MU-NLPC/Calc-aqua_rat huggingface dataset:
A rectangular-shaped carpet that measures x feet by y feet is priced at $20. What is the cost of the carpet, in dollars per square yard? (1 square yard = 9 square feet)	Choose the correct option:
A) 180xy  B) 180/(xy)  C) 20xy  D) 20xy/9  E) xy/180

Solution: The area of the carpet in feet is xy.   The area in square yards is xy / 9.   The price per square yard is 20 / (xy/9) = 180/(xy).   The answer is 180/(xy).
Answer: B
A pack of baseball cards consists of 12 outfielder cards and 8 infielder cards. What is the lowest number of outfielder cards that would have to be removed from the pack so that no more than 50 percent of the pack would be outfielder cards?
Pick.
A) 4 B) 5 C) 6 D) 7 E) 8

Solution: let the number of O card to be removed=X   then remaning cards=12-X   now this 12-X cards should count less than 50% of toatal Ocards   12-X<.5*12   X<12-6   X<6   X=5   Ans 5
Answer: B
The perimeters of two squares are 44 cm and 36 cm. Find the perimeter of a third square whose area is equal to the difference of the areas of the two squares?  Select
A) 76 cm B) 24 cm C) 25.2 cm D) 55 cm E) 34 cm

Solution: We know perimeter of square = 4(side)   So Side of first square = 44/4= 
44/4 = 11
11 cm   Side of second square= 36/4= 
36/4 = 9
9 cm   Area of third Square= 11*11 - 9*9= 
11*11 - 9*9 = 40
40 cm   So side of third square= 6.3 [because area of square = side*side]   Perimeter = 4*Side = 4*6.3= 
4*6.3 = 25.2
25.2 cm   Answer:25.2 cm
Answer: C
A 40 kg metal bar made of alloy of tin and silver lost 4 kg of its weight in the water. 10 kg of tin loses 1.375 kg in the water; 5 kg of silver loses 0.375 kg. What is the ratio of tin to silver in the bar?	Choose one: A) 1/4 B) 2/5 C) 1/2 D) 3/5 E) 2/3

Solution: you can simply use this formula to avoid confusion:   w1/w2 = (A2 - Aavg)/(Avg - A1)   Here is how you will find the values of A1 an A2.   We have an overall loss (average loss). The average loss is 4 kg when 40 kg alloy is immersed.   This is a loss of (4/40)*100= 
(4/40)*100 = 10
10%.   This is Aavg   The loss of tin is 1.375 kg for every 10 kg.   This means it loses   (1.375/10)*100= 
  (1.375/10)*100 = 13.75
13.75% of its weight in water.   This is A1.   The loss of silver is .375 kg for every 5 kg.   This means it loses   (.375/5)* 100= 
  (.375/5)* 100 = 7.5
7.5% of its weight in water.   This is A2.   Weight of Tin/Weight of Silver= (Silver's loss - Avg loss)/(Avg loss - Tin's loss)   X/Y = (7.5 - 10)/(10 - 13.75) = 2/3   2/3
Answer: E
How many times in a day, the hands of a clock are straight? Choose the correct choice from the following answers:
A) 22	B) 44	C) 48	D) 24	E) 36

Solution: The hands of a clock point in opposite directions (in the same straight line, making an angle 180° between them) 11 times in every 12 hours because between 5 and 7 they point in opposite directions at 6 'o clock only. Hence the hands point in the opposite directions 22 times in a day.   The hands of a clock coincide(0° between them) 11 times in every 12 hours (between 11 and 1, they coincide only once, at 12 o'clock). Hence the hands coincide 22 times in a day.   So In 24 hours, the hands come in opposite direction or coincide 44 times.   This is already given as a formula and it's is better to learn the answer by heart as 44   which can save time in competitive exams.(However you should know the theory behind). Answer: Option 44
Answer: B
A train 240 m in length crosses a telegraph post in 16 seconds. The speed of the train is?  Choose the correct choice:
A) 22
B) 77
C) 54
D) 87
E) 21

Solution: S = 240/16 * 18/5= 
240/16 * 18/5 = 54
54 kmph.Answer: 54
Answer: C
The area of a triangle will be when a = 1m, b = 2m, c = 3m, a, b, c being lengths of respective sides.  Select the correct option
A) 0 sq m	B) 3 sq m	C) 2 sq m	D) 6 sq m	E) 9 sq m

Solution: S = (1 + 2 + 3)/2= 
(1 + 2 + 3)/2 = 3
3=> No triangle exists   0 sq mNSWER:0 sq m
Answer: A
A and B started a partnership business investing some amount in the ratio of 3 : 5. C joined then after six months with an amount equal to that of B. In what proportion should the profit at the end of one year be distributed among A, B and C?  Options.
A) 3 : 5 : 2
B) 3 : 5 : 5
C) 6 : 10 : 5
D) 3 : 4 : 5
E) 4 : 6 : 8

Solution: Let the initial investments of A and B be 3x and 5x.   A : B : C = (3x x 12) : (5x x 12) : (5x x 6) = 36 : 60 : 30 = 6 : 10 : 5.   Answer: 6 : 10 : 5
Answer: C
A number is divided by 221, the remainder is 64. If the number be divided by 13 then remainder will be Choose the correct option:	A) 1	B) 2	C) 3	D) 4	E) 5

Solution: Let the given number when divided by 119   gives x as quotient and 19 as remainder. Then   Given number = 119x + 19   = 17 x 7x + 17 + 2   = 17 (7x + 1) + 2   so, the required remainder is 2.   ANSWER:2
Answer: B
By investing Rs. 1620 in 8% stock,Michael earns Rs. 135.The stock is then quoted at :
Choose the most appropriate option:
A) Rs. 80  B) Rs. 96  C) Rs. 106  D) Rs. 108  E) None of these

Solution: Solution   To earn Rs. 135, investment = Rs. 1620.   To earn Rs. 8, investment = Rs. (1620/135x8) =96   ∴ Market value of Rs. 100 stock = Rs. 96.   Answer Rs. 96
Answer: B
The list price of an article is Rs.65. A customer pays Rs.56.16 for it. He was given two successive discounts, one of them being 10%. The other discount is? Choose the correct choice from the following choices.
A) 7%
B) 4%
C) 2%
D) 1%
E) 8%

Solution: 65*(90/100)*((100-x)/100) = 56.16   x = 4%   Answer: 4%
Answer: B
An old man distributed all the gold coins he had to his two sons into two different numbers such that the difference between the squares of the two numbers is 49 times the difference between the two numbers. How many coins did the old man have?
Pick one
A) 24	B) 26	C) 30	D) 49	E) 40

Solution: Let the number of coins one son got be x and the number of coins another got be y. Total = x + y.   x^2 - y^2 = 49(x - y) --> x + y = 49.   Answer: 49.
Answer: D
What percent of 150 is 40?
Pick.
A) 0.25%  B) 26.67%  C) 25%  D) 40%  E) 250%

Solution: 150*x /100 = 40   x = 2*40/3   x = 26.67   Ans: 26.67%
Answer: B
On January 1, 2001 it was Monday. Which day of the week fall on January 1, 2005?	Choose the correct choice from the following choices:  A) Saturday  B) Wednesday  C) Monday  D) Tuesday  E) Friday

Solution: On 31st Dec. 2000 it was Sunday.   Number of odd days from 2001 to 2004=(1 + 1 + 1 + 2)= 
(1 + 1 + 1 + 2) = 5
5 odd days   31st Dec. 2004, it was Friday   Saturday was the day on 1st Jan. 2005   Saturdaynswer: Saturday
Answer: A
Raju purchases 550 ml. of milk every day. If the cost of one litter of milk is Rs.44. How much amount will he pay in 45 days? Options:
A) Rs.1098	B) Rs.1079	C) Rs.1089/-	D) Rs.1099	E) None of these

Solution: Explanation:   500 ml cost Rs.22   50 ml cost Rs.2.20   :.550 ml cost Rs.24.20   For 44 days the cost of milk = 45 x 24.20   = Rs.1089/-   Answer: Option Rs.1089/-
Answer: C
If A lends Rs.3500 to B at 10% per annum and B lends the same sum to C at 11.5% per annum then the gain of B in a period of 3 years is?
Pick
A) 157.53	B) 157.59	C) 157.5	D) 157.51	E) 157.56

Solution: (3500*1.5*3)/100= 
(3500*1.5*3)/100 = 157.5
> 157.50   Answer: 157.5
Answer: C
If P and Q are positive integers, P - 3 is divisible by 4 and Q - 1 is divisible by 4, all of the following could be the value of P - Q Except?  Choices.
A) 1 B) 2 C) 6 D) 18 E) 14

Solution: P-3 = 4Q   => P = 4Q + 3 = 3,7,11,15,19,23,27,31,35,39   Q-1 = 4P   => Q = 4P + 1 = 1,5,9,13,17,21,25,29,33,37,41   2=3-1   6=15-9   18=27-9   14=31-17   So , we can see that all the answer choices are possible here except 1
Answer: A
An article is bought for Rs.600 and sold for Rs.500, find the loss percent? Choose one.
A) 16 2/3%	B) 16 7/3%	C) 19 2/3%	D) 16 2/3%	E) 16 4/3%

Solution: 600 ---- 100   100 ---- ? => 16 2/3%   Answer: 16 2/3%
Answer: D
The value of (1-d3) / (1-d) is Answers:
A) > 1 if d > -1
B) >3 if d > 1
C) > 2 if 0 < d < 0.5
D) < 2 if d < -2
E) None

Solution: Explanation :   Let S = (1 - d3 ) / ( 1 - d ) = ( 1 + d2 + d) .   => d = 0 then S = 1 .   => d = 2 then S = 7 .   => d = 0.1 then S = 1.11 .   => d = -3 then S = 7 .   Hence, only the option 2 satisfy.   Answer : >3 if d > 1
Answer: B
How many multiples of 4 are there between 32 and 252 ?
Choose the correct option.
A) 67 B) 64 C) 54 D) 56 E) 60

Solution: It should be mentioned whether 32 and 252 are inclusive.   If 32 and 252 are inclusive, then the answer is   (252-32)/4+1= 
  (252-32)/4+1 = 56
56.   If 32 and 252 are NOT inclusive, then the answer is   (248-36)/4+1= 
  (248-36)/4+1 = 54
54.   Since OA is 54, then we have NOT inclusive case.
Answer: C
The volumes of two cubes are in the ratio 27: 125, what shall be the ratio of their surface areas?
Choose the correct answer:	A) 9:26	B) 9:24	C) 9:25	D) 9:20	E) 9:21

Solution: a13 : a23 = 27 : 125   a1 : a2 = 3 : 5   6 a12 : 6 a22   a12 : a22   =9:25   Answer:9:25
Answer: C
40 onions on a scale weigh 7.68 kg. When 5 onions are removed from the scale, the average weight of the 35 onions is 190 grams. What is the average weight (in grams) of the 5 onions which were removed?  Choose the correct choice.
A) 200  B) 202  C) 204  D) 206  E) 208

Solution: 35*190= 
35*190 = 6_650
6650.   The other 5 onions weigh a total of 1030 grams.   The average weight is  1030/5= 
 1030/5 = 206
206 grams.   The answer is 206.
Answer: D
The “length of integer x” refers to the number of prime factors, not necessarily distinct, that x has. (If x = 60, the length of x would be 4 because 60 = 2 × 2 × 3 × 5.) What is the greatest possible length of integer z if z < 3000? Pick:
A) 7
B) 9
C) 11
D) 13
E) 15

Solution: To maximize the length of z, we should minimize its prime base. The smallest prime is 2 and since 2^11 = 2048 < 3000, then the greatest possible length of integer z is 11.   The answer is 11.
Answer: C
The captain of a cricket team of 11 members is 24 years old and the wicket keeper is 3 years older. If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. What is the average age of the team?  Choose the correct choice from the following
A) 20 years	B) 21 years	C) 22 years	D) 23 years	E) 24 years

Solution: Explanation:   Let the average age of the whole team by x years.   11x â€“ (24 + 27) = 9(x -1)   11x â€“ 9x = 42   2x = 42   x = 21.   So, average age of the team is 21 years.   Answer 21 years
Answer: B
The perimeter of a triangle is 60 cm and the inradius of the triangle is 2.5 cm. What is the area of the triangle
Options: A) A)72 B) B)828 C) C)729 D) D)75 E) E)35

Solution: Explanation:   Area of a triangle = r * s   Where r is the inradius and s is the semi perimeter of the triangle.   Area of triangle = 2.5 * 60/2 = 35 cm2   Answer: Option 75
Answer: D
4 dice are thrown simultaneously on the board. Find the probability show the same face.	Choose the correct choice from the following answers:
A) 2/215 B) 2/131 C) 1/216 D) 2/217 E) 2/319

Solution: The total number of elementary events associated to the random experiments of throwing four dice simultaneously is:   =6×6×6×6=64=6×6×6×6=64   n(S)=64n(S)=64   Let XX be the event that all dice show the same face.   X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)}X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)}   n(X)=6n(X)=6   Hence required probability,   =n(X)n(S)=664=n(X)n(S)=664   =1/216   1/216
Answer: C
A box contain the number of balls which is as much times greater than 15 as much times lesser than 240.The no. of ball is?	Pick: A) 48 B) 75 C) 60 D) 54 E) 45

Solution: Answer   Let the number be x.   x/15=240/x   x^2=240*15= 
240*15 = 3_600
3600   x=√3600=60   60orrect Option: 60
Answer: C
Compound interest earned on a sum for the second and the third years are Rs.2000 and Rs.2500 respectively. Find the rate of interest? Choose the most appropriate option
A) 18% p.a.
B) 22% p.a.
C) 25% p.a.
D) 24% p.a.
E) None of these.

Solution: Rs.2500 - 2000 = Rs.500 is the interest on Rs.2000 for one year.   Rate of interest = (500/2000) / 100 = 25% p.a   ANSWER:25% p.a.
Answer: C
9548+7314=8362=? Choose the most appropriate option: A) 8230 B) 8410 C) 8500 D) 8600 E) None of them

Solution: =(9548+7314)=8362+x   16862=8362+x   x=16862-8362= 
16862-8362 = 8_500
8500   Answer is 8500
Answer: C
900 men have provisions for 15 days. If 200 more men join them, for how many days will the provisions last now? Select.
A) 12.88  B) 12.6  C) 12.55  D) 12.21  E) 12.27

Solution: 900*15 = 1100*x   x = 12.27.Answer: 12.27
Answer: E
Two same glasses are respectively 1/4th 1/5th full of milk. They are then filled with water and the contents mixed in a tumbler. The ratio of milk and water in the tumbler is? Choices
A) 9:36
B) 9:31
C) 9:39
D) 9:34
E) 9:32

Solution: 1/4 : 3/4 = (1:3)5 = 5:15   1/5 : 4/5 = (1:4)4 = 4:16   ------   9:31   Answer: 9:31
Answer: B
In the recent, climate conference in New York, out of 700 men, 500 women, 800 children present inside the building premises, 20% of the men, 40% of the women and 10% of the children were Indians. Find the percentage of people who were not Indian?
Choose the correct choice.
A) 77%	B) 73%	C) 79%	D) 83%	E) None

Solution: Solution: Number of Indians men present there = 700*20/100= 
700*20/100 = 140
140   Indian women= 500*40/100= 
500*40/100 = 200
200   Indian children= 800*10/100= 
800*10/100 = 80
80.   Total member present in climate conference= 700+500+800= 
700+500+800 = 2_000
2000   Total Indian= 200+140+80= 
200+140+80 = 420
420   Hence, % of Indian present there= 420*100/2000= 
420*100/2000 = 21
21%   % of people who were not Indian= 100-42 = 79%.   Answer 79%
Answer: C
Given that x = 2^b – (8^33 + 16^5), which of the following values for b yields the lowest value for |x|? Choose the correct choice from the following.
A) 97
B) 98
C) 99
D) 100
E) 119

Solution: 8^33 + 16^5 = 2^99 + 2^20   Compared to 2^99, the value of 2^20 is negligible.   2^99 - (2^99 +2^20) will minimize the value of |x|.   The answer is 99.
Answer: C
The y intercept of a line L is 10. If the slope of L is negative, which of the following could be the x intercept of L.
I. -1
II. 0
III. 6
Choose the correct choice from the following answers
A) I only B) II only C) III only D) I and II E) I and III

Solution: C) III only   The y-intercept is 10. Therefore we have y=mx+10   It is given that the slope is negative. Therefore the line must go from top left to bottom right.   i.e: the x-intercept has to be positive. That itself rules out III.   If you choose to go with the options directly, here's an approach.   y=mx+10. For the x-intercept, y=0.   i.e. mx+10=0.   We know that the slope m is negative. Therefore, if x=-1 or x=0, the equation mx+10 =0 would never be satisfied.   If x=6, we have 6m+10=0. A value of m=-5/3 would satisfy this equation.(ANSWER III only)
Answer: C
Mr. Jones sold two pipes at $1.20 each. based on the cost , his profit one was 20% and his loss on the other was 20%. on the sale of the pipes, he:  Select.
A) broke even	B) lost 4 cents	C) gained 4 cents	D) lost 10 cents	E) gained 10 cnets

Solution: 20%profit on $1.20=$20/100x1.20, =$0.20x1.20, = $0.24, similarly , 20 %loss on $1.20, =$20/100x1.20, =$0.20x1.20, =$0.24, therefoe, in one pipe his profit is $ 0.24 and in the other pipe his loss is $0.24. answer: broke even.correct answer will be (broke even)
Answer: A
A shipping company has four empty trucks that will head out in the morning, all four to the same destination. The clerk has four different boxes to ship to that same destination. All four boxes could go on any one of the trucks, or the boxes could be split up into any groupings and given to the trucks in any combinations (ie. two to one truck, one to another, and one to another). In how many different ways could the boxes be put on the four trucks?	Select the correct option
A) 16 B) 64 C) 256 D) 576 E) 4096

Solution: Where we put one box has absolutely no bearing on where we put any of the other boxes. The placement of the four boxes is completely independent of one another. For each box, we have four choices.   N = 4*4*4*4 = 16*16= 
16*16 = 256
256   Answer= (256)
Answer: C
By selling an article at Rs.250, a profit of 25% is made. Find its cost price? Choose one
A) s.486 B) s.455 C) s.220 D) s.480 E) s.200

Solution: SP = 250   CP = (SP)*[100/(100+P)]   = 250* [100/(100+25)]   = 250* [100/125]   = Rs.200   Answer: s.200
Answer: E
The side of a rhombus is 22 m and length of one of its diagonals is 16 m. The area of the rhombus is? Options:
A) 327.9	B) 325.9	C) 347.7	D) 357.9	E) 327.9

Solution: area of the rhombus = 1/2 * p * √4(a)2 - (p)2   a= 22 ; p = 16   327.9=1/2 * 16 *√4(22)2 - (16)2   =1/2 * 16 *√1936 - 256   =1/2 * 16 *√1680   327.9 =327.9   327.9nswer : 327.9
Answer: A
Bullock likes to keep a spare tyre in his car every time. On a certain day, he travels 1, 40,000 km and just to make the most of all the tyres, he changes the tyres between his journey such that each tyre runs the same distance.
What is the distance traveled by each tyre?
Select the correct option
A) 70,000
B) 112,000
C) 80,000
D) 90,000
E) 10,000

Solution: The distance traveled by each tyre:   4/5 * 1, 40, 000km = 112,000 km. 112,000
Answer: B
A and B can together finish a work in 30days. They worked together for 20days and then B left. After another 20days, A finished the remaining work. In how many days A alone can finish the job?
Choose the correct option
A) 20  B) 30  C) 60  D) 50  E) 80

Solution: A+B 20days work = 20*1/30 +  20= 
+  20 = 20
20*1/30= 2/3   Remaining work = 1-2/3 = 1/3   1/3 work is done by A in 20days   whole work will be done by A in 20*3= 
20*3 = 60
60days   Answer is 60
Answer: C
A software engineer has the capability of thinking 100 lines of code in five minutes and can type 100 lines of code in 10 minutes. He takes a break for five minutes after every ten minutes. How many lines of codes will he complete typing after an hour?	Options:	A) 450 lines	B) 200 lines	C) 350 lines	D) 250 lines	E) 150 lines

Solution: 5-think   5-type   5-break   5-type   5-think   5-break   5-type   5-type   5-break   5-think   5-type   5-break   so 5 times for 5 minutes SE types.   Total number of lines =250 lines   ANSWER:250 lines
Answer: D
Set X consists of 10 integers and has median of 30 and a range of 20. What is the value of the greatest possible integer that can be present in the set?  Choose the correct option.
A) 32
B) 37
C) C.40
D) 43
E) 50

Solution: Note that both median and range do not restrict too many numbers in the set. Range is only concerned with the smallest and greatest. Median only cares about the middle.   Quick check of each option starting from the largest:   (E) 50   Range of 20 means the smallest integer will be 30. So 20 cannot lie in between and hence cannot be the median.   (D) 43   Range of 20 means the smallest integer will be 23. So 20 cannot lie in between and hence cannot be the median.   (C) 40   Range of 20 means the smallest integer will be 20. 20 can lie in between such as:   20, 20, 20, 20, 20, 20, 20, 20, 20, 50   This is possible. Hence it is the greatest such number.   Answer (50)
Answer: E
A dishonest dealer professes to sell goods at the cost price but uses a false weight and gains 25%. Find his false weight age? Choose the correct choice from the following options:
A) 2288 B) 276 C) 800 D) 288 E) 277

Solution: 25 = E/(1000 - E) * 100   1000 - E = 4E   1000 = 5E => E = 200   1000 - 200= 
1000 - 200 = 800
800   Answer:800
Answer: C
A jogger running at 9 km/hr along side a railway track is 260 m ahead of the engine of a 120 m long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger?
Choose the correct option
A) 67 sec  B) 89 sec  C) 38 sec  D) 87 sec  E) 45 sec

Solution: Speed of train relative to jogger = 45 - 9= 
45 - 9 = 36
36 km/hr.= 36 * 5/18= 
36 * 5/18 = 10
10 m/sec.   Distance to be covered= 260 + 120= 
260 + 120 = 380
380 m.   Time taken= 380/10= 
380/10 = 38
38 sec.   Answer: 38 sec
Answer: C
Joel sailed for 3 hours at a speed of 20 miles per hour, then for 6 hours at 30 miles per hour and finally, 1 more hour at 40 miles per hour. What was the average speed of Joel during the whole sail?
.	Choose one
A) 25  B) 27.5  C) 28  D) 30  E) 32

Solution: 3 hours at a speed of 20 miles per hour gives us Distance = 20*3= 
20*3 = 60
60 miles   6 hours at a speed of 30 miles per hour gives us Distance= 30*6= 
30*6 = 180
180 miles   1 more hour at 40 miles per hour gives us Distance= 40*1= 
40*1 = 40
40 miles   Total Distance= 60+180+40= 
60+180+40 = 280
280 miles   Total Time= 3+6+1= 
3+6+1 = 10
10 Hours   Average Speed= 280 / 10= 
280 / 10 = 28
28 Miles per hour   ANSWER:28
Answer: C
A student must answer 7 out of 10 questions on an competitive examination. If at least 3 of the first 5 questions must be answered, how many possible combinations of 7 questions are available to the student?
Choose the most appropriate option.
A) 90
B) 80
C) 70
D) 100
E) 110

Solution: as there is ONLY one possiblity of choosing 7 out of 10, while choosing less than 3 in first five   choose 2 in first 5 and all 5 from later half..   ways = 5C2 = 10..   total ways = 10C3 = 120   ans = 120-10= 
120-10 = 110
110   110
Answer: E
A certain company has records stored with a record storage firm in 15-inch by 12-inch by 10-inch boxes. The boxes occupy 1.08 million cubic inches of space. If the company pays $0.4 per box per month for the record storage, what is the total amount that the company pays each month for record storage? Choices.
A) a. 150 B) b. 300 C) c. 600 D) d. 240 E) e. 200

Solution: Volume Per Box: 15x12x10 = 1,800   Total Volume: 1,080,000   Number of Boxes: Total Volume / Volume Per Box = 1,080,000 / 1,800 = 600   Price Per Month: Number of Boxes * Price Per Box = 600 * 0.4= 
600 * 0.4 = 240
240   Answer: d. 240
Answer: D
In an encryption code 'HOUSE' is written as '1S902' when encoded and 'DASH' is written as '4G01' when encoded. How is ''SHED" written in that encryption code? Choose the correct choice from the following
A) S109 B) 0SG1 C) 0124 D) G910 E) 102G

Solution: 0 = S   1 = H   2 = E   4 = D   Answer: Option 0124
Answer: C
Two trains of equal length, running with the speeds of 60 and 40 kmph, take 50 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?  Choose the correct choice from the following answers.
A) 18 sec
B) 17 sec
C) 14 sec
D) 10 sec
E) 11 sec

Solution: A   10 sec   RS = 60 -40= 
60 -40 = 20
20 * 5/18= 100/18   T = 50   10 sec = 50 * 100/18 = 2500/9   RS = 60 + 40= 
60 + 40 = 100
100 * 5/18   T= 2500/9 * 18/500= 
2500/9 * 18/500 = 10
10 sec
Answer: D
Kathleen can paint a room in 2 hours, and Anthony can paint an identical room in 5 hours. How many hours would it take Kathleen and Anthony to paint both rooms if they work together at their respective rates?
Choose the correct answer: A) 20/7 B) 4/3 C) 15/8 D) 9/4 E) 15/4

Solution: (1/2 + 1/5)t=2   t=20/7   20/7nswer: 20/7
Answer: A
If a is a positive integer, and if the units digit of a^2 is 9 and the units digit of (a+1)^2 is 6, what is the units digit of (a+2)^2?
Choose one
A) 1
B) 3
C) 5
D) 6
E) 8

Solution: If the units digit of a^2 is 9, then the units digit of a is either 3 or 7.   If the units digit of (a+1)^2 is 6, then the units digit of a+1 is either 4 or 6.   To satisfy both conditions, the units digit of a must be 3.   Then a+2 has the units digit of 5, thus the units digit of (a+2)^2 will be 5.   The answer is 5.
Answer: C
A wheel rotates 10 times every minute and moves 20 cm during each rotation. How many metres does
the wheel move in one hour?
Choose the correct choice from the following answers
A) 6 metre B) 12 metre C) 120 metre D) 1200 metre E) 2200 metre

Solution: Expl : Number of times wheel moves in 1 hour = 10 * 60= 
10 * 60 = 600
600   :. Distance moves= (600 *20)= 
(600 *20) = 12_000
12000 cms   In metres= 120 metre   Answer: 120 metre
Answer: C