MU-NLPC/Calc-aqua_rat huggingface dataset:
Two trains are running in opposite directions with the same speed. If the length of each train is 120 m and they cross each other in 12 sec, then the speed of each train is?	Choose the correct option:	A) 65 km/hr	B) 76 km/hr	C) 36 km/hr	D) 45 km/hr	E) 41 km/hr

Solution: Let the speed of each train be x m/sec.   Then, relative speed of the two trains = 2x m/sec.   So, 2x = (120 + 120)/12 => x = 10   Speed of each train = 10 m/sec.   = 10 * 18/5 =- 36 km/hr.   Answer:36 km/hr
Answer: C
Two trains of length 100 m and 200 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 54 kmph and 90 kmph. After how much time will the trains meet?	Choose the correct answer:
A) 20/8 sec
B) 20/4 sec
C) 5/2 sec
D) 22/7 sec
E) 60/7 sec

Solution: They are moving in opposite directions, relative speed is equal to the sum of their speeds.   Relative speed = (54 + 90)*5/18 = 8*5= 
8*5 = 40
40 mps.   The time required= d/s = 100/40 = 5/2 sec.Answer:5/2 sec
Answer: C
A train is running at a speed of 40 km/hr and it crosses a post in 19.8 seconds. What is the length of the train?
Choose the most appropriate option:  A) 190 metres  B) 160 metres  C) 200 metres  D) 220 metres  E) 250 metres

Solution: Speed of the train, v = 40 km/hr = 40000/3600 m/s = 400/36 m/s   Time taken to cross, t = 19.8 s   220 metresistance Covered, d = vt = (400/36)Ã— 19.8 = 220 m   220 metresistance covered is equal to the length of the train = 220 m   Correct answer is 220 metres   220 metres
Answer: D
Jack and Jill are marathon runners. Jack can finish a marathon (42 km) in 3.5 hours and Jill can run a marathon in 4.2 hours.What is the ratio of their average running speed? (Jack: Jill)	Answers
A) 14/15 B) 15/14 C) 4/5 D) 6/5 E) Cannot be determined

Solution: Average Speed of Jack =6/5istance/ Time   = 42 /(7/2) = 84/7   Average Speed of Jill = 42/(4.2)= 
42/(4.2) = 10
10   Ratio of Average speed of Jack to Jill= (84/7)/10 = 84/70 =6/5   Answer 6/5
Answer: D
In the equation ax^2 + bx + c = 0 a, b, and c are constants, and abc # 0. If one root of the equation is -2, and b = 10a then which of the following is c equal to?  Choose the correct option:
A) a/12	B) a/8	C) 6a	D) 8a	E) 16a

Solution: The sum of the roots is = -b/a = -10a/a = -10. Let the other root be x. Thus, x-2 = -10   x = -8. Again, the product of the roots is   -2*-8= 
  -2*-8 = 16
16. Thus, c/a= 16. c = 16a.   16a.
Answer: E
Rahim bought 52 books for Rs.1200 from one shop and 32 books for Rs.480 from another. What is the average price he paid per book ?
Choose the correct choice:
A) s.17	B) s.18	C) s.12	D) s.20	E) s.10

Solution: Average price per book   = (1200+ 480) / (52 + 32) = 1680/ 84   = Rs.20   Answer:s.20
Answer: D
John walks to a viewpoint and returns to the starting point by his car and thus takes a total time of 8 hours 40 minutes. He would have gained 2 hours by driving both ways. How long would it have taken for him to walk both ways.	Choose the correct choice from the following options
A) 8 h 40 min  B) 10 h 40 min  C) 9 h 40 min  D) 11 h 45 min  E) 8 h 25 min

Solution: 1.Walking to to a viewpoint+Driving back=8 hours 40 minutes   2.Driving to a viewpoint+Driving back=8 hours 40 minutes - 2 hours=6 hours 40 minutes, thereforeone way driving=6 hours 40 minutes/2 =3 hours 20 minutes.   3. From 1.one way driving=8 hours 40 minutes-3 hours 20 minutes=5 hours 20 minutes.   4.Walking to to a viewpoint+Walking back=5 hours 20 minutes+5 hours 20 minutes=10 hours 40 minutes.   Answer: 10 h 40 min
Answer: B
A number, y is chosen at random from the set of positive integers from 1 to 9. What is the probability that (9/y) > y?  Choose the correct choice from the following options:
A) 2/9
B) 1/9
C) 1/3
D) 2/3
E) 7/9

Solution: Number x has to be chosen from numbers 1-9   (9/y) > y   => 9 > y^2   =>y^2 - 9 < 0   y can have 2 values only 1 , 2   Therefore , probability = 2 / 9   2/9nswer 2/9
Answer: A
Find the area of a parallelogram with base 24 cm and height 10 cm? Pick.
A) 240 cm2  B) 384 cm2  C) 279 cm2  D) 200 cm2  E) 297 cm2

Solution: 240 cm2rea of a parallelogram   = base * height   = 24 * 10= 
24 * 10 = 240
240 cm2   240 cm2nswer:240 cm2
Answer: A
What is the 21th digit to the right of the decimal point in the decimal expansion of 1/37?  Choose one:  A) 0  B) 2  C) 4  D) 7  E) 9

Solution: 1/37=0.027027... So, we have a repeating cycle of 027. Every third digit (3rd, 6th, 9th, ...) to the right of the decimal point is 7, thus 21st digit to the right of the decimal point is also 7.   Answer: 7.
Answer: D
Let f(x) = ax2 - b|x|, where a and b are constant. Then at x =0, f(x) is
Select.
A) maximized whenever a>0, b>0  B) maximized whenever a>0, b<0  C) minimized whenever a>0, b>0  D) minimized whenever a>0, b<0  E) None of these

Solution: Explanation :   When a > 0, b < 0, ax2 and –b |x| are non negative for all x.   i.e. ax2 – b|x| ≥ 0.   ∴ ax2 – b |x| is minimum at x = 0 when a > 0, b < 0.   Answer : minimized whenever a>0, b<0
Answer: D
In a certain game, you perform three tasks. You flip a coin, and success would be heads. You roll a single dice, and success would be a point. You pick a card from a full playing-card deck, and success would be picking a spades card. If exactly one of these three tasks is successful, then you win the game. What is the probability of winning?	Choose the most appropriate option.
A) 11/16
B) 15/32
C) 23/48
D) 14/36
E) 17/56

Solution: The answer is 23/48   Probability of just one enent will be happining   So, Probability heads=1/2   Probability number point =1/6   Probability picking a spades card =1/4   so, Probability win by getting tails= 1/2*5/6*3/4 = 15/48   Probability win by getting number 6 = 1/2*1/6*3/4 = 3/48   Probability win by picking a spades card =1/2*5/6*1/4=5/48   Probability wining= 15/48+3/48+5/48 =23/48
Answer: C
Ragu purchased a refrigerator and a mobile phone for Rs. 20000 and Rs. 10000 respectively. He sold the refrigerator at a loss of 5 percent and the mobile phone at a profit of 10 percent. Overall he make a.	Select the correct option.
A) loss of Rs. 200  B) loss of Rs. 100  C) profit of Rs. 100  D) profit of Rs. 200  E) No loss No gain

Solution: Total C.P. = 20000+10000= 
20000+10000 = 30_000
30000   S.P. of refrigerator= 20000/100*95= 
20000/100*95 = 19_000
19000   S.P. of Mobile= 10000/100*110= 
10000/100*110 = 11_000
11000   Total S.P.= 19000 + 11000= 
19000 + 11000 = 30_000
30000   Tota. C.P. - Total S.P.= 30000 - 30000= 
30000 - 30000 = 0
0   No Loss No gain   Answer : No loss No gain
Answer: E
In a mixture of milk and water, the proportion of milk by weight was 80%. If, in a 180 gm mixture, 36 gms of pure milk is added, what would be the percentage of milk in the mixture formed? Choose the correct answer
A) 83.3% B) 12% C) 18% D) 9% E) 6%

Solution: Explanation:   Percentage of milk in the mixture formed = [80/100 (180) + 36] / (180 + 36) * 100% = (144 + 36)/216 * 100% = 5/6 * 100% = 83.33%.   Correct Option : 83.3%
Answer: A
A man can row a boat at 32 kmph in still water. If the speed of the stream is 8 kmph, what is the time taken to row a distance of 96 km downstream?	Choose the correct answer:
A) 12/4
B) 12/5
C) 12/6
D) 12/7
E) 12/8

Solution: Speed downstream = 32+8= 
32+8 = 40
40 kmph.   Time required to cover 60 km downstream= d/s = 96/40 = 12/5 hours. Answer:12/5
Answer: B
If all the sides of a right triangle increase in length by 8%, then by what percentage does the area of the triangle increase?	Pick one.
A) 8%  B) 16.64%  C) 24.32%  D) 32.84%  E) 36.16%

Solution: Let B be the base and H be the height of the original triangle.   The original area is (1/2)BH.   The area of the expanded triangle is (1/2)(1.0816.64%)(1.08H) = (1.08)(1.08)(1/2)16.64%H = 1.1664(1/2)16.64%H   The answer is 16.64%.
Answer: B
3 candidates in an election and received 1136, 7636 and 11628 votes respectively. What % of the total votes did the winningcandidate got in that election?	Choose the correct answer
A) 45%  B) 56%  C) 57%  D) 70%  E) 72%

Solution: Total number of votes polled = (1136 + 7636 + 11628)= 
(1136 + 7636 + 11628) = 20_400
20400   So, Required percentage= 11628/20400 * 100= 
11628/20400 * 100 = 57
57%   57%
Answer: C
A shopkeeper cheats to the extent of 10% while buying and selling, by using false weights. His total gain is.  Choose the correct choice from the following answers.
A) 22	B) 21	C) 8	D) 9	E) 81

Solution: Answer: 21) 21%
Answer: B
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. 5 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each?  Select
A) 4538 B) 2778 C) 2608 D) 4530 E) 2001

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 * 5 = Rs. 4530   Answer:4530
Answer: D
3500 – (1000 ÷ 20.50) is equal to :	Choose the correct choice:
A) 3451.21
B) 3029.0
C) 2993.03
D) 2984.36
E) None of these

Solution: Explanation:   Given exp. = 3500 - ((1000 ÷ 2050) * 100)   = 3451.21   3451.21NSWER 3451.21
Answer: A
If two balls are randomly selected from a green urn containing 6 black and 6 white balls and placed into a yellow urn initially containing 5 black and 3 white balls. What is the probability that the yellow urn will contain an equal number of black and white balls after the change?
Select:
A) A.2/9	B) B.4/9	C) C.5/9	D) D.1/3	E) E.5/22

Solution: To have equal number of black and white balls, the yellow urn must have 5 black and 5 white balls. So the balls we select out of the green urn must be both white.   Probability (first ball is white) = 6/12   Probability(second ball is white) = 5/11   Probability (both balls are white) = (6/12)*(5/11) = 5/22   Answer E.5/22
Answer: E
In a system of coding ACCESS is coded CEEGUU, POINTFF as HHKPQRV, LIMERICK as EGKKMNOT and LAMINATE as CCGKNOPV
Waht is likely to be the word of which the code is COTUV?	Choose the correct option.
A) TRAPS	B) PARTS	C) SMART	D) SMARR	E) None of the above

Solution: right answer is None of the aboveQVWX   SO NONNone of the above   ANSWNone of the aboveR:None of the above
Answer: E
A man can row his boat with the stream at 6 km/h and against the stream in 4 km/h. The man's rate is? Choose the correct choice from the following choices.
A) 1 kmph B) 9 kmph C) 6 kmph D) 8 kmph E) 2 kmph

Solution: DS = 6   US = 4   S = ?   S = (6 - 4)/2= 
(6 - 4)/2 = 1
1 kmph   1 kmphnswer: 1 kmph
Answer: A
A dishonest dealer professes to sell goods at the cost price but uses a weight of 800 grams per kg, what is his percent?
Choose the correct choice from the following.
A) 29%
B) 25%
C) 11%
D) 20%
E) 15%

Solution: 800 --- 200   100 --- ? => 25%   Answer: 25%
Answer: B
The banker’s discount on Rs. 1600 at 15% per annum is the same as true discount on Rs. 1680 for the same time and at the same rate. The time is :  Choices:
A) 2 months
B) 4 months
C) 6 months
D) 7 months
E) None

Solution: Sol.   S.I. on Rs. 1600 = R.D. on Rs. 1680.   ∴ Rs. 1600 is the P.W. of Rs. 1680, i.e., Rs. 80 is S.I. on Rs. 1600 at 15%.   ∴ Time = [100 * 80 / 1600 * 15] year = 1/3 year = 4 months.   Answer 4 months
Answer: B
Simplfy
b - [b -(a+b) - {b - (b - a+b)} + 3a]
Options:
A) -a B) 2a C) 4a D) 0 E) 1

Solution: Explanation:   b-[b-(a+b)-{b-(b-a+b)}+3a]   =b-[b-a-b-{b-(2b-a)}+3a]   =b-[-a-{b-2b+a}+3a]   =b-[-a-{-b+a}+3a]   =b-[-a+b-a+3a]   =b-[-2a+b+3a]   =b-b-a   =-a   Option -a
Answer: A
If a × b = 2a - 3b + ab, then 3 × 5 + 5 × 3 is equal to :	Choose the correct choice from the following options:
A) 22
B) 23
C) 24
D) 25
E) 26

Solution: Explanation:   3 × 5 + 5 × 3 = (2 × 3 - 3 × 5 + 3 × 5) + ( 2 × 5 - 3 × 3 + 5 × 3)   = (6 + 10 - 9 + 15)= 
(6 + 10 - 9 + 15) = 22
22.   22nswer: 22
Answer: A
If A,BCD is a four-digit positive integer such that A,BCD is equal to the product of the two-digit number AB and the three digit number ABC, which of the following two-digit numbers cannot be a factor of A,BCD? (Note: the first digit of a number cannot be equal to 0.)
I. AD
II. CD
III. CA Choose one:
A) None
B) II only
C) III only
D) II and III only
E) I, II, and III

Solution: Ideally, ABC * AB = ABCD should make you think of 1s and 0s. The digits needn't be unique so the first thing that comes to mind is   100*10= 
  100*10 = 1_000
1000. But since CA and CD are given as two digit numbers, next you should think of   101*10= 
  101*10 = 1_010
1010 or any such number. This satisfies all conditions so we can analyse using this example.   101 * 10= 
101 * 10 = 1_010
1010   AD= 10 - a factor of 1010   CD = 10 - a factor of 1010   CA = 11 - not a factor of 1010   Now the only thing left to figure is whether it is possible that C1 is a factor of 10C0 for some value of C.   10C0 = 1000 + C0 = 999 + C1   C1 is divisible by C1 but we don't know whether 999 is divisible by C1.   999 = 3^3*37   It has no two digit factor ending in 1 so it will not be divisible by C1.   Answer (III only)
Answer: C
If the cost price of 50 articles is equal to the selling price of 45 articles, then the gain or loss percent is?	Select
A) 11.11 B) 65 C) 78 D) 33 E) 25

Solution: Given that, cost price of 50 article is equal to selling price of 45 articles.   Let cost price of one article = Rs. 1   Selling price of 45 articles = Rs. 50   But Cost price of 45 articles = Rs. 45   Therefore, the trader made profit.\Percentage of profit = 5/45 * 100 = 11.11%   11.11nswer:11.11
Answer: A
The mass of the sun is approximately 2 × 10^20 kg and the mass of the moon is approximately 8 × 10^12 kg. The mass of the sun is approximately how many times the mass of the moon?  Choose the correct choice from the following answers
A) 4.0 × 10^(−18)	B) 2.5 × 10^17	C) 2.5 × 10^7	D) 2.5 × 10^19	E) 4.0 × 10^42

Solution: Mass of sun = x * Mass of moon   x = Mass of sun / Mass of moon = (2 × 10^20) / (8 × 10^12) = 2*2^-3*10^8 = 10^8/4 = 2.5*10^7   Ans. 2.5 × 10^7) 2.5 × 10^7
Answer: C
If seven machines working at the same rate can do 3/4 of a job in 30 minutes, how many minutes would it take two machines working at the same rate to do 3/5 of the job? Select the correct option:  A) 45  B) 60  C) 75  D) 84  E) 100

Solution: using the std formula   m1d1h1/w1=m2d2h2/w2   substituting the values we have   7*1/2*4/3=2*5/3*x (converted 30 min into hours =1/2)   14/3=10/3*x   x=7/5 hour   so 84 minutes   ANSWER:84
Answer: D
3 friends A, B, C went for week end party to McDonald’s restaurant and there they measure there weights in some order In 7 rounds. A, B, C, AB, BC, AC, ABC. Final round measure is 160kg then find the average weight of all the 7 rounds? Choices.
A) 91.4 kgs B) 88.5 kgs C) 86.5 kgs D) 67.5 kgs E) 88.2 kgs

Solution: 91.4 kgsverage weight = [(a + b + c + (a+b) + (b+c) + (c+a)+(a+b+c)] / 7 = 4 (a+b+c) /7 = 4 x 160/7 = 91.4kgs   91.4 kgsnswer:91.4 kgs
Answer: A
The ratio of the radius of two circles is 1: 3, and then the ratio of their areas is?	Choose the most appropriate option:
A) 1: 5  B) 1: 6  C) 1: 9  D) 1: 3  E) 1: 2

Solution: r1: r2 = 1: 3   Πr12: Πr22   r12: r22 = 1: 9   Answer: 1: 9
Answer: C
The average monthly income of P and Q is Rs. 5100. The average monthly income of Q and R is 6250 and the average monthly income of P and R is Rs. 5200. The monthly income of P is?  Pick one:
A) A)Rs.4050
B) B)Rs.4000
C) C)Rs.4029
D) D)Rs.4027
E) E)Rs.4020

Solution: Let P, Q and R represent their respective monthly incomes. Then, we have:   P + Q = (5050 * 2) = 10200 --- (i)   Q + R = (6250 * 2)= 
(6250 * 2) = 12_500
12500 --- (ii)   P + R= (5200 * 2)= 
(5200 * 2) = 10_400
10400 --- (iii)   Adding (i), (ii) and (iii), we get:   2(P + Q + R)= 33100 = P + Q + R = 16550 --- (iv)   Subtracting (ii) from (iv), we get, P = 4050.   P's monthly income = Rs.4050.   Rs.4050nswer: Rs.4050
Answer: A
The total weight of nine nougat nuggets is 7 oz. What is the average (arithmetic mean) weight of one such nougat nugget?
Choose the correct answer
A) 0.18 oz.  B) 0.5 oz.  C) 1.8 oz.  D) 0.77 oz.  E) 18 oz

Solution: Average = Total/Number of items   = 7/9 = 0.77.   Hence, 0.77 oz.
Answer: D
If x is the sum of six consecutive integers, then x is divisible by which of the following: I. 6 II. 7 III. 3
Select the correct option
A) II only  B) I only  C) I,II only  D) II,III only  E) III only

Solution: We're told that X is the SUM of 6 CONSECUTIVE INTEGERS. We're asked what X is divisible by....   Let's TEST VALUES....   IF we use the 6 consecutive integers: 8,9,10,11,12 and 13, then the sum = 63.   63 is divisible by 3   63 is NOT divisible by 6   63 is NOT divisible by 7   There's only one answer that 'fits' with these facts. Answer : III only
Answer: E
X and Y invested in a business. They earned some profit which they divided in the ratio of 2 : 4. If X invested Rs.40,000. the amount invested by Y is Choose one:	A) Rs.45,000	B) Rs.50,000	C) Rs.60,000	D) Rs.80,000	E) None

Solution: Solution   Suppose Y invested Rs.y   Then,	40000 /y = 2 / 4   â€¹=â€º y=(40000Ã—4 / 2).   â€¹=â€º y=80000.   Answer Rs.80,000
Answer: D
In an office, totally there are 800 employees and 25% of the total employees are males. 40% of the males in the office are at-least 50 years old. Find the number of males aged below 50 years?  Pick:
A) 120
B) 160
C) 132
D) 130
E) None of these

Solution: Number of male employees = 800 * 25/100= 
800 * 25/100 = 200
200   Required number of male employees who are less than 50 years old= 200* (100 - 40)%   = 200* 60/100= 
200* 60/100 = 120
120.   120NSWER:120
Answer: A
A man in a train travelling at 20km/hr notices that a train going in the opposite direction passes him in 5 sec.If the length of this train is 140m find its speed . Pick:	A) 30 km/hr	B) 40 km/hr	C) 81 km/hr	D) 60 km/hr	E) 70 km/hr

Solution: relative speed of trains = 140/5 mtrs/sec = 140*18/(5*5)= 101 km/hr   speed of 2nd train = 101-20= 
101-20 = 81
81 km/hr   ANSWER:81 km/hr
Answer: C
If 1 + x^4 + x^3 + x^2 + x = 80, then the average (arithmetic mean)W of x, x^2, x^3, x^4 and x^5 is equal to which of the following?	Choose the correct choice from the following options:
A) 12x  B) 13x  C) 14x  D) 16x  E) 20x

Solution: 1 + x^4 + x^3 + x^2 + x = 81   i.e. 1 +x+ x^2+ x^3+ x^4 = 81   x+ x^2+ x^3+ x^4 = 80   x(1 +x+ x^2+ x^3) = 80   x(81-x^4) = 80   81x - x^5 = 80   x^5 = 81x -80   Now x+ x^2+ x^3+ x^4+ x^5 = 80 + 81x -80 = 81x   Average of W{x, x^2, x^3, x^4, x^5} 80 + 81  -80= 
80 + 81  -80 = 81
81x   Average of W{x, x^2, x^3, x^4, x^5}= 81x/5 ~ 16x   Answer16x
Answer: D
A man took loan from a bank at the rate of 4 % p.a. S.I. After 10 years he had to pay Rs. 2000 interest only for the period. The principal amount borrowed by him was?
Choose the correct choice from the following choices
A) 5000  B) 4500  C) 3200  D) 6000  E) 1592

Solution: Principal = (100 * 2000) / (4 * 10)   = Rs.5000   5000nswer: 5000
Answer: A
A man can row a distance of 6 km in 60 min with the help of the tide. The direction of the tide reverses with the same speed. Now he travels a further 20 km in 10 hours. How much time he would have saved if the direction of tide has not changed?  Choose the correct choice from the following choices
A) 2
B) 8
C) 1
D) 6:41
E) 5

Solution: Explanation:   He covered 6 km in 1 hour , so he might cover 20 km in 3 hours 19 minutes.   But he took 10 hours.   He would have saved 10 â€“ 3 hours 19 minutes= 6 hours 41 minutes.   Answer: 6:41
Answer: D
A salesman’s terms were changed from a flat commission of 5% on all his sales to a fixed salary of Rs.1000 plus 2.5% commission on all sales exceeding Rs. 4,000. If his remuneration as per new scheme was Rs. 600 more than that by the previous schema, his sales were worth? Choose the correct choice from the following answers.
A) 12002	B) 12000	C) 12028	D) 12020	E) 12013

Solution: [1000 + (X-4000) * (2.5/100)] - X * (5/100)   = 600   X = 12000   Answer: 12000
Answer: B
A can give B 100 meters start and C 200 meters start in a kilometer race. How much start can B give C in a kilometer race?  Choose the correct choice from the following choices:
A) 109.12 m.
B) 104.12 m.
C) 111.12 m.
D) 211.12 m.
E) 132.12 m.

Solution: C   111.12 m.   A runs 1000 m while B runs 900 m and C runs 800 m.   The number of meters that C runs when B runs 1000 m,   = (1000 * 800)/900 = 8000/9 = 888.88 m.   B can give 111.12 m. = 1000 - 888.88= 
1000 - 888.88 = 111.12
111.12 m.
Answer: C
List Z consists of 12 consecutive integers. If -4 is the least integer in list Z, what is the range of positive integers in list Z? Choose the correct choice from the following answers:
A) 5
B) 6
C) 7
D) 11
E) 12

Solution: Since -4 is the least integer in list Z, then 7 is the largest integer in that list. Thus the range of the positive integers in the list is   7-1= 
  7-1 = 6
6.   Answer: 6.
Answer: B
An automotive test consisted of driving a car the same distance three separate times, first at an average rate of 40 miles per hour, then 50 miles per hour, then 60 miles per hour. If the test took 111 hours to complete, how many miles was the car driven during the entire test?
Answers
A) 5100  B) 5400  C) 5500  D) 5600  E) 5300

Solution: x is the segment to be traveled   x/40+x/50+x/60 =111   or 74x/1200 =111   x = 1800miles . total distance =3*1800= 
3*1800 = 5_400
5400 miles   5400
Answer: B
The y intercept of a line L is 8. If the slope of L is negative, which of the following could be the x intercept of L.
I. -1
II. 0
III. 6
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 8. Therefore we have y=mx+8   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+8. For the x-intercept, y=0.   i.e. mx+8=0.   We know that the slope m is negative. Therefore, if x=-1 or x=0, the equation mx+8 =0 would never be satisfied.   If x=6, we have 6m+8=0. A value of m=-4/3 would satisfy this equation.(ANSWER III only)
Answer: C
A boat having a length 3 m and breadth 2 m is floating on a lake. The boat sinks by 1 cm when a man gets into it. The mass of the man is ?  Select.
A) 77 kg  B) 60 kg  C) 77 kg  D) 55 kg  E) 47 kg

Solution: In this type of question, first we will calculate the volume of water displaces then will multiply with the density of water.   Volume of water displaced = 3*2*0.01= 
3*2*0.01 = 0.06
0.06 m cube   Mass of Man= Volume of water displaced * Density of water   = 0.06 * 1000= 
0.06 * 1000 = 60
60 kg   Answer: 60 kg
Answer: B
A larger cube has 8 cubic inch as a volume and in the cube there are 8 smaller cubes such that their volume is 1 cubic inch. What is the difference between the surface areas’ sum of the 8 smaller cubes and the surface area of the larger cube, in square inch? Choose the correct choice from the following.
A) 24
B) 64
C) 81
D) 108
E) 120

Solution: Volume of larger cube = 8 = 2^3   Side of larger cube = 2   Volume of smaller cube = 1 --> Side of smaller cube = 1   Surface area of larger cube = 6 * 2^2 = 24   Surface area of 27 smaller cubes = 8 * 6 * 1= 
8 * 6 * 1 = 48
48   Difference= 48 - 24= 
48 - 24 = 24
24   24nswer: 24
Answer: A
A certain club has 11 members, including Harry. One of the 11 members is to be chosen at random to be the president, one of the remaining 10 members is to be chosen at random to be the secretary, and one of the remaining 9 members is to be chosen at random to be the treasurer. What is the probability that Harry will either be the secretary or the member chosen to be the treasurer?	Pick one:	A) 1/4	B) 2/11	C) 3/11	D) 5/11	E) 8/11

Solution: Each member out of 11, including Harry, has equal chances to be selected for any of the positions (the sequence of the selection is given just to confuse us). The probability that Harry will be selected to be the secretary is 1/11 and the probability that Harry will be selected to be the treasurer is also 1/11. So, the probability that Harry will be selected to be either the secretary or the the treasurer is 1/11+1/11=2/11.   Answer: 2/11.
Answer: B