MU-NLPC/Calc-aqua_rat huggingface dataset:
What is the value of the following expression?
(1/ (2^2 – 1)) + (1/ (4^2 – 1)) + (1/ (6^2 – 1)) + .... + (1/ (22^2 – 1))  Answers:
A) a. 9/19
B) b. 10/19
C) c. 10/21
D) d. 11/23
E) e. 11/19

Solution: it can be written into   1/3+1/15+ 1/35.....1/483   i.e   1/3+1/2*(1/3-1/5)+1/2*(1/5-1/7).... til last term - 1/2*(1/23)   all terms from 1/5 .. to second last term get cancelled   left with   1/3+1/6-1/46=1/2-1/46=22/46=11/23 d. 11/23
Answer: D
Kamal started a business investing Rs. 9000. After five months, Sameer joined with a capital of Rs. 8000. If at the end of the year, they earn a profit of Rs. 8610, then what will be the share of Sameer in the profit?
Pick:
A) s.2323  B) s.2940  C) s.2329  D) s.2329  E) s.2312

Solution: Kamal : Sameer = (9000 * 12) : (8000 * 7)   = 108:56 = 27:14   Sameer's share = 8610 * 14/41   = Rs.2940.   Answer: s.2940
Answer: B
An error 38% in excess is made while measuring the side of a square. Now What is the percentage of error in the calculated area of the square?	Pick one.
A) 6.64%
B) 16.64%
C) 15.64%
D) 26.64%
E) 90.44%

Solution: Percentage error in calculated area   =(38+38+(38Ã—38)/100)%=90.44%   ANSW90.44%R:90.44%
Answer: E
In how many different number of ways 4 men and 2 women can sit on a shopa which can accommodate persons?
Answers
A) A)60  B) B)70  C) C)90  D) D)120  E) E)30

Solution: 6p2 = 6 × 5 x 4 = 120   Option '120'
Answer: D
When n is divided by 19 , the remainder is 6. When n is divided by 11, the quotient is equal to Z, and the remainder is equal to 6. Z must be divisible by which of the following numbers?	Choose the correct option: A) 3 B) 7 C) 10 D) 13 E) nineteen

Solution: N = 19 q + 6   N = 11 z + 6   Equating   19 Q + 6 = 11z+6   11z=19q   11z/19 = q   since q is an integer Z must be divisible by 19.   ANSWnineteenR:nineteen
Answer: E
Twenty four men can do a work in 42 days. How many men are required to complete the work in 36 days? Choose the correct option.
A) 20
B) 28
C) 50
D) 40
E) 60

Solution: B   28   We have M1 D1 = M2 D2   So, 24 * 42 = M2 * 36 => M2 = 28.   Answer is 28
Answer: B
There are 6 red shoes, 2 green shoes. If one draw randomly a shoe what is the probability of getting a red shoe
Pick.
A) 1/9	B) 2/9	C) 5/9	D) 3/4	E) 2/3

Solution: total 8 from take one.   8c1=8   red 6 from one   6c1=6   6/8=3/4   ANSWER:3/4
Answer: D
In 1 kg mixture of sand and iron, 20% is iron. How much sand should be added so that the proportion of iron becomes 10%?	Choose the correct choice: A) 1 kg B) 200gms C) 1.8kg D) 4.5kg E) 500gms

Solution: There are 200 grams of iron in 1 kg (1,000 grams) of the mixture.   If we add x grams of sand, the total amount would be 1,000 + x grams of mixture and we need 200 grams of iron to be 10% of that: 0.1(1,000 + x) = 200 --> x = 1,000.   Answer: A.   Or: for 200 grams of iron to be 10 of the mixture, the mixture must be 2,000 grams, thus 2,000 - 1,000 = 1,000 grams of sand should be added.   1 kgnswer: 1 kg.
Answer: A
In an election between two candidates, one got 55% of the total valid votes, 20% of the votes were invalid. If the total number of votes was 8000, the number of valid votes that the other candidate got, was: Pick.
A) 3500
B) 3600
C) 3270
D) 3700
E) 4000

Solution: Number of valid votes = 80% of 8000 = 6400.   Valid votes polled by other candidate = 45% of 8000   =(45/100)X8000 =3600   ANSWER =3600
Answer: B
A pipe can empty 2/3rd of a cistern in 12mins. In 6 mins, what part of the cistern will be empty? Pick one:	A) 2/3	B) 3/7	C) 4/9	D) 3/8	E) 1/3

Solution: 2/3 ---- 12   ? ----- 6 ==> 1/3   1/3
Answer: E
By selling 66 metres of cloth a man loses the selling price of 22 metres. Find the loss percent.
Answers.
A) 20% B) 25% C) 30% D) 35% E) None of these

Solution: Loss = C.P. of 66 metres – S.P. of 66 metres   = S.P. of 22 metres   ⇒ C.P. of 66 metres = S.P. of 88 metres   % loss = loss/C.P.of 66metres×100   = S.P.of22metres /C.P.of66metres×100   = S.P.of22metres /S.P.of88metres×100   = 22⁄88 × 100 = 25%   Answer 25%   * Try to solve by shortcut method
Answer: B
Find the odd man out. 241, 263, 248, 271, 255, 277, 262
Select:
A) 277  B) 271  C) 263  D) 241  E) 248

Solution: Alternatively 22 is added and 15 is subtracted from the terms. Hence, 271 is wrong   241   241 + 22= 
241 + 22 = 263
263   263 - 15= 
263 - 15 = 248
248   248 + 22= 
248 + 22 = 270
270   270 - 15= 
270 - 15 = 255
255   255 + 22= 
255 + 22 = 277
277   277 - 15= 
277 - 15 = 262
262   Answer is 271
Answer: B
The food in a camp lasts for 25 men for 40 days. If ten more men join, how many days will the food last?
Choose the correct choice from the following answers.
A) 40 days  B) 29 days  C) 60 days  D) 50 days  E) 45 days

Solution: one man can consume the same food in 25*40= 
25*40 = 1_000
1000 days.   10 more men join, the total number of men= 35   The number of days the food will last = 1000/35 = 29 days.   ANSWER:29 days
Answer: B
A bag contains 12 red marbles. If someone were to remove 2 marbles from the bag, one at a time, and replace the first marble after it was removed, the probability that neither marble would be red is 9/16. How many marbles are in the bag? Choose the correct choice from the following answers
A) 48
B) 24
C) 60
D) 72
E) 84

Solution: ok let me see if i can explain what went on in the previous post   lets say i have x marbles in the bag in total --> out of them 12 are red   so the probability of pulling a non-red marble is (x -12) / x   now the marble is placed back in the bag and we have x marbles again, of which again 12 are red. so the probability of pulling a non-red marble out is (x-12) / x   probability theorm states that if the probability of event 48 occuring is m and the probability of event B occuring is n then the probability of both 48 and B occuring is m*n   so therefore the probability of 2 non-red marbles getting pulled out is [(x-12)/x ] * [(x-12)/x]   this is given as 9/16   -->(x-12)^2= 16/25   x^2   48   square rooting u have x-12/x = 3/4 or 4x-48 =3x or x = 48
Answer: A
A farmer had d animals, all of which the farmer bought for the same price. The farmer decided to sell the animals. 22 of the animals were sold at a profit of 10% each while the rest were sold at a loss of 20% each. Overall, the farmer made neither a profit nor a loss. Which of the following is equal to d?  Select.
A) 21 B) 24 C) 27 D) 30 E) 33

Solution: Let P be the price the farmer paid for each animal.   The total profit on the 22 animals is 22*0.1*P.   The total loss on the other (d-22) animals is (d-22)*0.2*P.   (d-22)*0.2*P = 22*0.1*P   0.2*d = 2.2 + 4.4   d = 33   The answer is 33.
Answer: E
If a number Q between 0 and 1 is selected at random, which of the following will the number most likely be between?  Select:
A) 0 and 3/20  B) 3/20 and 1/5  C) 1/5 and 1/4  D) 1/4 and 3/10  E) 3/10 and 1/2

Solution: The number Q will most likely be between the largest range.   A. 0 and 3/20 --> range 3/20;   B. 3/20 and 4/20 --> range 1/20;   C. 4/20 and 5/20 --> range 1/20;   D. 5/20 and 6/20 --> range 1/20;   E. 6/20 and 10/20 --> range 4/20.   Answer: 3/10 and 1/2.
Answer: E
A local restaurant recently renovated its dining space, purchasing new tables and chairs to use in addition to the original tables and chairs. The new tables each seat six customers, while the original tables each seat four customers. Altogether, the restaurant now has 40 tables and is capable of seating 220 customers. How many more new tables than original tables does the restaurant have?
Choose the correct choice.
A) 10 B) 20 C) 30 D) 34 E) 36

Solution: X = Number of original tables   Y = Number of new tables   Capacity of original tables = 4   Capacity of new tables = 6   Total number of tables = X + Y = 40.....(1)   Total capacity = 4X + 6Y = 220.......(2)   (2) - 4*(1) --> 2Y = 60 --> Y = 30, X = 10   How many more new tables than original tables does the restaurant have? --> Y - X = 30 - 10= 
30 - 10 = 20
20   Answer: 20
Answer: B
A train 400 m long can cross an electric pole in 20 sec and then find the speed of the train?  Choose the correct choice.
A) 72	B) 70	C) 60	D) 85	E) 90

Solution: Length = speed*time   S=400/20= 
400/20 = 20
20 m/sec   Speed= 20*18/5= 
20*18/5 = 72
72 kmph   72NSWER 72
Answer: A
Three candidates contested an election and received 1136, 7636 and 11628 votes respectively. What percentage of the total votes did the winning candidate get?	Choose the correct choice from the following.
A) 57%
B) 50%
C) 52%
D) 60%
E) None of these

Solution: Explanation :   Votes received by the winning candidate = 11628   Total votes = 1136 + 7636 + 11628= 
1136 + 7636 + 11628 = 20_400
20400   Required percentage= (11628/20400) × 100 = 11628/204 = 2907/51 = 969/17= 
969/17 = 57
57%   57%nswer : Option 57%
Answer: A
Two cars start from the opposite places of a main road, 150 km apart. First car runs for 25 km and takes a right turn and then runs 15 km. It then turns left and then runs for another 25 km and then takes the direction back to reach the main road. In the mean time, due to minor break down the other car has run only 35 km along the main road. What would be the distance between two cars at this point?  Choose the correct choice from the following options
A) 65 km
B) 75 km
C) 80 km
D) 85 km
E) 95 km

Solution: 150-((25+25)+35)   65 kmNSWER:65 km
Answer: A
A hiker walked for 3 days. She walked 25 miles on the first day, walking 5 miles per hour. On the second day she walked for one less hour but she walked one mile per hour, faster than on the first day. On the third day she walked the same number of hours as on the first day, but at the same speed as on the second day. How many miles in total did she walk?  Choose the correct choice from the following choices.
A) 24	B) 79	C) 58	D) 60	E) 62

Solution: She walked 25 miles on the first day, walking 5 miles per hour i.e. total time of walk on Day-1 = 25/5= 
25/5 = 5
5 Hours   Second day time of walk= 5-1= 
5-1 = 4
4 hours and Speed= 5+1= 
5+1 = 6
6 miles per hour i.e. Distance walked on second day= 4*6= 
4*6 = 24
24 miles   Third day time of walk= 5 hours and Speed = 6 miles per hour i.e. Distance walked on second day = 5*6= 
5*6 = 30
30 miles   Total Distance travelled on three days= 25+24+30= 
25+24+30 = 79
79   Answer: Option 79
Answer: B
Find the area of trapezium whose parallel sides are 20 cm and 18 cm long, and the distance between them is 15 cm.	Choose the correct option.
A) 225 cm2 B) 275 cm2 C) 285 cm2 D) 315 cm2 E) None of these

Solution: Area of a trapezium = 1/2 (sum of parallel sides) * (perpendicular distance between them) = 1/2 (20 + 18) * (15) = 285 cm2   ANSWER:285 cm2
Answer: C
The dimensions of a rectangular solid are 4 inches, 5 inches, and 12 inches. If a cube, a side of which is equal to one of the dimensions of the rectangular solid, is placed entirely within thespherejust large enough to hold the cube, what the ratio of the volume of the cube to the volume within thespherethat is not occupied by the cube?
Choices
A) 10:17  B) 2:5  C) 5:16  D) 25:7  E) 10:21

Solution: Answer: 10:21.
Answer: E
A train running at the speed of 60 km/hr crosses a pole in 18 seconds. Find the length of the train?
Choose the correct choice from the following answers:  A) 150 meter  B) 876 meter  C) 300 meter  D) 719 meter  E) 169 meter

Solution: Speed = 60*(5/18) m/sec = 50/3 m/sec   Length of Train (Distance) = Speed * Time     (50/3) * 18= 
  (50/3) * 18 = 300
300 meter   Answer: 300 meter
Answer: C
What is the units' digit of the following expression (6)^3*(14)^5*(2)^5?
Pick
A) 0
B) 1
C) 3
D) 5
E) 8

Solution: We do not have to do any calculations or find units digit of remaining numbers...   all three terms - 6,14,2 - are 8V8N and since the PRODUCT contains 8, the units digit of the product will remain 8   8
Answer: E
138.009 + 341.981 – 146.305 = 123.6 + ?
Choose the correct choice from the following choices.
A) 120.085
B) 120.85
C) 220.085
D) None of these
E) Cannot be determined

Solution: Solution   Let 138.009 + 341.981 - 146.305 = 123.6 + x.   Then, x = (138.009 + 341.981) - (146.305 + 123.6) = 479.99 - 269.905= 
479.99 - 269.905 = 210.085
210.085 . Answer None of these
Answer: D
My grandson is about as many days as my son in weeks, and my grandson is as many months as I am in years. My grandson, my son and I together are 120 years. Can you tell me my age in years ? Select the correct option:
A) 65 B) 72 C) 44 D) 73 E) 89

Solution: B   I am 72 years old.   Let m be my age in years. If s is my son's age in years, then my son is 52s weeks old. If g is my grandson's age in years, then my grandson is 365g days old. Thus,   365g = 52s.   Since my grandson is 12g months old,   12g = m.   Since my grandson, my son and I together are 120 years,   g + s + m = 120.   The above system of 3 equations in 3 unknowns (g, s and m) can be solved as follows.   m / 12 + 365 m / (52 x 12) + m = 120 or   52 m + 365 m + 624= 
+ 624 = 624
624 x 120 or   m= 624 x 120 / 1041 = 72.   So, I am 72 years old.
Answer: B
The average age of the mother and her six children is 12 years which is reduced by 5 years if the age of the mother is excluded. How old is the mother?  Choose the correct choice from the following options
A) 40 years	B) 42 years	C) 48 years	D) 50 years	E) None

Solution: Sol.   Therefore age of the mother   = ( 12 × 7 – 7 × 6)   = 42 years.   Answer 42 years
Answer: B
When positive integer w is divided by 13, the remainder is 2. When n is divided by 8, the remainder is 5. How many such values are less than 180?	Choices.
A) 0  B) 1  C) 2  D) 3  E) 4

Solution: the equation that can be formed w is 13x+2=8y+5..   13x-3=8y...   as we can see x can take only odd values as the RHS will always be even..   Also x can take values till 13 as 13*14>180..   now we have to substitue x as 1,3,5,7,9,11,13...   once we find 7 fitting in , any other value need not be checked as every 4th value will give us answer so next value will be 15..   ans 1.. 1
Answer: B
A sum of money at simple interest amounts to Rs. 825 in 3 years and to Rs. 840 in 4 years. The sum is?  Options
A) s. 738 B) s. 638 C) s. 777 D) s. 730 E) s. 735

Solution: S.I. for 1 year = (841 - 825) = Rs. 16   S.I. for 3 years = 16 * 3 = Rs. 48   Principal = (825 - 48) = Rs. 777.   ANSWER:s. 777
Answer: C
A person takes 20 minutes more to cover a certain distance by decreasing his speed by 20%. What is the time taken to cover the distance at his original speed?
Choose the correct choice:
A) 1 hour 37 minutes	B) 1 hour 40 minutes	C) 1 hour 20 minutes	D) 1 hour 30 minutes	E) 1 hour 23 minutes

Solution: Let the distance and original speed be d km and k kmph respectively.   d/0.8k - d/k = 20/60 => 5d/4k - d/k = 1/3   => (5d - 4d)/4k = 1/3 => d = 4/3 k   Time taken to cover the distance at original speed   = d/k = 4/3 hours = 1 hour 20 minutes.   Answer: 1 hour 20 minutes
Answer: C
Train speed 36kph. Dist travelled in 3minutes in meters
Pick
A) 1600	B) 1700	C) 1800	D) 1900	E) 2000

Solution: 36kmph=10m/sec   d=10*180= 
10*180 = 1_800
1800 meters   ANSWER:1800
Answer: C
If f(x)=4x−1 and g(x)=2x+2 for all integers, which of the following is a possible value of g(f(x))?  Answers:
A) -23	B) -17	C) 2	D) 16	E) 20

Solution: g(f(x)) = 2*f(x)+2 = 2*(4x-1)+2 = 8x   Of these five options, only 16 has the form 8x.   The answer is 16.2*(4 -1)+2= 
2*(4 -1)+2 = 8
8x   Of these five options, only 16 has the form 8x.   The answer is 16.
Answer: D
Raj invested an amount of Rs.17400 for two years. Find the rate of compound interest that will fetch him an amount of Rs.1783.50 at the end of two years?	Choices:
A) R=7  B) R=4  C) R=3  D) R=5  E) R=2

Solution: Let the rate of interest be R% p.a.   17400[1 + R/100]2 = 17400 + 1783.50   [1 + R/100]2 = (17400 + 1783.50)/17400   = 1 + 1025/10000 = 1 + 41/400   = 441/400 = [21/20]2   [1 + R/100] = 21/20   R/100 = 1/20   Therefore R=5   Answer:R=5
Answer: D
Line Y has the equation 3x + y = 7. Which of the following lines is perpendicular to Line Y?  Choose the correct choice from the following options: A) y = 3x + 4 B) y = –3x – 6 C) y = (1/3)x – 1 D) y = (–1/3)x + 2 E) y = (–7/3)x – 5

Solution: I first rewrote the equation in the standard y=mx+b form. Therefore, Line Y as presented, 3x + y = 7, can be rewritten as follows: y=-3x+7.   Thought process next is what line would be perpendicular to Line Y? Any line with a reciprocal of the slope but in the opposite direction. The reciprocal of any fraction/integer is 1 over that number/integer. Therefore the reciprocal of -3 is -1/3 - need to drop the negative sign because the line would kinda run parallel and we want perpendicular. Scan the answers choices and notice y = (1/3)x – 1 as the only one.
Answer: C
If the sides of a triangle are 26 cm, 24 cm and 10 cm, what is its area?  Choose one.
A) 120 B) 277 C) 288 D) 265 E) 291

Solution: The triangle with sides 26 cm, 24 cm and 10 cm is right angled, where the hypotenuse is 26 cm.   120rea of the triangle = 1/2 * 24 * 10= 
1/2 * 24 * 10 = 120
120 cm2.120nswer: 120
Answer: A
A man buys an article and sells it at a profit of 20%. If he had bought it at 20% less and sold it for Rs.77 less, he could have gained 25%. What is the cost price?  Options.
A) s.370
B) s.385
C) s.375
D) s.350
E) s.300

Solution: CP1 = 100 SP1 = 120   CP2 = 80 SP2 = 80 * (125/100)= 
80 * (125/100) = 100
100   20 ----- 100   77 ----- ?=> 385   ANSWER:s.385
Answer: B
Among 600people, 56% like strawberry jam, 44% like apple jam, and 40% like raspberry jam. If 30% of the people like both strawberry and apple jam, what is the largest possible number of people who like raspberry jam but do not like either strawberry or apple jam? Choose the correct choice from the following choices:
A) 20
B) 60
C) 80
D) 150
E) 180

Solution: 56%+44%-30%=70% who like either Strawberry, Apple, or both.   That means 100%-70% 56 +44 -30= 
56 +44 -30 = 70
70% who like either Strawberry, Apple, or both.   That means 100%-70% = 30% do not like either Apple of Strawberry jam.   30% is the most possible that like raspberry jam but do not like either strawberry or apple (assuming nobody in the group does not like any)   180  100 -70= 
  100 -70 = 30
30% do not like either Apple of Strawberry jam.   30% is the most possible that like raspberry jam but do not like either strawberry or apple (assuming nobody in the group does not like any)   180
Answer: E
a,b,c weighted separately 1st like a, b, c , then a & b, then b & c ,then c & a at last a & b & c, the last weight was 167,then what will be the average weight of the 7 reading?
Choose the correct choice from the following options:
A) 95	B) 95.42	C) 95.45	D) 94	E) 93

Solution: The sum of 7 weights = weights of[a+b+c+(a+b)+(b+c)+(c+a)+(a+b+c)]= weights of[4*(a+b+c)=4*167= 
4*167 = 668
668   Therefore The average weight of 7 readings is 668/7=95.428   ANSWER:95.42
Answer: B
A person buys an article at Rs.500. At what price should he sell the article so as to make a profit of 20%?
Choose one
A) 600	B) 88	C) 66	D) 55	E) 33

Solution: Cost price = Rs.500   profit = 20% of 500 = Rs.100   Selling price = Cost price + Profit   = 500 + 100= 
500 + 100 = 600
600   600nswer:600
Answer: A
The area of an isosceles trapezoid with sides of length 5 and bases of length 11 and 17 is?	Choices:
A) 48
B) 52
C) 54
D) 56
E) 46

Solution: Isosceles trapezoid indicates that if we draw perpendicular from two vertex of the smaller side, the longer side with side 17 will be divided into 3 parts= 11, 3 and 3 (Making one square and two right triangles)   For the right triangle, height will be= (5^2-3^2)^1/2= 4   And the area of trapezoid = 1/2 (B1+B2)H= 1/2*28*4= 
1/2*28*4 = 56
56   56 is the answer
Answer: D
The number of sequences in which 4 players can throw a ball, so that the youngest player may not be the last is ?	Options
A) 24  B) 22  C) 10  D) 16  E) 18

Solution: x Not younger   The last ball can be thrown by any of the remaining 4 players. The first 6 players can throw the ball in 3P3 ways.   The required number of ways = 3(3!)   = 18   Answer:18
Answer: E
Thefactor countof an integer n greater than 1 is the number of distinct prime factors of n. For example, the factor count of 36 is 2, since 2 and 3 are the distinct prime factors of 36 = 2 x 2 x 3 x 3. For which of the following integers is the factor count greatest Q?	Select the correct option.
A) 60 B) 61 C) 62 D) 63 E) 64

Solution: 60 = 2*2*3*5 factor count =3   61= prime number   62 = 2*31 factor count=2   63=3*3*7 factor count=2   64=2*2*2*2*2*2 factor count=1=Q   answer is 60.
Answer: A
rahul played weel in this season.his current batting averagge is 53.if he score 78 runs in today match.his batting average will become 58.how many matches had he played in this season.
Pick one:
A) 4
B) 10
C) 9
D) 6
E) 5

Solution: 53x+78=58(x+1)   =>5x=20   =>x=4   4NSWER:4
Answer: A
The length of the bridge, which a train 130 meters long and travelling at 45 km/hr can cross in 30 seconds, is:	Select.
A) 249  B) 178  C) 245  D) 277  E) 121

Solution: Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time   = 30 sec. Let the length of bridge be x meters. Then, (130 + X)/30 = 25/2   ==> 2(130 + X) = 750   ==> X   = 245 m   Answer: 245
Answer: C
A bowl has only 4 apples and 4 bananas. If one piece of fruit is selected from the bowl at random, and a second piece is selected from the bowl without replacing the first, what is the probability that both pieces of fruit chosen are apples?	Choose the correct choice from the following answers:	A) 1/10	B) 1/5	C) 3/14	D) 2/5	E) 1/2

Solution: 4/8 * 3/7   =3/14   C. 3/14
Answer: C
John makes $60 a week from his job. He earns a raise and nowmakes $70 a week. What is the % increase?  Select:
A) 16%
B) 16.66%
C) 17%
D) 17.2%
E) 18%

Solution: Increase = (10/60)*100 = (1/6)*100 = 16.66%.   16.66%
Answer: B
A car crosses a 600 m long bridge in 5 minutes. What is the speed of car in km per hr?	Choose the correct option.
A) 7 km/hr	B) 7.2 km/hr	C) 7.5 km/hr	D) 8 km/hr	E) 8.9 km/hr

Solution: Speed = 600 m/sec.   5 x 60   = 2 m/sec.   Converting m/sec to km/hr (see important formulas section)   = 2 x 18 km/hr   5   = 7.2 km/hr   7.2 km/hr
Answer: B
Two cyclist start from the same places in opposite directions. One is going towards north at 30kmph and the other is going towards south 40kmph. What time will they take to be 50km apart? Options: A) 1.32hr B) 0.714hrs C) 3.231hrs D) 0.515hrs E) 6.214hrs

Solution: To be (30+40) km apart, they take 1 hour   To be 50 km apart, they take 1/70 *50 = 0.714 hrs   Answer is 0.714hrs
Answer: B
Half a number plus 5 is 11.What is the number?
Choose the most appropriate option:	A) 8	B) 9	C) 10	D) 11	E) 12

Solution: Let x be the number. Always replace "is" with an equal sign   (1/2)x + 5 = 11   (1/2)x + 5 - 5 = 11 - 5   (1/2)x = 6   2 × (1/2)x = 6 × 2   x = 12   correct answer is 12)12
Answer: E
If the product of the integers from 1 to n is divisible by 378, what is the least possible value of n? Choose the correct choice from the following answers:
A) 7
B) 8
C) 9
D) 10
E) 11

Solution: 378 = 2 x 3 x 3 x 3 x 7   N must include at least 3, 2*3, and 3*3.   The answer is 9.
Answer: C
5n + 2 > 12 and 7n - 5 < 23; n must be between which numbers?	Pick
A) 1 and 8 B) 2 and 4 C) 0 and 9 D) 2 and 7 E) 2 and 9

Solution: 5n > 10 --> n > 2   7n < 28 --> n < 4   2 < n < 4   Answer: 2 and 4
Answer: B
George is 8 years more than Christopher and Ford is 2 years younger than Christopher. The sum of their ages is 60. Find the ages of Ford. Pick one:
A) 14
B) 15
C) 16
D) 17
E) 18

Solution: 16hristopher age = x   George age, y = x + 8---------->(1)   Ford age, z = x - 2------------>(2)   Sum of their ages, x+y+z=60---->(3)   Substitute z and y values in equation (3)   Therefore, x+(x+8)+(x-2)=60   => 3x+8-2=60   => 3x=60-6   => 3x=54 =>x=54/3= 
54/3 = 18
18(16hristopher's age)   Substitute x value in equation 1 & 2   y=x+8   y=18+8= 
18+8 = 26
26(George's age)   z=x-2   z=18-2= 
18-2 = 16
16(Ford's age)   ANSWER:16
Answer: C