MU-NLPC/Calc-aqua_rat huggingface dataset:
1/4 of all married couples have more than one child. 1/5 of all married couples have more than 3 children. What fraction of all married couples have 2 or 3 children? Options:
A) 1/5  B) B.1/4  C) 1/20  D) 3/5  E) It cannot be determined from the given information.

Solution: Plug in simple numbers. Take 100 couples for example.   1/4 of 100 couples have more than one child = 25 couples.   1/5 of 100 couples have more than 3 kids = 20 couples.   This implies that 20 couples are a subset of 25 couples and the complement of 25 couples within those 100 couples, which equals 75 couples have either one or no kids at all.   We need to find couples that have 2 or 3 kids, so essentially, it is  25 - 20= 
 25 - 20 = 5
5. Fraction will be 5/100= 1/20.   Option 1/20
Answer: C
If Rs.7500 are borrowed at C.I at the rate of 4% per annum, then after 1 year the amount to be paid is? Choose the correct choice from the following answers:
A) 8118	B) 8127	C) 8618	D) 7800	E) 8128

Solution: A = 7500(26/25)1   = 7800   Answer: 7800
Answer: D
Pumping alone at their respective constant rates, one inlet pipe fills an empty tank to 1/2 of capacity in 3 hours and a second inlet pipe fills the same empty tank to 2/3 of capacity in 4 hours. How many hours will it take both pipes, pumping simultaneously at their respective constant rates, to fill the empty tank to capacity?	Choose the correct option:
A) 3  B) 3.6  C) 4.2  D) 4.4  E) 5.5

Solution: Time taken by First tank Fill 1/2 the tank = 3 hours   i.e. Time taken by First tank to Fill 1 complete the tank = 6 hours   Time taken by Second tank Fill 2/3 the tank = 4 hours   i.e. Time taken by First tank to Fill 1 complete the tank = (3/2)*4= 
(3/2)*4 = 6
6 hours   in 1 Hour, Both tanks together Fill the tank= (1/6)+(1/6) = 1/3 tank   i.e. Time taken by Both tank to Fill 1 complete the tank = 3 hours   3
Answer: A
A man buys Rs. 48 shares paying 9% dividend. The man wants to have an interest of 12% on his money. The market value of each share is:  Choose the correct choice from the following options:  A) s. 12  B) s. 15  C) s. 18  D) s. 21  E) s. 36

Solution: Dividend on Rs. 48 = Rs.	9/100	x 48 =Rs.	4.32	.   Rs. 12 is an income on Rs. 100.   Rs.	4.32	is an income on Rs.100/12 x 4.32	= Rs. 36.   Answer: Option s. 36
Answer: E
A person can row at 9 kmph and still water. He takes 7 1/2 hours to row from A to B and back. What is the distance between A and B if the speed of the stream is 1 kmph?
Choose the correct option:
A) 60 km	B) 87 km	C) 33 km	D) 67 km	E) 20 km

Solution: Let the distance between A and B be x km.   Total time = x/(9 + 1) + x/(9 - 1) = 7.5   => x/10 + x/8 = 15/2 => (4x + 5x)/40 = 15/2 => x   = 33 km.   Answer:33 km
Answer: C
Two prime numbers are considered consecutive if no other prime lies between them on the number line. If p1p1 and p2p2 are consecutive primes, with |p1–p2|>2, what is the smallest possible absolute value of the coefficient of the x term in the distributed form of the expression (x–p1)(x–p2)?  Choose the correct choice from the following answers:  A) 5  B) 8  C) 12  D) 18  E) 24

Solution: (x−p1)∗(x−p2)=x2−(p1+p2)x+p1p2   Value of (p1+p2) will be min. for the min consecutive primes which satisfy |p1-p2|>2   So the min. value p1 & p2 can take = 7, 11   p1+p2= 7+11= 
7+11 = 18
18   Answer. 18
Answer: D
Find the odd man out. 742, 743, 588, 853, 871, 990, 532 Choose the correct choice.
A) 532  B) 990  C) 588  D) 742  E) None of these

Solution: Explanation :   In all numbers except 588, the difference of third and first digit is the middle digit. Answer : Option 588
Answer: C
For a certain set of numbers, if x is in the set, then x - 4 is also in the set. If the number 1 is in the set , which of the following must also be in the set ?
a) 4
b) -3
c) -6
Choose one.
A) a only,  B) b only,  C) c only,  D) a and b only  E) b and c only

Solution: Notice that the question asks which of the following MUST be in the set, not COULD be in the set.   Since 1 is in the set, then so must be 1-4=-3. Similarly, since -3 is in the set, then so must be -3-3=-6. Could 4 and -1 be in the set? Certainly, but we don't know that for sure.   Answer: E.   Regarding your question: we don't know which is the source integer in the set, if it's 1, then 4 won't be in the set but if the source integer is say 7, then 4 will be in the set. So, 4 may or may not be in the set.
Answer: E
Two trains of equal lengths take 12 sec and 20 sec respectively to cross a telegraph post. If the length of each train be 120 m, in what time will they cross other travelling in opposite direction? Choices:	A) 17 sec	B) 15 sec	C) 16 sec	D) 11 sec	E) 18 sec

Solution: Speed of the first train = 120/12= 
120/12 = 10
10 m/sec.   Speed of the second train= 120/20= 
120/20 = 6
6 m/sec.   Relative speed= 10 + 6= 
10 + 6 = 16
16 m/sec.   Required time= (120 + 120)/16= 
(120 + 120)/16 = 15
15 sec.   Answer:15 sec
Answer: B
The owner of a furniture shop charges his customer 15% more than the cost price. If a customer paid Rs. 6400 for a computer table, then what was the cost price of the computer table?	Choose the correct choice from the following choices.
A) Rs.5565 B) Rs.6298 C) Rs.6290 D) Rs.6725 E) Rs.6708

Solution: CP = SP * (100/(100 + profit%))   = 6400(100/115) = Rs.5565.   Rs.5565nswer: Rs.5565
Answer: A
A vender sold two things at same cost of 12 RS with one item at 25%profit and other at 20%loss,by this transaction he made profit or loss by how much Choose the most appropriate option:
A) 0.60 loss B) 0.70 loss C) 0.80 loss D) 0.50 loss E) 0.40 loss

Solution: CP when profit of 25% = 9.60   CP when loss of 20% = 15   Total CP = 24.60   Total SP = 24.00   Total loss = 0.60   0.60 lossNSWER:0.60 loss
Answer: A
If a man buys 10 lollipops for $90 and sold them for $2 dollars determine his loss. Pick
A) 50 B) 60 C) 70 D) 80 E) 90

Solution: 70ost of 10 lollipops = $90   Sold each lollipop for $2   So he sold 10 lollipops for $(10 × 2) = $20   Loss = $(90 – 20) = $70   answer :70   Therefore, loss = $ 70.
Answer: C
A shopkeeper sold an article offering a discount of 4% and earned a profit of 20%. What would have been the percentage of profit earned if no discount was offered?	Pick:
A) 25
B) 28
C) 30
D) 32
E) 34

Solution: Let C.P. be Rs. 100.   Then, S.P. = Rs. 120   Let marked price be Rs. x. Then, 96/100 x = 120   x = 12000/96 = Rs. 125   Now, S.P. = Rs. 125, C.P. = Rs. 100   Profit % = 25%.   25NSWER:25
Answer: A
In a division sum, the quotient is 20, the divisor 66 and the remainder 55, find the dividend? Select.
A) 1375 B) 1376 C) 1875 D) 1365 E) 1345

Solution: Explanation:   20 * 66 + 55= 
20 * 66 + 55 = 1_375
1375   1375nswer : 1375
Answer: A
Aunt Marge is giving candy to each of her nephews and nieces. She has 20 pieces of candy and she gives all the candy to the children according to her wish. If Robert gets 2 more pieces than Kate, Bill gets 6 less than Mary, Mary gets 2 more pieces than Robert, and Kate gets 2 more pieces than Bill, how many pieces of candy does Kate get?	Choices
A) 2 B) 4 C) 6 D) 8 E) 10

Solution: Use the initial letter of each name as a variable:   r=k+2   b=m−6   m=r+2= 
+2 = 2
2+bk==r−2   b=k−2=(r−2)−2=r−4   m=r+2   r+b+m+k=20   r+r−4+r+2+r−2=20   r=6   k=r−2=6−2=4   Answer: 4
Answer: B
Ravi purchased a refrigerator and a mobile phone for Rs. 10000 and Rs. 8000 respectively. He sold the refrigerator at a loss of 4 percent and the mobile phone at a profit of 10 percent. Overall he make a.	Choose the correct choice from the following answers
A) loss of Rs. 200 B) loss of Rs. 100 C) profit of Rs. 100 D) profit of Rs. 400 E) None of these

Solution: Total C.P. = 10000+8000= 
10000+8000 = 18_000
18000   S.P. of fridge= 10000/100*96= 
10000/100*96 = 9_600
9600   S.P. of Mobile= 8000/100*110= 
8000/100*110 = 8_800
8800   Total S.P.= 9600 + 8800= 
9600 + 8800 = 18_400
18400   Tota. S.P. - Total C.P.= 18400 - 18000= 
18400 - 18000 = 400
400   Answer : profit of Rs. 400
Answer: D
My brother is 2 years elder to me. My father was 28 years of age when my sister was born while my mother was 26 years of age when I was born. If my sister was 1 years of age of when my brother was born, then, what was the age of my father and mother respectively when my brother was born?  Answers
A) 32 yrs, 23 yrs  B) 30 yrs, 25 yrs  C) 35 yrs, 29 yrs  D) 35 yrs, 33 yrs  E) none

Solution: Sol.   Clearly, my brother was born 2 years before I was born and 1 years after my sister was born.   So, father's age when brother was born = (28 + 2)= 
(28 + 2) = 30
30 years.   mother's age when was born= (26 - 1)= 
(26 - 1) = 25
25 years.   Answer 30 yrs, 25 yrs
Answer: B
Two dogsled teams raced across a 200-mile course in Alaska. Team A finished the course in 2 fewer hours than team B. If team A’s average speed was 5 miles per hour greater than that of team B, what was team B’s average speed, in miles per hour?  Pick:	A) 12	B) 15	C) 18	D) 20	E) 25

Solution: Let v be team B's average speed.   Time = Distance/Rate and the time difference was 2 hours.   200/v - 200/(v+5)= 2   200v + 1000 - 200v = 2(v)(v+5)   500 = (v)(v+5)   (20)(25) = (v)(v+5)   v = 20 mph   The answer is 20.
Answer: D
When the integer n is divided by 17, the quotient is x and the remainder is 7. When n is divided by 23, the quotient is y and the remainder is 14. Which of the following is true? Pick:	A) 23x + 17y =19	B) 17x –23y = 7	C) 17x +23y =19	D) 14x + 5y = 6	E) 5x – 14y = -6

Solution: From the problem it follows:   n=17x+7   n=23y+14   So, 17x+7=23y+14   17x-23y=7   The answer is 17x –23y = 7
Answer: B
If a person walks at 14 km/hr instead of 10 km/hr, he would have walked 20 km more. What is the actual distance travelled by him?	Choose the correct choice from the following options:
A) 33
B) 11
C) 38
D) 50
E) 12

Solution: Assume that the person would have covered x km if travelled at 10 km/hr   ⇒Speed = 50istanceTime=x10.....(Equation1)   Give that the person would have covered (x + 20) km if travelled at 14 km/hr   ⇒Speed = 50istanceTime=(x+20)14.....(Equation2)   From Equations 1 and 2,   x10=(x+20)1414x=10x+2004x=200x=2004=50   Answer : 50
Answer: D
R is the set of positive odd integers less than 40, and S is the set of the squares of the integers in R. How many elements does the intersection of R and S contain ?
Choose the correct choice from the following answers
A) None B) Three C) Four D) Five E) Seven

Solution: squares < 40 {1,4,9,16,25,36}   S = {1,9,25}   R = {1,3,.....40}   Hence Three.
Answer: B
A straight fence is to be constructed from posts 7 inches wide and separated by lengths of chain 5 feet long. If a certain fence begins and ends with a post, which of the following couldnotbe the length of the fence in feet? (12 inches = 1 foot)  Pick:
A) 17 B) 28 C) 35 D) 39 E) 50

Solution: The fence begins and ends with a post: {post = 0.5 feet}{chains = 5 feet}{post = 0.5 feet}...{chains = 5 feet}{post = 0.5 feet}   The minimum length is with 2 posts = 0.5 + 5 + 0.5= 
0.5 + 5 + 0.5 = 6
6 feet. To increase the fence, each time we should add{post= 0.5 feet}{chains = 5 feet}, so 5.5 feet. Thus, the lengths could be:   6 feet;   7+ 5.5= 
7+ 5.5 = 12.5
12.5 feet;   11.5 + 5.5= 18 feet;   17 + 5.5 = 23.5 feet;   22.5 + 5.5 = 29feet;   28 + 5.5 = 34.5 feet;   33.5 + 5.5 = 40 feet.   ...   We skipped 39 feet.   Answer: 39.
Answer: D
Anu normally takes 4 hours more than the time taken by Sachin to walk D km. If Anu doubles her speed, she can make it in 2 hours less than that of Sachin. How much time does Sachin require for walking D km?  Choices:
A) 10 hours	B) 4 hours	C) 8 hours	D) 9 hours	E) None

Solution: Explanation :   Let Sachin takes x hours to walk D km.   Then, Anu takes (x + 4) hours to walk D km.   With double of the speed, Anu will take (x + 4)/2 hours.   x – (x + 4)/2 = 2    (  + 4)/2= 
 (  + 4)/2 = 2
2=> 2x – (x + 4) = 4    (  + 4)= 
 (  + 4) = 4
4=> 2x – x – 4 = 4   x = 4 + 4= 
4 + 4 = 8
8 hours   Answer – 8 hours
Answer: C
Convert the following into a fraction: 0.5% Pick one.
A) 1/5
B) 1/2
C) 5/10
D) 2/5
E) None of the Above

Solution: 0.5 =5/10 (Simplify: both are divisible by 5)= 1/2   Answer is 1/2.
Answer: B
If 5 < x < 12 and y = x + 3, what is the greatest possible integer value of x + y?
Choose the correct choice from the following options:
A) 23
B) 24
C) 25
D) 26
E) 27

Solution: x+y = x+x+3 = 2x+3   We need to maximize this value and it needs to be an integer.   2x is an integer when the decimal of x is .0 or .5   The largest such value is 11.5   Then x+y = 11.5 + 14.5= 
11.5 + 14.5 = 26
26.   The answer is 26.
Answer: D
The average weight of 9 person's increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg. What is the weight of the new person?	Choose the most appropriate option
A) 85.5  B) 86.5  C) 87.5  D) 88.5  E) 89.5

Solution: Total increase in weight =9 × 2.5 = 22.5   If x is the weight of the new person, total increase in weight = x−65   => 22.5 = x - 65   => x = 22.5 + 65= 
22.5 + 65 = 87.5
87.5   ANSWER:87.5
Answer: C
Ron begins reading a book at 4: 30 p.m. and reads at a steady pace of 30 pages per hour. Michelle begins reading a copy of the same book at 6: 00 p.m. If Michelle started 5 pages behind the page that Ron started on and reads at an average pace of 50 pages per hour, at what time would Ron and Michelle be reading the same page?
Pick one
A) 7: 00 p.m.  B) 7: 30 p.m.  C) 7: 45 p.m.  D) 8: 00 p.m.  E) 8: 30 p.m.

Solution: Ron's speed is 30 pages per hour =1/2 page per minute   Time at which he starts reading is 4:30 pm   now,   by the time Michelle beings reading (6:00 pm) Ron has already covered  (1/2)*90= 
 (1/2)*90 = 45
45 pages   as per the question   Michelle starts 5 pages behind the page Ron started and her speed is 5/6 pages per minute   relative speed= 5/6-1/2=1/3   pages left =45+5= 
45+5 = 50
50   time taken to read those pages=50/(1/3)= 
50/(1/3) = 150
150 minutes   Thus time taken to reach the same page   6:00 pm + (150 minutes)=8:30 pm   ANSW8: 30 p.m.R:8: 30 p.m.
Answer: E
By selling an article at Rs.120, a profit of 25% is made. Find its cost price?
Choose one:  A) s.96  B) s.45  C) s.120  D) s.180  E) s.189

Solution: SP = 120   CP = (SP)*[100/(100+P)]   = 120* [100/(100+25)]   = 120* [100/125]   = Rs.96   s.96nswer: s.96
Answer: A
Mudit's age 16 years hence will be thrice his age four years ago. Find Mudit's present age? Pick.
A) 14  B) 19  C) 27  D) 18  E) 15

Solution: Explanation:   Let Mudit's present age be 'm' years.   m + 16 = 3(m - 4)   => 2m = 28 => m = 14 years.   14nswer:14
Answer: A
Anna left for city A from city B at 5.20 a.m. She travelled at the speed of 80 km/hr for 2 hrs 15 min. After that the speed was reduced to 60 km/hr. If the distance between two cities is 350 kms, at what time did Anna reach city A?  Pick one:  A) 10.25 a.m  B) 9.25 a.m  C) 11.25 a.m  D) 12.25 a.m  E) 01.25 a.m

Solution: A   10.25 a.m   Distance covered in 2 hrs 15 min i.e., 2 1/4 hrs = 80 * 9/4= 
80 * 9/4 = 180
180 hrs.   Time taken to cover remaining distance= (350 - 180)/60 = 17/6 hrs   = 2 5/6 = 2 hrs 50 min   Total time taken = (2 hrs 15 min + 2 hrs 50 min) = 5 hrs 5 min.   So, 10.25 a.mnna reached city 10.25 a.m at 10.25 a.m.
Answer: A
John and Karen begin running at opposite ends of a trail until they meet somewhere in between their starting points. They each run at their respective constant rates until John gets a cramp and stops. If Karen runs 50% faster than John, who is only able to cover 25% of the distance q before he stops, what percent longer would Karen have run than she would have had John been able to maintain his constant rate until they met. Choices:	A) 25%	B) 50%	C) 75%	D) 100%	E) 200%

Solution: John and Karen begin running at opposite ends of a trail until they meet somewhere in between their starting points. They each run at their respective constant rates until John gets a cramp and stops. If Karen runs 50% faster than John, who is only able to cover 25% of the distance q before he stops, what percent longer would Karen have run than she would have had John been able to maintain his constant rate until they met.   Lets say the distance of the trail is 100 miles. Lets also say that J rate = 10 miles/hour and K rate = 15 miles/hour.   If John stops at the 25% mark that means he travels 25 miles in 2.5 hours. It would take Karen t=d/r t=75/15= 
75/15 = 5
5 hours to reach john. If John had not stopped, their combined rate would 10+15= 
10+15 = 25
25 miles/hour meaning they would have met in 4 hours. Therefore, she ran one hour longer (25%) longer than she would have needed to if John ran for the entire time.   25%NSWER: 25%) 25%
Answer: A
A began business with Rs.45000 and was joined afterwards by B with Rs.5400. When did B join if the profits at the end of the year were divided in the ratio of 2:1?	Choose the correct choice from the following choices:
A) 5  B) 6  C) 7  D) 9  E) 3

Solution: 45*12 : 54*x = 2: 1   x = 5   12 -5= 
12 -5 = 7
7   Answer:7
Answer: C
The equal amounts of money are deposited in two banks each at 15% per annum for 3.5 years and 10 years respectively. If the difference between their interests is Rs.144, find the each sum?  Options:	A) Rs.117.69	B) Rs.147.69	C) Rs.137.69	D) Rs.157.69	E) Rs.127.69

Solution: (P*10*15)/100 - (P*3.5*15)/100 = 144   => P = Rs.147.69   ANSWER:Rs.147.69
Answer: B
A person's present age is two-fifth of the age of his mother. After 8years, he will be one - half of the age of his mother. How old is the mother at present ? Choices
A) 25
B) 40
C) 32
D) 45
E) 28

Solution: Let the mother's present age be x years   Then the person's present age = 2x/5   (2x/5)+8 = 1/2(x+8)   2(2x+40) = 5 (x+8)   x = 40   Answer is 40
Answer: B
A group of men decided to do a work in 20days, but 2 of them became absent. If the rest of the group did the work in 22days, Find the original number of men?
Choose the correct choice: A) 15 B) 22 C) 27 D) 29 E) 18

Solution: Original number of men = 2*22 / (22-20)= 
2*22 / (22-20) = 22
22   Answer is 22
Answer: B
If the weight of 13 meters long rod is 23.4 kg. What is the weight of 6 meters long rod ?
Options
A) 7.2 kg.
B) 10.8 kg.
C) 12.4 kg.
D) 18.0 kg
E) None

Solution: Answer   ∵Weight of 13 m long rod = 23.4 kg   ∴ Weight of 1 m long rod = 23.4 / 13 kg   ∴ Weight of 6 m long rod = 23.4 x 6 / 13   = 10.8 kg   Option: 10.8 kg.
Answer: B
The difference between the length and breadth of a rectangle is 23 m. If its perimeter is 206 m, then its area is: Choose the correct choice from the following choices:
A) 1520 m2 B) 2420 m2 C) 2480 m2 D) 2520 m2 E) None

Solution: EXPLANATION   We have: (l – b) = 23 and 2(l + b) = 206 or (l + b) = 103.   Solving the two equations, we get: l = 63 and b = 40.   Area = (l x b) = (63 x 40) m2 = 2520 m2.   Answer 2520 m2
Answer: D
A boatman goes 2 km against the current of the stream in 1 hour and goes 1 km along the current in 10 minutes. How long will it take to go 5 km in stationary water?	Choose the correct choice from the following answers
A) 40 minutes	B) 1 hour	C) 1 hr 15 min	D) 1 hr 30 min	E) 1 hr 40 min

Solution: 2km in 1hr=2km/hr   1 km in 10 minutes means [1/10]*60=6km/hr   speed in still water is 1/10 *60= 
 1/10 *60 = 6
6km/hr   speed in still water is=1/2(6+2)=4km/hr   Required time=[5/4]hrs means 1hr 15 minutes   ANSWER:1 hr 15 min
Answer: C
John walked to the bus stop at a speed of 3 kph, but walked home at a speed of 6 kph. What was his average speed walking to and from the bus stop?	Pick.
A) 9 kph	B) 3 kph	C) 4.5 kph	D) 6 kph	E) 18 kph

Solution: (3 kph + 6 kph)/2= 4.5 kph   4.5 kphorrect answer is 4.5 kph
Answer: C
A word is defined as a sequence of four dots arranged in a row. Each dot is colored either yellow or blue. How many distinct words can be formed?	Choose the correct choice from the following answers.
A) 4	B) 8	C) 12	D) 16	E) 20

Solution: 2^4 = 16   The answer is 16.
Answer: D
The ratio between the sale price and the cost price of an article is 7:5. What is the ratio between the profit and the cost price of that article?	Pick
A) 2:8
B) 2:1
C) 2:2
D) 2:4
E) 2:5

Solution: Explanation:   Let C.P. = Rs. 5x and S.P. = Rs. 7x.   Then, Gain = Rs. 2x   Required ratio = 2x : 5x = 2:5   Answer:2:5
Answer: E
Find the probability if a two digit number multiplied by 3 but not 5	Choose the correct choice from the following choices:
A) 2/15
B) 3/15
C) 4/15
D) 5/15
E) 6/15

Solution: sample space of 2 digit number = (99-10)+1= 
(99-10)+1 = 90
90   probability of number multiplied by 3 but not 5= total no. multiplied by 3 - total no. multiplied by 5   = 30 - 6= 
30 - 6 = 24
24   so, probability= 24/90 = 4/15   ANSWER:4/15
Answer: C
In Rwanda, the chance for rain on any given day is 1/2. What is the probability that it rains on 5 out of 8 consecutive days in Rwanda? Select the correct option.
A) 4/7	B) 3/7	C) 7/32	D) 4/28	E) 28/135

Solution: using Binomial. theorem   n7/32r (p)^r (q)^n-r   87/325 (1/2)^5 (1/2)^r   which is 7/32   Answer is 7/32.
Answer: C
The pilot of a small aircraft with a 40-gallon fuel tank wants to fly to Cleveland, which is 480 miles away. The pilot recognizes that the current engine, which can fly only 10 miles per gallon, will not get him there. By how many miles per gallon must the aircraft’s fuel efficiency be improved to make the flight to Cleveland possible?  Pick.
A) 2  B) 4  C) 12  D) 40  E) 160

Solution: Actual miles/gallon is = 480/40= 
480/40 = 12
12 miles/gallon.   Current engine miles/gallon is 10 miles/gallon.   Additional 2 miles/gallon is required to match the actual mileage.   IMO option 2.
Answer: A
Average of 5 numbers is zero. At most how many numbers may be greater than zero	Choices:  A) 0  B) 4  C) 5  D) 9  E) 10

Solution: Answer: Option 4
Answer: B
A table is bought for Rs.400/- and sold at Rs.500/- find gain or loss percentage	Choices:
A) 25% gain
B) 20% gain
C) 20% loss
D) 15% gain
E) None

Solution: Formula = (Selling price ~ Cost price)/Cost price * 100   = (500 - 400)/400 = 25% gain   25% gain
Answer: A
A train is moving at a speed of 132 km/hr. If the length of the train is 150 meters, how long will it take to cross a railway platform 235 meters long Answers:	A) 6 ½ sec	B) 7 ½ sec	C) 8 sec	D) 10 ½ sec	E) 9 sec

Solution: Explanation:   Speed of train = 132 ×(5/18) m/sec = 110/3 m/sec.   Distance covered in passing the platform = (150 + 235)= 
(150 + 235) = 385
385 m.   Time taken=385 ×(3/110) sec =21/2 sec = 710½ sec   Answer: Option 10 ½ sec
Answer: D
If x is a sum of all even integers on the interval 13...65 and y is their number, what is the GCD (x, y)?  Choose the correct choice:
A) 1
B) 13
C) 26
D) 52
E) 1014

Solution: x = 14 + 16 + ... + 64 = (largest + smallest)/2 *(# of terms) = (14 + 64)/2*26 = 39*26.   GCD of 26 and 39*26 is 26.   Answer: 26.
Answer: C
How many pages the book have, if total 300 digits are used to form the page numbers?
Choose the correct choice from the following options
A) 135 pages B) 136 pages C) 137 pages D) 138 pages E) 139 pages

Solution: First 9 pages .. 9 digits   next 90 pages .. 180 digits   next 37 pages ... 111 digits   ----------------------   Total ...136 pages ...300 digits   ANSWER:136 pages
Answer: B
The sum of two numbers is 16. The difference is 4. What are the two numbers?  Choose the correct choice from the following:	A) 10-6	B) 8-8	C) 9-7	D) 11-5	E) 13-3

Solution: Let x be the first number. Ley y be the second number   x + y = 16   x - y = 4   Solve the system of equations by elimination   10-6dding the left sides and the right sides gives:   x + x + y + -y = 16 + 4   2x = 20   x = 10   Since x + y = 16, 10 + y = 16   10 + y = 16   10 - 10 + y = 16 - 10= 
16 - 10 = 6
6   The numbers are 10 and 6   correct answer is 10-6)10-6
Answer: A
How many four digit even numbers can be formed using the digits {2, 3, 5, 1, 7, 9}	Pick one
A) 76	B) 88	C) 77	D) 67	E) 60

Solution: The given digits are 1, 2, 3, 5, 7, 9   A number is even when its units digit is even. Of the given digits, two is the only even digit.   Units place is filled with only '2' and the remaining three places can be filled in ⁵P₃ ways.   Number of even numbers = ⁵P₃ = 60.   Answer:60
Answer: E
For the sequence a1, a2, a3. ..an, an is defined by an=1/2n−1−1/2n for each integer n≥1. What is the sum of the first 8 terms of the sequence?  Pick
A) 63/64
B) 127/128
C) 255/256
D) 511/512
E) 513/512

Solution: a1=1/2^0−1/2^1   a2=1/2^1−1/2^2....   a8=1/2^7−1/2^8   a1+a2+...+a8=1/2^0−1/2^8=255/256   The answer is 255/256.
Answer: C