MU-NLPC/Calc-aqua_rat huggingface dataset:
A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If two marbles are drawn at random, what is the probability that at least one is green?
Choose the correct option.
A) 23/35  B) 23/39  C) 23/36  D) 23/32  E) 23/33

Solution: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles.   Probability that at least one green marble can be picked in the random draw of two marbles = Probability that one is green + Probability that both are green   = (⁶C₁ * ⁹C₁)/¹⁵C₂ + ⁶C₂/¹⁵C₂   = (6 * 9 * 2)/(15 * 14) + (6 * 5)/(15 * 14) = 36/70 + 1/7   = 46/70 = 23/3523/35nswer: 23/35
Answer: A
Which of the following is the equation of the line in the xy-plane that has slope 0
(I) x = -2
(II) y = 3
(III) x + y = 0 Choose the correct choice from the following
A) I	B) III	C) II	D) I&II	E) II&III

Solution: y =mx+c therefore y-c= mx then m =(y-c)/x   m=0 means y = c constant ..= II   II
Answer: C
The population of a town is 176400. If it increase at the rate of 5% per annum. What was its population 5 years ago?	Select the correct option
A) 152460	B) 214560	C) 138214	D) 210000	E) 200000

Solution: population 2 years ago = 176400/(1 + 5/100)^5   Answer is 138214
Answer: C
Jisha walked for 3 days. She walked 18 miles on the first day, walking 3 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? Select
A) 24  B) 44  C) 58  D) 60  E) 62

Solution: Jisha walked 18 miles on the first day, walking 3 miles per hour i.e. total time of walk on Day-1 = 18/3= 
18/3 = 6
6 Hours   Second day time of walk= 6-1= 
6-1 = 5
5 hours and Speed= 3+1= 
3+1 = 4
4 miles per hour i.e. Distance walked on second day= 5*4= 
5*4 = 20
20 miles   Third day time of walk= 6 hours and Speed = 4 miles per hour i.e. Distance walked on second day = 6*4= 
6*4 = 24
24 miles   Total Distance travelled on three days= 18+20+24= 
18+20+24 = 62
62   Answer: Option 62
Answer: E
In the equation ax^2 + bx + c = 0 a, b, and c are constants, and abc # 0. If one root of the equation is -3, and b = 8a then which of the following is c equal to?
Select the correct option:
A) a/12
B) a/8
C) 15a
D) 8a
E) 12a

Solution: The sum of the roots is = -b/a = -8a/a = -8. Let the other root be x. Thus, x-3 = -8   x = -5. Again, the product of the roots is   -3*-5= 
  -3*-5 = 15
15. Thus, c/a= 15. c = 15a.   15a.
Answer: C
Three hundred multiples of seven are chosen at random, and 700 multiples of eight are chosen at random. Approximately what percentage of the 1000 selected numbers are odd? Choose the correct choice from the following options.
A) 15%	B) 25%	C) 35%	D) 50%	E) 80%

Solution: About half the multiples of seven will be odd while all the multiples of eight are even.   The percentage of odd numbers is about (1/2)(300) / 1000 = 15%   The answer is 15%.
Answer: A
If a college has 15 staff for every 700 students, then what is the number of staff for 1400 students?	Pick one:  A) 30  B) 14  C) 12  D) 17  E) 19

Solution: 15/700=x/1400   x = 30   30nswer is 30
Answer: A
A man purchased 3 blankets @ Rs.100 each, 5 blankets @ Rs.150 each and two blankets at a certain rate which is now slipped off from his memory. But he remembers that the average price of the blankets was Rs.160. Find the unknown rate of two blankets?	Choose the correct choice from the following choices.
A) 420 B) 550 C) 490 D) 450 E) 457

Solution: 10 * 160= 
10 * 160 = 1_600
1600   3 * 100 + 5 * 150= 
3 * 100 + 5 * 150 = 1_050
1050   1600 – 1050= 550   Answer:550
Answer: B
X is a prime number bigger than 10. Also, Y = X+X^3+X^5+X^7. What is definitely true about Y?  Choose the correct choice from the following choices
A) Y is a prime number.  B) Y is odd.  C) Y is even.  D) Y is divisible by 3.  E) Y is divisible by 7.

Solution: Assume X= 11 (Since there can be only one unique answer)   Therefore Y= 11 + 11^3 + 11^5 + 11^7   Y=[ Odd + Odd ] + [Odd +Odd]   Y= Even + Even   Y= Even   Ans: Y is even.
Answer: C
The successive discounts 20% and 15% are equal to a single discount of?  Pick
A) 43%	B) 72%	C) 32%	D) 44%	E) 29%

Solution: C   32%   Let the CP of an article be Rs. 100   Given that successive discounts are 20% and 15%.   SP = 85% of 80% of 100 = (85/100)(80/100)(100)   => SP = Rs. 68   32%learly, single discount is 32%.
Answer: C
A certain store sold pens for $0.35 each and pencils for $0.25 each. If a customer purchased both pens and pencils from the store for a total of $1.80, what total number of pens and pencils did the customer purchase?  Choose the correct choice from the following options
A) 6	B) 9	C) 10	D) 11	E) 12

Solution: Answer: Algebraically, the question looks like this: 2.5 = 0.35x + 0.25y There are three possible numbers of pens that fit that requirement:   1 pen: $0.35   2 pens: $0.70   3 pens: $1.05 and 3 pencils for $0.25 each. That's 3 pens and 3 pencils for a total of 6 pens and pencils. Choice (6) is correct.
Answer: A
A reduction of 20% in the price of oil enables a house wife to obtain 4kgs more for Rs.600, what is the reduced price for kg? Answers
A) 20 B) 40 C) 36 D) 30 E) 35

Solution: 600*(20/100)= 
600*(20/100) = 120
120 ---- 4   ? ---- 1=> Rs.30   Answer:30
Answer: D
Danny drove his old car 100 kilometers, from his home to a friend. To prevent the engine from overheating, he stopped his car for 11 minutes every time he completed 40 kilometers of continuous driving. When the car was moving, Danny drove it at an average speed of 60 kilometers per hour. What was Danny's average speed on that trip?	Pick.
A) 37.5 kilometers per hour	B) 48 kilometers per hour	C) 49.2 kilometers per hour	D) 75 kilometers per hour	E) 100 kilometers per hour

Solution: Time taken to reach first 40 km is 40/60 = 2/3 hr   Time taken to reach next 40 km is 40/60 = 2/3 hr   Time taken to reach next 20 km is 20/60 = 1/3 hr   Danny stopped twice on his way at 40 km from starting point and at 80km from the starting point...   Each stop was of 11 min , so two 11min break = 2*11/60 => 11/30 hr   Total time taken to reach 100 km is (2/3 + 2/3 + 1/3+11/30 ) = 61/30 hrs   So, Average speed is 100/(61/30) = 49.2km/hour   Answer will be (49.2 kilometers per hour)
Answer: C
The ratio of two numbers is 3 : 4 and their H.C.F. is 4. Their L.C.M. is:	Select the correct option.
A) 12
B) 16
C) 24
D) 48
E) 36

Solution: Let the numbers be 3x and 4x. Then, their H.C.F. = x. So, x = 4.   So, the numbers 12 and 16.   L.C.M. of 12 and 16 = 48.   Answer: Option 48
Answer: D
The product of a and b is equal to 11 more than twice the sum of a and b. If b = 5, what is the value of b - a?	Choose the correct choice from the following answers:  A) -2  B) 5  C) 7  D) 24  E) 35

Solution: ab= 11 + 2(a+b)   5a= 11+2a +10   3a= 21   a=7   b-a= 5-7=-2   -2 is the answer
Answer: A
3 gentlemen and 3 gentlewomen are candidates for 2vacancies. A voter has to vote for 2candidates. In how many ways can one cast his vote?
Choose the correct choice from the following answers:  A) 8  B) 10  C) 15  D) 17  E) 19

Solution: There are 6 candidates and a voter has to vote for any two of them.   So, the required number of ways is,   = 6C2 = 6!/2!*4!   = 15.   15
Answer: C
If P represents the product of the first 14 positive integers, then P is not a
multiple of:
Options.
A) a) 99	B) b) 84	C) c) 72	D) d) 65	E) e) 57

Solution: a) 99 = 9*11   b) 84 = 4*7*3   c) 72 =9*11   d) 65 = 5*13   e) 57 =19*3   since 19 is not there in first 15 positive numbers it is the only possibility   e) 57
Answer: E
For which of the following values of n is (500+n)/n NOT an integer? Choose the correct option:
A) 1 B) 2 C) 3 D) 4 E) 5

Solution: Solution:   This problem is easiest solved by plugging in each answer choice.   A) (500 + 1)/1 = 501/1= 
501/1 = 501
501   Answer choice A yields an integer.   B) (500 + 2)/2= 502/2= 
502/2 = 251
251   Answer choice B yields an integer.   C) (500 + 3)/3= 503/3 = 167, remainder 2   Answer choice C DOES NOT yield an integer.   Although we believe answer choice C is correct, we should still test the other answer choices.   D) (500 + 4)/4 = 504/4= 
504/4 = 126
126   Answer choice D yields an integer.   E) (500 + 5)/5= 505/5= 
505/5 = 101
101   Answer choice E yields an integer.   Thus, the correct answer is answer choice 3.
Answer: C
The sum of the squares of three numbers is 138, while the sum of their products taken two at a time is 131. Their sum is: Choose the correct choice from the following answers
A) 20 B) 40 C) 50 D) 60 E) 80

Solution: Let the numbers be a, b and C. Then,   a2 + b2 + c2 = 138 and (ab + bc + ca) = 131   (a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca)   138 + 2 * 131= 
138 + 2 * 131 = 400
400   (a + b + c)= âˆš400 = 20   20NSWER 20
Answer: A
Three partners shared the profit in a business in the ratio 5 : 7 : 8. They had partnered for 14 months, 8 months and 7 months respectively. What was the ratio of their investments?
Choose one:
A) 5 : 7 : 8
B) 20 : 49 : 64
C) 38 : 28 : 21
D) 30 : 20 : 15
E) None of these

Solution: Explanation:   Let their investments be Rs. x for 14 months, Rs. y for 8 months and Rs. z for 7 months respectively.   Then, 14x : 8y : 7z = 5 : 7 : 8.   Now,	14x	/8Y=5/7 =>98x = 40y =>y =	49/20X   And,	14x /7Z =5/8 => 112X=35Z=>z =	112/35 X 16/5X   x : y : z = x :49/20 X 16/5X =20 : 49 : 64.   ANSWER IS 20 : 49 : 64
Answer: B
When positive integer N is divided by positive integer P, the quotient is 18, with a remainder of 7. When N is divided by (P + 2), the quotient is 10 and the remainder is 3. What is the value of N?  Choose the correct choice:
A) 151
B) 331
C) 511
D) 43
E) 87

Solution: N/P=18 7/P= 18P+7   N/(P+2)=10 1/(P+2)=10P+20+3   solving these two equations   we get P=2 N= 43 answer is 43
Answer: D
Gary’s Gas Station serves an average of 13 cars per hour on Saturdays, 10 cars per hour on Sundays, and 9 cars per hour on all other days of the week. If the station is open from 6 a.m. to 10 p.m. every day, how many cars does Gary’s station serve over the course of a typical week?	Choose the most appropriate option
A) 1,088	B) 1,200	C) 1,240	D) 1,280	E) 1,320

Solution: 6 a.m. to 10 p.m. = 16 hours   Number of cars serviced on weekdays = (16 * 9 * 5)   Number of cars serviced on Saturday = (16 * 13)   Number of cars serviced on Sunday = (16 * 10)   Number of cars served in a week = 16(45 + 13 + 10) = 16 * 68= 
16 * 68 = 1_088
1088   1,088nswer: 1,088
Answer: A
If m is an integer such that (-2)^2m=2^(18-m) then m=?  Choose the correct answer.
A) 1 B) 2 C) 3 D) 5 E) 6

Solution: (-2)^(2m) = 4^m   and   2^(18-m) = 4^((18-m)/2)   Therefore,   m = (18-m)/2   2m = 18 - m   m = 6   Answer 6
Answer: E
There are two numbers. If 30% of the first number is added to the second number, then the second number increases to its five-fourth. Find the ratio of the first number to the second number?  Choose the correct choice from the following choices.
A) A)3/7 B) B)5/8 C) C)6 D) D)5/6 E) E)7

Solution: Let the two numbers be x and y.   30/100 * x + y = 5/4y   => 3/10 x = 1/4 y => x/y = 5/6   5/6)
Answer: D
One side of a rectangular field is 16 m and one of its diagonal is 18 m. Find the area of the field.  Choose the correct option.
A) 100  B) 120  C) 150  D) 180  E) None

Solution: Solution   Other side = √(18)2 - (16)2   = √324 - 256= 
324 - 256 = 68
√68= 8.2 m.   ∴ Area = (16 x 8.2)m2 = 131.2 m2.   Answer None
Answer: E
If two sides of a triangle have lengths 6 and 8, which of the following could be the perimeter of the triangle? I. 9 II. 16 III. 19	Options
A) None B) I only C) II only D) III only E) I, II, and III

Solution: The length of any side of a triangle must be larger than the positive difference of the other two sides, but smaller than the sum of the other two sides.   Therefore:   (8-6) < {third side} < (8+6).   2 < {third side} < 14.   Perimeter = {third side} + 8 + 6 = {third side} + 14.   16 < {perimeter} < 28.   answer III only
Answer: D
If the sum of 6 consecutive integers is x, which of the following must be true?
I. x is a multiple of 6
II. x is an odd number
III. x is aneven number Pick one
A) I only B) II only C) III only D) I and III E) II and III

Solution: III. If you start off with an even number, the sum (x) is even, and if you start off with an odd number the sum (x) is odd. Therefore this is not always true.   II. Same as above. This need not be always true.   I. Say, the first number is p. Then the sum of the five numbers = p + (p+1) + (p+2)...... + (p+4)   = 6p + 12 = 6 (p+2) => divisible by 6. There this must be true in all cases.   Therefore I only is the answer.
Answer: A
How many positive integers between 1 and 300 are there such that they are multiples of 21?  Pick one
A) 14	B) 16	C) 17	D) 13	E) 15

Solution: Multiples of 21 = 21,42,63,-----294   Number of multiples of 21 => 21*14= 
21*14 = 294
294   14nswer is 14
Answer: A
100 students appeared in 2 tests.60 students passed 1st test. 40 students passed in the 2nd test. 20 students passed in both 1 and 2 tests. what is the probability of the students who failed in both tests?  Choose the correct answer:
A) 10%  B) 15%  C) 20%  D) 25%  E) 30%

Solution: 20 student passed both two test   40 student passed only 1st test   20 student passed only 2nd test   so  100-(20+40+20)= 
 100-(20+40+20) = 20
20 student failed in both sub   so ans is 20%   ANSWER:20%
Answer: C
The length of a rectangular floor is more than its breadth by 200%. If Rs. 324 is required to paint the floor at the rate of Rs. 3 per sq m, then what would be the length of the floor?  Select the correct option
A) 11 B) 12 C) 18 D) 77 E) 12

Solution: Let the length and the breadth of the floor be l m and b m respectively.   l = b + 200% of b = l + 2b = 3b   Area of the floor = 324/3= 
324/3 = 108
108 sq m   l b= 108 i.e., l * l/3 = 108   l2 = 324 => l = 18.Answer: 18
Answer: C
You collect baseball cards. Suppose you start out with 13. Maria takes half of one more than the number of baseball cards you have. Since you're nice, you give Peter 1 baseball card. Since his father makes baseball cards, Paul decides to triple your baseball cards. How many baseball cards do you have at the end?  Choose one:	A) 15	B) 18	C) 19	D) 20	E) 21

Solution: Solution   Start with 13 baseball cards.   Maria takes half of one more than the number of baseball cards you have. So Maria takes half of 13 + 1 which is 7,   so you're left with   13 - 7= 
  13 - 7 = 6
6.   Peter takes 1 baseball card from you:  6 - 1= 
 6 - 1 = 5
5 baseball cards.   Paul triples the number of baseball cards you have: 5 Ã— 3= 15 baseball cards.   So you have 15 at the end.   Correct answer : 15
Answer: A
A large research project was scheduled over the course of a 30-month period, and a budget of $84,000 was allotted for the course of the entire project. After seven months, the project had spent $19,800. Was the project at this point over budget or under budget, and by how much? Choose the correct option
A) under, $4200
B) 0ver, $200
C) under, $700
D) over $1800
E) over $5800

Solution: cost per month = 84,000/30 = 2,800.   Now, multiply by seven months: 7*($2800) = $19,600. That would be the budgeted amount, the amount theoretically supplied to the project. The real amount spent is more than this, so it is over budget.   $19,600 â€“ #19,800 = -$200   Answer = (0ver, $200)
Answer: B
In a certain Parallelogram the degree measure of one angle exceeds that of the other by 10 what is the degree measure of the smaller angle? Choose the correct choice from the following choices.
A) 75
B) 80
C) 85
D) 90
E) 95

Solution: In a parallelogram opposite angles are equal and the angles at each side are supplementary to each other (supplementary angles are two angles that add up to 180°).   Given: x+(x+10)=180 --> x=85.   Answer: 85.
Answer: C
The speed of a boat in upstream is 80 kmph and the speed of the boat downstream is 128 kmph. Find the speed of the boat in still water and the speed of the stream?	Choose the correct choice from the following answers.
A) 24
B) 99
C) 88
D) 66
E) 23

Solution: Speed of the boat in still water = (80+128)/2= 
(80+128)/2 = 104
104 kmph. Speed of the stream= (80-60)/2 = 24 kmph. 24nswer:24
Answer: A
In how many seconds will a train 180 meters long pass an oak tree, if the speed of the train is 36 km/hr?
Choose the correct choice from the following
A) 14  B) 16  C) 18  D) 20  E) 22

Solution: speed = 36 * 5/18= 
36 * 5/18 = 10
10 m/s   time= 180/10= 
180/10 = 18
18 seconds   The answer is 18.
Answer: C
There are 4 more women than men on Centerville's board of education. If there are 12 members on the board, how many are women?
Choose the correct choice from the following answers.
A) 3	B) 4	C) 6	D) 7	E) 8

Solution: Given: M=W-4 so, W+(W-4)=12 --> W=8.   Answer: 8.
Answer: E
An amount at compound interest sums to Rs.17640/- in 2 years and to Rs.18522/- in 3 years at the same rate of interest. Find the rate percentage? Options
A) 5%  B) 7%  C) 9%  D) 11%  E) 12%

Solution: Explanation:   The difference of two successive amounts must be the simple interest in 1 year on the lower amount of money.   S.I = 18522/- - 17640/- = Rs. 882/-   Rate of interest = (882/17640) × (100/1) => 8820/1764= 
8820/1764 = 5
5%   Principal= 5%mount/(1 + R/100)2   = 17640/(1 + 5/100)2   = 17640/(21/20 × 21/20)   = 17640/(1.05 × 1.05)   = 17640/1.1025= 
17640/1.1025 = 16_000
16000   Thus the principal is Rs.16000/- and the rate of interest is 5%   5%nswer: Option 5%
Answer: A
In how many ways can the letters of the word "CORPORATION" be arranged so that vowels always come together. Choose the correct choice from the following choices
A) 5760
B) 50400
C) 2880
D) None of above
E) 2487

Solution: Explanation:   Vowels in the word "CORPORATION" are O,O,A,I,O   Lets make it as CRPRTN(OOAIO)   This has 7 lettes, where R is twice so value = 7!/2!   = 2520   Vowel O is 3 times, so vowels can be arranged = 5!/3!   = 20   Total number of words = 2520 * 20= 
2520 * 20 = 50_400
50400   Option 50400
Answer: B
If three distinct positive divisors of 128 are randomly selected, what is the probability that their sum will be less than 32?  Select the correct option.
A) 2/7
B) 3/14
C) 5/28
D) 9/56
E) 11/64

Solution: The positive divisors are 1, 2, 4, 8, 16, 32, 64, 128.   If any of the first five are chosen, the sum will be less than 32.   P(sum is less than 32) = 5/8 * 4/7 * 3/6 = 60/336 = 5/28   The answer is 5/28.
Answer: C
An author received $0.80 in royalties for each of the first 100,000 copies of her book sold, and $0.30 in royalties for each additional copy sold. If she received a total of $260,000 in royalties, how many copies of her book were sold?
Choose the correct choice from the following options
A) 700,000  B) 300,000  C) 380,000  D) 400,000  E) 420,000

Solution: Total royalties for first 100.000 books = .8*100,000= 80,000   Total royalties for the rest of the books = 260,000-80,000 = 180,000   Remaining books = 180,000/0.3 = 600,000   Total books = 600,000+100,000 = 700,000 700,000nswer 700,000
Answer: A
The average age of a class of 15 students is 10 years. If the age of the teacher be included, then the average increased by 1year. Find the age of the teacher? Answers:
A) 22
B) 23
C) 26
D) 29
E) 31

Solution: Total age of 15 persons = 15*10= 
15*10 = 150
150 years   Average age of 16 persons= 11years   Total age of 16 persons = 16 * 11= 
16 * 11 = 176
176 years   Age of the teacher= 176-150= 
176-150 = 26
26 years   Answer is 26
Answer: C
Jerome anticipated that the WebWeb.com stock price would fall and sold all his WebWeb.com stocks for $5 per stock. He paid $10,000 tax on the revenue. A week later, Jerome became convinced that the WebWeb.com stock price would rise, and he used the money that he had gotten from selling the WebWeb.com stocks to purchase them again, this time at $6 per stock. If Jerome ended up having 4000 WebWeb.com stocks fewer than the number he had before selling them, how many WebWeb.com stocks did he have originally? Choose the correct choice from the following answers
A) 10,000  B) 11,600  C) 12,000  D) 14,000  E) 16,400

Solution: Let the number of shares be x.   5*x -10000(money paid in taxes) = 6(x- 4000)   Solving for x, we get the shares as 14000.   Ans :(Option 14,000)
Answer: D
What is the greatest prime factor of (13!12!) + (13!14!)?
.	Choices.
A) 11
B) 13
C) 47
D) 61
E) 71

Solution: 13!12! + 13!14!   = 13!12! + 13! * 14 * 13 * 12!   = 13!12!(1 + 169+13)   = 13! 12! * 61 * 3   GC61 = 61   Answer = 61 = 61
Answer: D
For a race a distance of 224 meters can be covered by P in 7 seconds and Q in 32 seconds. By what distance does P defeat Q eventually?
Choose the correct choice from the following answers: A) 800m B) 838m C) 834m D) 831m E) 836m

Solution: Explanation:   This is a simple speed time problem. Given conditions:   =>Speed of P= 224/7= 
224/7 = 32
32m/s=>Speed of Q=224/32= 
224/32 = 7
7m/s=>Difference in time taken =25 seconds   Therefore, Distance covered by P in that time= 32m/s x 25 seconds = 800 metres   800mNSWER: 800m
Answer: A
In how many ways can a cricket eleven be chosen out of a batch of 15 players.	Select:
A) 1745	B) 1230	C) 1365	D) 2410	E) 3564

Solution: Required number of ways   = 151365 11 = 151365 (15-11)   = 15 1365 4   1513654 = 15 * 14 * 13 * 12 / 4 * 3 * 2 *1   = 1365   Ans: 1365
Answer: C
John bought 9.25m of cloth for $425.50. Find the cost price per metre.	Answers.
A) 46 B) 47 C) 58 D) 56 E) 54

Solution: Cloth bought by John = 9.25 m   Cost of 9.25 m = $425.50   Cost per metre = 425.50 ÷ 9.25   The cost of the cloth per metre = $ 46   46nswers: 46
Answer: A
Look at this series: 2, 1, (1/2), (1/4), (1/8), ... What number should come next?	Select the correct option.
A) (1/3) B) (1/5) C) (1/6) D) (1/10) E) (1/16)

Solution: This is a simple division series; each number is one-half of the previous number.   In other terms to say, the number is divided by 2 successively to get the next result.   4/2= 
4/2 = 2
2   2/2= 
2/2 = 1
1   1/2= 1/2   (1/2)/2 = 1/4   (1/4)/2 = 1/8   (1/8)/2= 1/16 and so on.   Answer is (1/16)
Answer: E
A girl swims downstream 40 km and upstream 16 km taking 4 hours each time, what is the speed of the girl in still water? Choose the correct choice from the following answers.
A) 3	B) 4	C) 5	D) 6	E) 7

Solution: 40 --- 4 DS = 10   ? ---- 1   16 ---- 4 US = 4   ? ---- 1 M = ?   M = (10 + 4)/2= 
(10 + 4)/2 = 7
7   Answer:7
Answer: E
On my sister's birthday, she was 143 cm in height, having grown 10% since the year before. How tall was she the previous year?
Choose the correct choice from the following answers:
A) 140 cm B) 136 cm C) 130 cm D) 127 cm E) 125 cm

Solution: Let the previous year's height be x.   1.1x = 143   x = 130   The answer is 130 cm.
Answer: C
A goods train runs at the speed of 72 kmph and crosses a 350 m long platform in 26 seconds. What is the length of the goods train? Choices
A) 230 m
B) 140 m
C) 160 m
D) 170 m
E) None of these

Solution: Explanation:   Speed =[ 72 x (5/18) ]m/sec= 20 m/sec.   Time = 26 sec.   Let the length of the train be x metres.   Then,[ (x+350)/26 ]= 20   => x + 350 = 520   => x = 170. Answer: 170 m
Answer: D
How many 3-digit numbers can be formed with the digits 1,4,7,8 and 9 if the digits are not repeated?	Pick one
A) 60	B) 41	C) 42	D) 62	E) 61

Solution: Three digit numbers will have unit's, ten's and hundred's place.   Out of 5 given digits any one can take the unit's place.   This can be done in 5 ways ------- (i)   After filling the unit's place, any of the four remaining digits can take the ten's place.   This can be done in 4 ways ------- (ii)   After filling in ten's place, hundred's place can be filled from any of the three remaining digits.   This can be done in 3 ways ------- (iii)   => By counting principle, the number of 3 digit numbers =5×4×3==5×4×3= 60   Option is 60
Answer: A
M = {-6, -5, -4, -3, -2}
T = {-2, -1, 0, 1, 2, 3, 4}
If an integer is to be randomly selected from set M above and an integer is to be randomly selected from set T above, what is the probability that the product of the two integers will be negative?
Answers:	A) 0	B) 1/3	C) 2/5	D) 1/2	E) 4/7

Solution: We will have a negative product only if 1, 2, 3, or 4 are selected from set T.   P(negative product) = 4/7   The answer is 4/7.
Answer: E