 month B) 13 years C) 14 years 8 month D) 15 years 7 month E) 16 years 9 month

Solution: (d) Let No. of passed candidates are x   So, x * 39 + (120 – x) 15= 120 * 35   x = 100   2.(a) Total increase = 8 * 2= 
8 * 2 = 16
16 years   So, total age of two women= 35 + 45 +16= 
35 + 45 +16 = 96
96   Average age of two women=96/2= 
96/2 = 48
48 years   3(d) Total decrease= 20 * 2= 
20 * 2 = 40
40 month= 3 years 4 month   So, age of new boy = 18 years – 3 years 4 month   = 14 years 8 month   14 years 8 month
Answer: C
What is the approx. value of W, if W=(1.5)11, Given log2 = 0.301, log3 = 0.477 Choose the correct choice from the following choices
A) 85
B) 84
C) 86
D) 87
E) 99

Solution: Explanation :   W = (1.5)11   Take log both sides:   => logW = 11 x log(1.5) =11 x log(3/2)   => logW = 11 x (log3 - log2) = 11 x 0.176 = 1.936   => W = 101.936   => W = 86 (approx)   Answer : 86
Answer: C
Jane had an average of 87 on his first 7 tests. She had an average score of 90 on her first 6 tests. What did he score on the 7th test?	Choose the correct choice from the following answers:	A) 69	B) 75	C) 90	D) 86	E) 50

Solution: The sum of Jane's first 7 scores is 7 Â· 87 and the sum of her first 6 scores is 6 Â· 90, so she received   7 Â· 87 âˆ’ 6 Â· 90 on her 7th quiz. You can do the arithmetic or notice that the answer ends in a 9. The correct answer is 69.
Answer: A
Find the remainder when 6^23 is divided by 5 ?
Choose the correct choice from the following.
A) 3	B) 2	C) 1	D) 0	E) 4

Solution: 6^23 = 6^(4*5+3) = 6^(20) * 6^3 last 3 digits = 216   216/5 remainder = 1   ANSWER:1
Answer: C
60 percent of movie theatres in Town X have 3 screens or less. 20% of those theatres sell an average of more than $300 worth of popcorn per showing. 50 percent of all the movie theatres in Town X sell $300 or less of popcorn per showing. What percent of all the stores on the street have 4 or more screens and sell an average of more than $300 worth of popcorn per day?
Pick:
A) 12
B) 18
C) 32
D) 40
E) 44

Solution: Lets take numbers here.   Assume that the total number of movie theaters in the town = 100   Then number of movie theaters with 3 screens or less = 60   => Number of movie theaters with 4 screens or more = 40   Movie theaters with 3 screens or less selling popcorn at more than $300 = 20% of 60 = 12   Number of movie theaters selling popcorn at $300 or less = 56   => Number of movie theaters selling popcorn at more than $300 = 100-56= 
100-56 = 44
44   Of these 44 theaters, 12 are those with 3 screens or less   Therefore 44 (44-12) must be those with four screens or more   44 is the answer
Answer: E
Which is the least number that must be subtracted from 1856 so that the remainder when divided by 7, 12, 16 is 6?	Select the correct option:
A) 168	B) 172	C) 170	D) 174	E) 176

Solution: First we need to figure out what numbers are exactly divisible by 7,12,16. This will be the set {LCM,LCMx2,LCMx3,...}   LCM(7,12,16) = 48*7= 
48*7 = 336
336   The numbers which will leave remainder 6 will be {336+6, 336x2 +6, 336x3 +6,...}   The largest such number less than or equal to 1856 is 336x5+6 or 1686   To obtain this you need to subtract 170.   170
Answer: C
There are 40 people in a party. If everyone is to shake hands with one another, how many hand shakes are possible?
Options
A) 780
B) 667
C) 661
D) 297
E) 261

Solution: Explanation:   Total number of persons = n = 40   Shake hands involve only 2 persons = r = 2   Number of shake hands = nCr = 40C2   40C2 = (40 * 39) /(2 * 1)= 
(40 * 39) /(2 * 1) = 780
780   780NSWER:780
Answer: A
A and B invests Rs.10000 each, A investing for 9 months and B investing for all the 12 months in the year. If the total profit at the end of the year is Rs.21000, find their shares? Choose the correct choice from the following answers
A) 1300,1500  B) 9000,12000  C) 7290,8000  D) 15000,12000  E) 72821,75000

Solution: The ratio of their profits A:9000,12000 = 9:12 = 3:4   Share of A in the total profit = 3/7 * 21000 = Rs.9000   Share of 9000,12000 in the total profit = 4/7 * 21000 = Rs.12000   Answer:9000,12000
Answer: B
A can do a piece of work in 3days of 8 hours each and B alone can do it in 4 days of 9 hours each.how long will they take it to do working together
7 1/5 hours a day?	Choose the correct choice from the following answers.
A) 3 days
B) 2 days
C) 5 days
D) 7 days
E) 4 days

Solution: A's work per hour=1/24   B's work per hour=1/36   A & B's work per hour together=(1/24)+(1/36)=5/72   so A & B together complete the work in 72/5 hours...   if they work 7 1/5=36/5 hours a day,   it will take  (72/5)/(36/5)= 
 (72/5)/(36/5) = 2
2 days...   ANSWER:2 days   ANSWER:2 days
Answer: B
If n > 0 , which of the following must be true?
I n^2 > 1
II	n - n^2 < 0
III	2n - 1 < 0	Choose the correct choice from the following answers:  A) I only  B) II only  C) III only  D) I and II only  E) none

Solution: I. True for all values of n except 1   When n = 1 ; n^2 = 1   II. True for all values of n except 1   When n = 1 ; n - n^2 = 1 - 1= 
1 - 1 = 0
>0   III	false for all values of n   Hence the correct answer will be (I and II only)
Answer: D
What value of K gives the equation,3k-2=2k-1?	Options.
A) ONE B) TWO C) THREE D) FOUR E) NONE

Solution: 3k-2=2k-1   If k=1   3(1)-22 -1= 
2 -1 = 1
1   3(1)-2=2(1)-1   3-2=2-1   1=1   Option ONE is answer
Answer: A
How many paying stones, each measuring 2 1/2 m * 2 m are required to pave a rectangular court yard 30 m long and 16 1/2 m board? Select:  A) 99  B) 88  C) 77  D) 55  E) 22

Solution: 99nswer: Option 99   Explanation:   30 * 33/2 = 5/2 * 2 * x => x = 99   99nswer: 99
Answer: A
The average temperature for Tuesday, Wednesday and Thursday was 42°C. The average temperature for Wednesday, Thursday and Friday was 44°C. If the temperature on Friday be 43°C, what was the Temperature on Tuesday?  Choose the correct choice from the following options:
A) 39°C
B) 44°C
C) 37°C
D) 42°C
E) None of these

Solution: Explanation:   T + W + T = 42 × 3 = 126°37°C   W+ T+ F = 44 × 3 = 132°37°C   Also, temperature on Friday = 43°37°C   Temperature on Tuesday = 126 +43 - 132= 
126 +43 - 132 = 37
37°37°C   Answer: Option 37°C
Answer: C
A trader has 40 kg of rice, a part of which he sells at 14% profit and rest at 6% loss. On the whole his loss is 4% . What is the quantity sold at 14% profit and that at 6% loss?  Answers:
A) 4 and 36 kg	B) 10 and 40 kg	C) 15 and 35 kg	D) 20 and 30 kg	E) 40 and 30 kg

Solution: 4 and 36 kglligation Method   I P4 and 36 kgRT II P4 and 36 kgRT   14 (x1) -6 (x2)   \ /   x   / \   (x2-x) (x-x1)   2 18   1 9   Ratio of quantities sold at 14% profit and 6% loss = 1: 9   Quantity sold at 14% profit = 40/1+9 *1 = 4 kg   Quantity sold at 6% loss = 40/1+9 *9 = 36kg   4 and 36 kgNSWER:4 and 36 kg
Answer: A
The dimensions of a room are 25 feet * 15 feet * 12 feet. What is the cost of white washing the four walls of the room at Rs. 9 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each?	Choose the correct choice from the following choices.
A) s.4538  B) s.8154  C) s.4518  D) s.4530  E) s.4517

Solution: Area of the four walls = 2h(l + b)   Since there are doors and windows, area of the walls = 2 * 12 (15 + 25) - (6 * 3) - 3(4 * 3) = 906 sq.ft.   Total cost = 906 * 9 = Rs.8154   Answer: s.8154
Answer: B
The no. of girls in a class are seven times the no. of boys, which value cannever be the of total students? Select the correct option:
A) 10
B) 15
C) 30
D) 34
E) 36

Solution: Let the boys are X, then girls are 7X, total = X+7X = 8X   So it should be multiple of 8, 30 is not a multiple of 8.   30
Answer: C
Divide $672 among A,B in the ratio 5:3. How many $ that A get?	Choose the most appropriate option:
A) $120 B) $500 C) $420 D) $610 E) $315

Solution: Sum of ratio terms = 5+3= 
5+3 = 8
8   A= 672*5/8= 
672*5/8 = 420
$420   Answer is $420
Answer: C
P alone can complete a job in 5 days. The work done by Q alone in one day is equal to one-fourth of the work done by P alone in one day. In how many days can the work be completed if P and Q work together? Choose the correct choice from the following options
A) 2.5	B) 3.0	C) 3.5	D) 4.0	E) 4.5

Solution: P's rate is 1/5   Q's rate is 1/20   The combined rate is 1/5 + 1/20 = 1/4   If they work together, the job will take 4 days.   The answer is 4.0.
Answer: D
Find the compound ratio of (2:3), (5:11) and (11:2) is
Choose the most appropriate option:
A) 3:2  B) 2:1  C) 1:2  D) 4:5  E) 5:3

Solution: Required ratio = 2/3 * 5/11 * 11/2 = 2/1 = 5:3   Answer is 5:3
Answer: E
A and B start a business, with A investing the total capital of Rs.50000, on the condition that B pays A interest @ 10% per annum on his half of the capital. A is a working partner and receives Rs.1500 per month from the total profit and any profit remaining is equally shared by both of them. At the end of the year, it was found that the income of A is twice that of B. Find the total profit for the year?	Options:
A) 28999 B) 27888 C) 27838 D) 59000 E) 28992

Solution: Interest received by A from B = 10% of half of Rs.50000 = 10% * 25000 = 2500.   Amount received by A per annum for being a working partner = 1500 * 12 = Rs.18000.   Let 'P' be the part of the remaining profit that A receives as his share. Total income of A = (2500 + 18000 + P)   Total income of B = only his share from the remaining profit = 'P', as A and B share the remaining profit equally.   Income of A = Twice the income of B   (2500 + 18000 + P) = 2(P)   P = 20500   Total profit = 2P + 18000   = 2*20500 + 18000= 
2*20500 + 18000 = 59_000
59000   Answer: 59000
Answer: D
How many seven-digit numbers that do not contain the digits 2 or 9 are there? Pick:
A) 178546
B) 44786544
C) 435786
D) 1599678
E) 1835008

Solution: We can have 7 digits ( 1,3,4,5,6,7,8) for the first place ( million's place).   and similarly 8 digits for hundred thousands, ten thousands, thousands, hundred's, tenth's and unit digit. ( 0,1,3,4,5,6,7,8)   So in total 7*8*8*8*8*8*8= 
7*8*8*8*8*8*8 = 1_835_008
1835008   Hence 1835008
Answer: E
A salesman's income consists of a commission and a base salary of $370 per week. Over the past 5 weeks, his weekly income totals have been $406, $413, $420, $436 and $395. What must his average (arithmetic mean) commission be per week over the next two weeks so that his average weekly income is $500 over the 7-week period?  Choose the most appropriate option:	A) $150	B) $345	C) $365	D) $715	E) $730

Solution: Total weekly income over 5 weeks=$406+$413+$420+$436+$395=$2070   For avg weekly income to be $500 over 7 weeks, we need total weekly income over 7 weeks406+ 413+ 420+ 436+ 395= 
406+ 413+ 420+ 436+ 395 = 2_070
$2070   For avg weekly income to be $500 over 7 weeks, we need total weekly income over 7 weeks=$3500   Now, $3500-$2070=$1430   From this, we subtract base salary for 2 weeks i.e $370*2= 
370*2 = 740
$740   Therefore, commission=$1430-$740=$690 for 2 weeks   Avg weekly commission1430- 740= 
1430- 740 = 690
$690 for 2 weeks   Avg weekly commission=$345   Answer $345
Answer: B
A certain characteristic in a large population has a distribution that is symmetric about the mean m. If 60 percent of the distribution lies within one standard deviation d of the mean, what percent of the distribution is less than m + d ?  Choose the most appropriate option:
A) 80%	B) 32%	C) 48%	D) 84%	E) 92%

Solution: This is easiest to solve with a bell-curve histogram. m here is equal to µ in the Gaussian normal distribution and thus m = 50% of the total population.   So, if 60% is one st.Dev, then on either side of m we have  60/2= 
 60/2 = 30
30%. So, 30% are to the right and left of m (= 50%). In other words, our value m + d = 50 + 30= 
50 + 30 = 80
80% goingfrom the mean m, to the right of the distributionin the bell shaped histogram.. This means that 80% of the values are below m + d.   Like I said, doing it on a bell-curve histogram is much easier to fullygethow this works, or you could apply GM80%T percentile jargon/theory to it   80%
Answer: A
If the average ages of three groups of 30, 40, 50 people respectively is 30,40,50 what is the average ages of all the people?  Choose the correct choice from the following
A) 23.78 B) 41.66 C) 34.67 D) 23.9 E) 43.98

Solution: Average ages of group 1 =30   people in group 1 = 30   Total ages of group 1 = 30*30   Average ages of group 2 = 40   people in group 2 = 40   Total ages of group 2 = 40*40   Average ages of group 3 = 50   people in group 3 = 50   Total ages of group 3 = 50*50   Total people = 40 + 30 + 50= 
40 + 30 + 50 = 120
120   Average ages of all the people=((40*40)+(50×50)+(30×30))/120   =125/3   =41.66   Answer is 41.66.
Answer: B
The probability that a number selected at random from the first 50 natural numbers is a composite number is?	Choose one.
A) 17/22  B) 17/25  C) 17/21  D) 17/91  E) 17/12

Solution: The number of exhaustive events = ⁵⁰C₁ = 50.   We have 15 primes from 1 to 50.   Number of favourable cases are 34.   Required probability = 34/50 = 17/25.   Answer:17/25
Answer: B
If a large pizza has a radius that is 50% larger that that of a medium pizza, what is the percent increase in area between a medium and a large pizza? Choose the correct choice from the following:  A) 25%  B) 50%  C) 75%  D) 125%  E) 150%

Solution: Let the radius of medium pizza be r. Then the radius of large pizza is 1.5r.   The area of the medium pizza is pi*r^2   The area of the large pizza is pi*(1.5*r)^2 = 2.25*pi*r^2, an increase of 125%.   The answer is 125%.
Answer: D
Raju age before 5 years will be 2 times his age 5 years back, What is the present age of Raju	Choose one
A) 9 years  B) 8 years  C) 5 years  D) 6 years  E) 7 years

Solution: Explanation:   5 yearslearly,   x-5 = 2(x-5)   => x = 5   Option 5 years
Answer: C
If integers c and b are distinct factors of 30, which of the following CANNOT be a factor of 30?
I. cb + b^2
II. (c + b)^2
III. c + b
Select the correct option.
A) I only	B) II only	C) III only	D) I and II only	E) I, II, and III

Solution: Factors of 30 are: 1, 2, 3, 5, 6, 10, 15, and 30.   I. cb + b^2 --> if c=1 and b=2 then cb + b^2=6, which is a factor of 30. OK;   II. c + b)^2 --> (c + b)^2 is a perfect square, no perfect square (but 1) is a factor of 30. DISCARD;   III. c + b --> if c=1 and b=2 then c + b=3, which is a factor of 30. OK.   Answer: II only.
Answer: B
A train 165 metres long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going ?	Choose the correct choice
A) 9 sec  B) 6 sec  C) 7 sec  D) 10 sec  E) None

Solution: Solution   Speed of train relative to man =(60+6) km/hr= 66km/hr   =(66x5/18) m/sec =(55/3) m/sec   ∴ Time taken to pass the man = (165x3/55)sec = 9 sec   9 secnswer 9 sec
Answer: A
A letter lock consists of five rings each marked with four different letters. The number of distinct unsuccessful attempts to open the lock is at the most ?	Choose the correct choice from the following choices.
A) 3177
B) 3124
C) 3215
D) 168
E) 167

Solution: Since each ring consists of four different letters, the total number of attempts possible with the five rings is   = 5 * 5 * 5 * 5 *5= 
5 * 5 * 5 * 5 *5 = 3_125
3125. Of these attempts, one of them is a successful attempt.   Maximum number of unsuccessful attempts= 3125- 1= 
3125- 1 = 3_124
3124.   Answer: 3215
Answer: C
A soft drink company had 6000 small and 15000 big bottles in storage. If 12% of small 14% of big bottles have been sold, then the total bottles remaining in storage is Choose the correct choice from the following options.
A) 15360	B) 16010	C) 18180	D) 14930	E) 16075

Solution: 6000 + 15000 - (0.12*6000 + 0.14*15000)= 
6000 + 15000 - (0.12*6000 + 0.14*15000) = 18_180
18180.   Answer: 18180.
Answer: C
A dog has 15 bones, then he finds 8 more bones. Now how many bones does he have. Select
A) A) 7
B) B) 27
C) C) 23
D) D) 19
E) E) 21

Solution: 15 + 8= 
15 + 8 = 23
23. Answer is 23.
Answer: C
Car Dealership X, the total profit from sales increased by 30 percent over the previous years, while the number of cars sold decreased by 30 percent over the previous years. Approximately what was the average percent increase in profit per car over the previous year.  Choose the correct choice from the following options
A) 18%  B) 30%  C) 52%  D) 63%  E) 85.71%

Solution: Let Profit be x and cars sold be y   Originally Profit/Car = x/y   Now it is 1.3x / 0.7 y = 13/7 (x/y)   Increase in profit per car = ((6/7) (x/y)) / (x/y) * 100 = 85.71%   Answer = 85.71%
Answer: E
The average age of a group of 10 persons was decreased by 3 years when one person, whose age was 46 years, was replaced by a new person. Find the age of the new person?  Pick:  A) 18  B) 56  C) 16  D) 17  E) 14

Solution: Initial average age of the 10 persons be P.   Age of the new person Q.   Sum of the ages of the initial 10 persons = 10P   New average   = (P-3) 10(P-3)   = 10P - 46 + Q   => Q = 16   Answer:16
Answer: C
A batsman scored 120 runs which included 3 boundaries and 8 sixes. What percent of his total score
did he make by running between the wickets  Choose one:
A) 40%	B) 50%	C) 60%	D) 70%	E) None of these

Solution: Explanation:   Number of runs made by running = 110 - (3 x 4 + 8 x 6)   = 120 - (60)= 
120 - (60) = 60
60   Now, we need to calculate 60 is what percent of 120.=> 60/120 * 100= 
60/120 * 100 = 50
50 %   Answer: Option 50%
Answer: B
In a race of 150 m, A gives B a start of 20 m. What distance will be covered by B ?	Choose the correct choice from the following answers
A) 100 m	B) 130 m	C) 170 m	D) 160 m	E) 180 m

Solution: Required distance = (150 - 20)= 
(150 - 20) = 130
130 m   Answer :130 m
Answer: B
A train 285 m long, running with a speed of 54 km / hr will pass a tree in	Pick.
A) 19 sec B) 15 sec C) 16 sec D) 20 sec E) None

Solution: Sol.   Speed = (54 x 5/18) m/sec.   = 15 m / sec.   Time taken = (285 x 1/15) sec = 19 sec   19 secnswer 19 sec
Answer: A
A certain family has 3 sons: Richard is 6 years older than David, and David is 8 years older than Scott. If in 8 years, Richard will be twice as old as Scott, then how old was David 6 years ago?
Choose the correct choice from the following choices:
A) 8
B) 10
C) 12
D) 14
E) 16

Solution: Let's say   Age of Richard is "R"   Age of David is "D"   Age of Scott is "S"   Now   Richard is 6 years older than David,   i.e. R = D +6   David is 8 years older than Scott   i.e. D = S +8   If in 8 years, Richard will be twice as old as Scott   i.e. R+8 = 2x(S+8)   i.e. R+8 = 2S + 16   i.e. R = 2S+8   But R = D+6 = (S+8)+6 = S+14   therefore, 2S + 8 = S +14   i.e. S = 6   i.e. R = 20   i.e. D = 14   Now,   how old was David 6 years ago?   i.e. D-6 = 14-6= 
14-6 = 8
8 years   8NSWER:8
Answer: A
A cricketer scored 132 runs which included 12 boundaries and 2 sixes. What percent of his total score did he make by running between the wickets. Choose the correct choice:
A) 46.2%	B) 54.54 %	C) 63%	D) 70%	E) None of these

Solution: Explanation :   Number of runs made by running = 132 - (12 x 4 + 2 x 6)   = 132 - (60)= 
132 - (60) = 72
72   Now, we need to calculate 72 is what percent of 132.=> 72/132 * 100 = 54.54 %   Answer : 54.54 %
Answer: B
the ratio of type of pen and type of notebook is 5:4.and in 80 ways one can start writing.tell me the no. of pen and no. of notebook.  Pick one:  A) 6,12  B) 10,6  C) 10,8  D) 8,4  E) 6,8

Solution: let the ratio constant be x.   no. of pen=5x,no. of notebook =4x.   total no. of ways of start writing=5x*4x=20(square of x)5 *4= 
5 *4 = 20
20(square of x)=80   x=âˆš4=2   pen=10,notebook=8   answer 10,8
Answer: C
A train 150 m long is running at a speed of 68 kmph. How long does it take to pass a man who is running at 8 kmph in the same direction as the train?  Choose one:
A) 5 sec
B) 9 sec
C) 12 sec
D) 18 sec
E) 15 sec

Solution: Answer : B.   Speed of the train relative to man = (68 - 8) kmph   = (60* 5/18) m/sec = (50/3)m/sec   Time taken by the train to cross the man   = Time taken by It to cover 150 m at 50/3 m / sec = 150 *3/ 50= 
150 *3/ 50 = 9
9sec
Answer: B
The average age of 15 students of a class is 15 years. Out of these, the average age of 5 students is 13 years and that of the other 9 students is 16 years, The age of the 15th student is  Choose the most appropriate option: A) 11 B) 16 C) 13 D) 14 E) 15

Solution: Explanation:   Age of the 15th student = [15 * 15 - (13 * 5 + 16 * 9)= 
15 * 15 - (13 * 5 + 16 * 9) = 16
16 years. Answer: 16
Answer: B
What is the average of the first 10 multiples of 11?  Pick:
A) 55.5  B) 61.5  C) 53.5  D) 78.5  E) 60.5

Solution: (11 + 22 + ... + 110)/10   =11(1 + 2 + ... + 10)/10   =11(10)(11)/(10*2)   =121/2= 
121/2 = 121/2 = around 60.5
60.5   Option 60.5
Answer: E
Two trains are traveling on parallel tracks in the same direction. The faster train travels at 110 miles per hour, while the slower train travels at 100 miles per hour. At 1 o’clock the faster train is 40 miles behind the slower one. How far apart are the two trains at 7 o'clock? Choose the correct choice from the following options:
A) 20 miles
B) 80 miles
C) 90 miles
D) 120 miles
E) 400 miles

Solution: Answer = A. 20 miles   Relational speed = 110 - 100= 
110 - 100 = 10
10 miles per hour   In 6 hours, difference= 10 * 6= 
10 * 6 = 60
60 miles   Fast train trailing 40 miles, so effective difference= 60 - 40= 
60 - 40 = 20
20 miles
Answer: A
A man can do a piece of work in 5days, but with the help of his son, he can finish it in 3days. In what time can the son do it alone? Answers:
A) 5 B) 5 1/2 C) 7 1/2 D) 6 E) 9 1/2

Solution: Son's 1day work = 1/3 - 1/5 = 2/15   Son alone can do the work in 15/2days = 7 1/2 days   Answer is 7 1/2
Answer: C
The Natural Woman, a women's health food store, offers its own blends of trail mix. If the store uses 3 different ingredients, how many bins will it need to hold every possible blend, assuming that each blend must have at least two ingredients? (Also assume that each bin can hold one and only one blend.)
Choose the correct answer:	A) 1	B) 4	C) 7	D) 11	E) 10

Solution: We're told that there are 3 ingredients (we'll call them A, B, C ); we're told that each 'mix' must include AT LEAST 2 ingredients...   2 ingredient blends:   A4   AC   4C   3 ingredient blends:   A4C   Total blends = 3+1= 
3+1 = 4
4   4
Answer: B
The largest natural number which exactly divides the product of any four consecutive natural numbers is:  Choose the correct choice from the following answers:
A) 6 B) 12 C) 24 D) 120 E) 160

Solution: Required number= 1*2*3*4= 
1*2*3*4 = 24
24   Answer: 24
Answer: C