MU-NLPC/Calc-aqua_rat huggingface dataset:
In a class of 25 students, 2 students did not borrow any books from the library, 10 students each borrowed 1 book, 8 students each borrowed 2 books, and the rest of the students each borrowed at least 3 books. If the average (arithmetic mean) number of books borrowed per student was 2, what is the maximum number of books that any single student could have borrowed ? Choose the correct choice from the following choices:
A) 8
B) 10
C) 12
D) 13
E) 15

Solution: The average number of books per student was 2means that total of   2*25= 
  2*25 = 50
50 books were borrowed;   2+10+8= 
2+10+8 = 20
20 students borrowed total of  2*0+10*1+8*2= 
 2*0+10*1+8*2 = 26
26 books;   So  50-26= 
 50-26 = 24
24 books are left to distribute among 25-20= 
25-20 = 5
5 students, these 5 arethe rest who borrowed at least 3 books;   Tomaximizethe number of books one student from above 5 could have borrowed we shouldminimizethe number of books other 4 students from 5 could have borrowed. Minimum these 4 students could have borrowed is 4 books per student, so total number of books they could have borrowed is 4*3= 
4*3 = 12
12 books. So the 5th student could have borrowed is  24-12= 
 24-12 = 12
12 books.   Answer: 12.
Answer: C
AB + CD = JJJ, where AB and CD are two-digit numbers and JJJ is a three digit number; A, B, C, and D are distinct positive integers. In the addition problem above, what is the value of C? Select the correct option
A) 1	B) 3	C) 7	D) 9	E) Cannot be determined

Solution: AB and CD are two digit integers, their sum can give us only one three digit integer of a kind of JJJ it's 111.   So, A=1. 1B+C9=111   Now, C can not be less than 9, because no to digit integer with first digit 1 (mean that it's<20) can be added to two digit integer less than 90 to have the sum 111 (if C9<90 meaning C<9 C9+1B<111) --> C=9   Answer: 9.
Answer: D
A single discount equivalent to the discount series of 20%, 15% and 5% is? Select
A) 31.6 B) 35.4 C) 31.6 D) 31.1 E) 31.5

Solution: 100*(80/100)*(85/100)*(95/100)   = 68.4   100 - 64.6= 
100 - 64.6 = 35.4
35.4   Answer: 35.4
Answer: B
325.124 x 12.98 Ã· 3.001 + 21.21 = ?	Choose the most appropriate option
A) 1430.08	B) 1420.06	C) 781.189	D) 656.112	E) 456.512

Solution: Explanation:   ? = 325.124 x 12.98 Ã· 3.001 + 21.21 = ?   â‰ˆ (325.124 x 13/3) + 21.21 â‰ˆ 1408.87 + 21.21 â‰ˆ 1430.080   1430.08nswer: Option 1430.08
Answer: A
There is food for 760 men for 22 days. How many more men should join after two days so that the same food may last for 19 days more? Options
A) 16	B) 40	C) 18	D) 19	E) 11

Solution: 760 ---- 22   760 ---- 20   x ----- 19   x*19 = 760*20   x = 800   760   -------   40   Answer:40
Answer: B
Suresh and Ramesh started a business investing Rs. 24,000 and Rs. 40,000 respectively. Out of total profit of Rs. 19,000, what is Suresh's share? Select the correct option.
A) s. 7125	B) s. 8125	C) s. 9125	D) s. 9372	E) s. 9875

Solution: Explanation:   Ratio of Suresh and Ramesh's share = 24,000 : 40,000 = 3 : 5   Suresh's share = Rs. (19000 x 3 / 8) = Rs. 7125   s. 7125NSWER: s. 7125
Answer: A
10 x 0.5 = ?
Choices
A) 0.0001
B) 0.001
C) 0.01
D) 0.1
E) 5

Solution: Explanation:   10 x 5 = 50.   Sum of decimal places = 1   10 x 0.5 = 5   Answer- 5
Answer: E
If (t-8) is a factor of t^2-kt-43, then k=  Choose the correct choice from the following choices
A) 16
B) 12
C) 2
D) 3
E) 14

Solution: t^2-kt-48 = (t-8)(t+m) where m is any positive integer.   if 48/8= 
48/8 = 6
6, then we know as a matter of fact that:   m= +6   and thus k = 8-6 = 3   t^2-kt-m = (t-a)(t+m) where a>m   t^2+kt-m = (t-a)(t+m) where a<m   t^2-kt+m = (t-a)(t-m)   t^2+kt+m = (t+a)(t+m)   3
Answer: D
If there are 6 pairs of twins, and a committee will be formed with 3 members. In how many ways this committee formed in a way that no siblings in a group? Options
A) 32	B) 24	C) 56	D) 144	E) 160

Solution: Firstly, there are 6 ways to choose 3 groups from the 4 groups. Hence 6C3.   Next, with the 3 groups chosen, there are 2^3 choices of choosing either one of the siblings.   Hence, the total number of ways are 6C3 * (2^3) = 160   160
Answer: E
Find the compound interest on Rs. 10000 at 12% rate of interest for 1 year, compounded half-yearly Choose the correct choice:	A) Rs. 1036	B) Rs. 1236	C) Rs. 1186	D) Rs. 1206	E) Rs. 1226

Solution: Amount with CI = 10000 [1+ (12/2 * 100)]2 = Rs. 11236   Therefore, CI = 11236 – 10000 = Rs. 1236 ANSWER :Rs. 1236
Answer: B
In how many no. between 100 and 1000 exactly one of the digits is 3?  Choose the correct choice from the following options:  A) 648  B) 512  C) 252  D) 225  E) 26

Solution: Another approach can be   total nos. between 100 and 1000 are 899   nos. in which all digits are 3 = 1   nos. in which digit 3 is in two places = 8 + 9 + 9= 
8 + 9 + 9 = 26
26 (for thousand , tens and once as different digit)   nos. in which no digit is 3= 8*9*9 - 1 = 648 - 1 (for 100 not to be included)   required nos = 899 - 1 - 26 - 647= 
899 - 1 - 26 - 647 = 225
225   answer is 225
Answer: D
a manufacturing company has 15% cobalt ,25% led and 60% of copper. if 5kg of led is used in a mixture how much copper we need to use	Choices.
A) 12 kg B) 13 kg C) 22 kg D) 14 kg E) 15 kg

Solution: 25%=5kg   100%=20kg   60% of 20 kg= 12kg   12 kg   12 kgNSWER:12 kg
Answer: A
A boy has nine trousers and 15 shirts. In how many different ways can he select a trouser and a shirt? Select the correct option: A) 88 B) 98 C) 106 D) 135 E) 111

Solution: Explanation:   The boy can select one trouser in nine ways.   The boy can select one shirt in 15 ways.   The number of ways in which he can select one trouser and one shirt is   9 * 15= 
  9 * 15 = 135
135 ways   135)
Answer: D
A person crosses a 600 m long street in 5 minutes. What is his speed in km per hour? Choose the correct choice
A) 5.2 km/hr.  B) 8.2 km/hr.  C) 7.2 km/hr.  D) 3.2 km/hr.  E) 4.2 km/hr.

Solution: C   7.2 km/hr.   Speed=(600/5 * 60) m/sec   = 2 m/sec.   7.2 km/hr.onverting m/sec to km/hr   =(2*18/5) km/hr   = 7.2 km/hr.
Answer: C
The expression (3x-2)/(x+3) is equivalent to which of the following?	Choose the most appropriate option:
A) (5-2)/3
B) 5 – (2/3)
C) 3 – (11)/(x+3)
D) 5 – (17)/(x+3)
E) 5 + (17)/(x+3)

Solution: Easiest way is to pick any number and put in (3x-2)/(x+3). Then check the options with the same number.   I took x=1 and got 3 – (11)/(x+3) as the answer.
Answer: C
A completes 80% of a work in 20 days. Then B also joins and A and B together finish the remaining work in 3 days. How long does it need for B if he alone completes the work? Choose the correct choice from the following choices:
A) 35 1/2	B) 36 1/2	C) 37 1/2	D) 38 1/2	E) 39 1/2

Solution: Explanation:   Work done by A in 20 days = 80/100 = 8/10 = 4/5   Work done by A in 1 day = (4/5) / 20 = 4/100 = 1/25 --- (1)   Work done by A and B in 3 days = 20/100 = 1/5 (Because remaining 20% is done in 3 days by A and B)   Work done by A and B in 1 day = 1/15 ---(2)   Work done by B in 1 day = 1/15 â€“ 1/25 = 2/75   => B can complete the work in 75/2 days = 37 (1/2) days   ANSWER IS 37 1/2
Answer: C
In a 100m race, Sam beats John by 4 seconds. On the contrary, if Sam allowed John to start 24m ahead of Sam, then Sam and John reach the finishing point at the same time. How long does Sam take to run the 100m race?  Options:
A) 4 seconds	B) 25 seconds	C) 19 seconds	D) 21 seconds	E) 6.25 seconds

Solution: Their difference is 4 second but this difference is 0 if john allows Sam to start the race from 24m ahead . that means Jhon was 24m away from finishing line when they started together . so He will cover 24 m in 4 seconds . so his speed =24/4= 
24/4 = 6
6 metre / second . so time taken=100/4= 
100/4 = 25
25 seconds . so Sam took= 19 seconds .   correct answer = 19 seconds
Answer: C
A sum of 13,400 amounts to 14,400 in 2 years at the rate of simple interest. What is the rate of interest? Choose the correct option
A) 2%
B) 1%
C) 6%
D) 4%
E) 8%

Solution: D   4%   S.I. = (14400 - 13400)= 
(14400 - 13400) = 1_000
1000.   Rate= (100 x 1000)/(13400x2)% = 4%
Answer: D
The rate of Interest on a sum of money is 5% p.a. for the first 3 years, 4% p.a. for the next 4 years, and 5% for the period beyond 7 years. If the S.I, Occured on the sum for the total period of 8 years is Rs. 540/-, the sum is
Pick:
A) 1,500
B) 2,000
C) 2,100
D) 2,250
E) 2,540

Solution: Explanation:   I1 = (P x 3 x 5)/100 = 3P/20   I2 = (P x 4 x 4)/100 = 4P/25   I3 = (P x 1 x 5)/100 = P/20   3P/20 + 4P/25 + P/20 = 540   9P/25 = 540   P = 1500   1,500nswer: Option 1,500
Answer: A
A family consists of two grandparents, two parents and three grandchildren. The average age of the grandparents is 67 years, that of the parents is 35 years and that of the grandchildren is 6 years. What is the average age of the family?	Choose the correct choice from the following options.
A) 31 5/7	B) 32	C) 33	D) 35	E) 37

Solution: Required average   = 67 x 2 + 35 x 2 + 6 x 3   2 + 2 + 3   = 134 + 70 + 18   7   =	222   7   = 31 5	years.   7   Option 31 5/7
Answer: A
When the smallest of 3 consecutive odd integers is added to four times the largest, it produces a result 732 more than 4times the middle integer. Find the numbers? Select:  A) 732  B) 678  C) 698  D) 710  E) 729

Solution: x + 4 (x + 4) = 732 + 4 (x + 2)   Solve for x and find all three numbers   x + 4 x + 16 = 732 + 4 x + 8   x = 724   x + 2 = 726   x + 4 = 728   Check: the smallest is added to four times the largest   724 + 4 * 728= 
724 + 4 * 728 = 3_636
3636   four times the middle   4 * 726= 
4 * 726 = 2_904
2904   3636 is more than 2904 by   3636 - 2904= 
3636 - 2904 = 732
732   732
Answer: A
A certain company retirement plan has arule of 70provision that allows an employee to retire when the employee's age plus years of employment with the company total at least 70. In what year could a female employee hired in 1989 on her 32nd birthday first be eligible to retire under this provision?  Answers:
A) 2008 B) 2004 C) 2005 D) 2006 E) 2007

Solution: She must gain at least 70 points, now she has 32 and every year gives her two more points: one for age and one for additional year of employment, so 32 + 2*(# of years) = 70 --> (# of years) = 19 --> 1989+19=2008.   2008nswer: 2008.
Answer: A
A and B complete a work in 10 days. A alone can do it in 14 days. If both together can do the work in how many days?	Pick one
A) 3.75 days B) 5.8 days C) 4.5 days D) 4.7 days E) 5.75 days

Solution: 1/10 + 1/14 =6/35   35/6 = 5.8 days   Answer:5.8 days
Answer: B
10 men, working 8 hours a day can complete a work in 18 days. How many hours a day must 15 men work to complete the work in 12 days ?  Choices: A) 4 hours a day B) 5 hours a day C) 6 hours a day D) 7 hours a day E) 8 hours a day

Solution: 8 hours a dayxplanation:   More Men, Less Hours {Indirect Proportion}   Less Days, More Hours {Indirect Proportion}   [men 15 10   days 12 18] ::8:x   =>xâˆ—15âˆ—12=10âˆ—18âˆ—8   =>x=10âˆ—18âˆ—8/ 15âˆ—12   =>x=8   Option 8 hours a day
Answer: E
A, B and C invested Rs.6300, Rs.4200 and Rs.10500 respectively, in a partnership business. Find the share of A in profit of Rs.12300 after a year?
Choose the correct choice from the following.
A) 3630	B) 3690	C) 3630	D) 3631	E) 3635

Solution: 6300:4200:10500   3:2:5   3/10 * 12300= 
3/10 * 12300 = 3_690
3690   Answer: 3690
Answer: B
At the start of an experiment, a certain population consisted of 3 animals. At the end of each month after the start of the experiment, the population size was double its size at the beginning of that month. Which of the following represents the population size at the end of 11 months?	Select the correct option
A) 2^3 B) 3^2 C) 2(3^10) D) 3(2^11) E) 3(10^2)

Solution: 3*2^n where n is the #of month --> 3*2^11 Answer (3(2^11))
Answer: D
If n is the product of three consecutive integers, and n is divisible by 5, which of the following is not necessarily a divisor of n ? Choose the correct answer.
A) 210  B) 220  C) 230  D) 240  E) 250

Solution: IF ONE NO. IS 5 THEN OTHER CONSEQUTIVE NO. 210RE 3*4*5= 
3*4*5 = 60
60 , 4*5*6=120 , 5*6*7 =210   210 WILL NO BE DIVISOR OF N   210
Answer: A
If 280 people, constituting 5 percent of the population of a town, ride bicycles, and the others do not, then how many people in the town do not ride bicycles?  Choose the correct choice from the following choices.
A) 5930 B) 5600 C) 5320 D) 5110 E) 4980

Solution: 5 % of X is 280   5/100 * X = 280   X = 280*100/5= 
280*100/5 = 5_600
5600   So C. 5320 is the correct Answer   No. of people Not Riding Bike= 5600 - 280= 
5600 - 280 = 5_320
5320   answer is 5320
Answer: C
In one hour, a boat goes 14 km/hr along the stream and 8 km/hr against the stream. The speed of the boat in still water (in km/hr) is:
Choose the most appropriate option.
A) 12 km/hr	B) 11 km/hr	C) 10 km/hr	D) 8 km/hr	E) 15 km/hr

Solution: EXPLANATION   Let speed of the boat in still water = a and speed of the stream = b   Then   a + b = 14   a - b = 8   Adding these two equations, we get 2a = 22   => a = 11   ie, speed of boat in still water = 11 km/hr   ANSWER IS 11 km/hr
Answer: B
50 square stone slabs of equal size were needed to cover a floor area of 72 sq.m. Find the length of each stone slab?  Choose the correct choice from the following answers.
A) 120cm  B) 767cm  C) 88cm  D) 666cm  E) 776cm

Solution: 120cmrea of each slab   =72/50m2=1.44m2   Length of each slab √1.44=1.2m=120cm
Answer: A
If the average (arithmetic mean) of a and b is 45 and the average of b and c is 70, what is the value of c − a?
Options: A) 25 B) 50 C) 90 D) 140 E) It cannot be determined from the information given.

Solution: the arithmetic mean of a and b =(a+b)/2=45 -- a+b=90 --1   similarly for b+c=140 --2   subtracting 1 from 2 we have   c-a=50 ANSWIt cannot be determined from the information given.R:It cannot be determined from the information given.
Answer: E
If one of the followings is the product of the two 3-digit integers 8K1 and 6L5 (K and L denote the tens digit of the respective integers), then that product must be
Choose one.
A) 478,823
B) 511,913
C) 531,875
D) 538,424
E) 569,114

Solution: To know the unit digit you can multiply both digit number: 1 x 5 = 5   This eliminates A, B, D, and E, because the number must end with a 5   So the answer is 531,875
Answer: C
If a: b = 6:4, b: c =7: 8, find a: b: c?	Select: A) 24: 28: 32 B) 42: 28: 36 C) 42: 28: 38 D) 42: 28: 32 E) 22: 28: 32

Solution: a: b = 6:4   b: c =7: 8   a: b: c = 42: 28: 32   Answer : 42: 28: 32
Answer: D
An escalator is descending at constant speed. A walks down and takes 50 steps to reach the bottom. B runs down and takes 90 steps in the same time as A takes 10 steps. How many steps are visible when the escalator is not operating?	Choose one
A) 80
B) 90
C) 100
D) 110
E) 120

Solution: Lets suppose that A walks down 1 step / min and   escalator moves n steps/ min   It is given that A takes 50 steps to reach the bottom   In the same time escalator would have covered 50n steps   So total steps on escalator is 50+50n.   Again it is given that B takes 90 steps to reach the bottom and time   taken by him for this is equal to time taken by A to cover 10 steps i.e   10 minutes. So in this 10 min escalator would have covered 10n steps.   So total steps on escalatro is 90 + 10n   Again equating 50 + 50n = 90 +10n we get n = 1   Hence total no. of steps on escalator is 100.   ANSWER:100
Answer: C
A sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 854 in 4 years. The sum is :	Choose the correct choice from the following options:  A) Rs. 700  B) Rs. 690  C) Rs. 650  D) Rs. 698  E) Rs. 690

Solution: Simple Interest (SI) for 1 year = 854-815= 
854-815 = 39
39   Simple Interest (SI) for 3 years= 39 × 3 = 117   Principal = 815 - 117 = Rs.698   answer : Rs. 698
Answer: D
Two ants, Arthur and Amy, have discovered a picnic and are bringing crumbs back to the anthill. Amy makes twice as many trips and carries one and a half times as many crumbs per trip as Arthur. If Arthur carries a total of m crumbs to the anthill, how many crumbs will Amy bring to the anthill, in terms of m? Choose the most appropriate option:	A) x/2	B) x	C) 3m/2	D) mx	E) mx

Solution: Lets do it by picking up numbers. Let Arthur carry 2 crumbs per trip, this means Amy carries 3 crumbs per trip. Also let Arthur make 2 trips and so Amy makes 4 trips.   Thus total crumbs carried by Arthur (m) = 2 x 2 = 4, total crumbs carried by Amy = 3 x 4 = 12. 12 is 3 times 4, so mx
Answer: E
The area of a triangle is with base 4m and height 5m? Choose the correct answer:
A) 20 sq m
B) 10 sq m
C) 5 sq m
D) 3 sq m
E) 12 sq m

Solution: Explanation:   1/2 * 4 * 5= 
1/2 * 4 * 5 = 10
10 m2   ANSWER IS 10 sq m
Answer: B
A sum of money at simple interest amounts to $ 700 in 3 years and to $764 in 4 years. The sum is: Pick one.
A) $508
B) $698
C) $398
D) $549
E) $675

Solution: A   $508   S.I. for 1 year = $(764 - 700)= 
(764 - 700) = 64
$64.   S.I. for 3 years= $(64 x 3) = $192.   Principal = $(700 - 192)= 
(700 - 192) = 508
$508.
Answer: A
A train 700 m long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 min, then the length of the tunnel is?  Select:
A) 298 m
B) 468 m
C) 600 m
D) 667 m
E) 781 m

Solution: Speed = 78 * 5/18 = 65/3 m/sec.   Time = 1 min = 60 sec.   Let the length of the train be x meters.   Then, (700 + x)/60 = 65/3   x = 600 m.   Answer: 600 m
Answer: C
A grocer has a sale of Rs. 4000, Rs. 6524, Rs. 5689, Rs. 7230 and Rs. 6000 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 7000?
Select:
A) s. 12557
B) s. 14993
C) s. 15560
D) s. 12589
E) s. 12500

Solution: Total sale for 5 months = Rs. (4000 + 6524+ 5689 + 7230 + 6000) = Rs.29443   Required sale = Rs. [ (7000 x 6) - 29443 ]   = Rs. (42000 - 29443)   = Rs. 12557.   Option s. 12557
Answer: A
3 cooks have to make 80 burgers. They are known to make 20 pieces every minute working together.The 1st cook began workin alone and made 20 pieces having worked for sometime more than 3 mins.The remaining part of the work was done by second and 3rd cook working together.It took a total of 8 minutes to complete the 80 burgers.How many minutes would it take the 1st cook alone to cook 160 burgers?	Options
A) 16 minutes B) 24 mins C) 32 mins D) 40 mins E) 30 mins

Solution: Denote by A, B, C the rates of the three cooks in units of burgers/minute.   A + B + C = 20.   Let t be the time in minutes it took the first cook A to make the 20 burgers. So, A*t = 20, and we know that t > 3.   We need to find 8t, as 160 burgers will be made by A in 8 times more than making 20 burgers.   We already know that 8t >  8*3= 
 8*3 = 24
24, so we can eliminate answers (A) and (B).   In addition, (B + C)(8 - t)= 60, or (20 - A)(8 - t) = 60.   Since 20 - A < 20 and 8 - t < 5, looking for integer solutions, we find the only acceptable solution 20 - A = 15 and 8 - t = 4, so t = 4.   I am assuming integer numbers for the solutions based on the answer choices.   Anyway, testing the answer choices, only (C) is a solution.   Therefore, A will make 160 burgers in 8*4= 
8*4 = 32
32 minutes.   Answer 32 mins
Answer: C
A person travels equal distances with speeds of 3 km/hr, 4 km/hr and 5 km/hr and takes a total time of 47 minutes. The total distance is?  Choose the correct choice:  A) 1  B) 3  C) 4  D) 45  E) 4

Solution: Let the total distance be 3x km.   Then, x/3 + x/4 + x/5 = 47/60   47x/60 = 47/60 => x = 1.   Total distance = 3 * 1= 
3 * 1 = 3
3 km.   Answer:3
Answer: B
X starts a business with Rs.45000. Y joins in the business after 3 months with Rs.30000. What will be the ratio in which they should share the profit at the end of the year?	Choices
A) 1:2
B) 2:1
C) 1:3
D) 3:1
E) None of these

Solution: Explanation :   Ratio in which they should share the profit   = Ratio of the investments multiplied by the time period   = 45000 * 12: 30000 * 9   = 45 * 12: 30 * 9   = 3*12: 2 * 9   = 2:1. Answer : Option 2:1
Answer: B
An engineer undertakes a project to build a road 10 km long in 300 days and employs 30 men for the purpose. After 100 days, he finds only 2 km of the road has been completed. Find the (approximate) number of extra men he must employ to finish the work in time. Choose the correct choice from the following:  A) 20  B) 25  C) 30  D) 35  E) 40

Solution: 30 workers working already   Let x be the total men required to finish the task in next 200 days   2 km done hence remaining is 8 km   Also, work has to be completed in next 200 days (300 - 100 = 200)   We know that, proportion of men to distance is direct proportion   and, proportion of men to days is inverse proportion   Hence, X = (30 * 8 * 100) / (2 *200)   thus, X = 60   Thus, more men needed to finish the task = 60-30= 
60-30 = 30
30   Answer : 30
Answer: C
What is the least number of square tiles required to pave the floor of a room 11 m 50cm long and 1m 50 cm broad?
Choose the correct choice.
A) 724
B) 804
C) 69
D) 844
E) None

Solution: Solution   Length of largest tile = H.C.F. of 1150cm & 150cm = 50cm.   Area of each tile = (50 x 50)cm2   ∴ Required number of tiles	= [1150x150/50x50]   = 69.   Answer 69
Answer: C
Mrs. Evans gave a test to her freshmen economics class, which has 29 students enrolled and 24 of them answered question 1 correctly. If 22 answered question 2 correctly and 5 did not take the test then how many answered both questions correctly?  Answers.
A) 18 B) 19 C) 22 D) 20 E) 19

Solution: Total number of enrolled students = 29   Number of students who did not take test = 5   Hence, number of students who took test = 29 - 5= 
29 - 5 = 24
24   Number of students who answered Q2 correctly=24, therefore, all students who took test answered Q2 correctly.   So, number of students who answered Q1 correctly, also answered Q2 correctly = 22.   Number of students who answered both Q1 & Q2 correctly = 22.   ANSWER:22
Answer: C
If x is an odd negative integer and y is an even integer, which of the following statements must be true?
I. (3x + 2y) is negative integer
II. (xy)^2 is negative integer
III. (y^2 - x) is negative integer  Choose the correct choice from the following answers:
A) None of these
B) I Only
C) II only
D) IIIonly
E) I,II only

Solution: I. It is true if x > y   II. It is always positive   III. It is not true   None of thesenswer : None of these
Answer: A
How many positive even integers less than 100 contain digits 3 or 7? Choose the correct choice from the following:
A) 16 B) 17 C) 18 D) 10 E) 20

Solution: Two digit numbers:   3 at tens place: 30,32,34,36,38   7 at tens place: 70,72,74,76,78   If 3 and 7 is at units place, the number cant be even   Total:5+5= 
5+5 = 10
10   Answer 10
Answer: D
A school has only four classes that contain 10, 20, 30 and 40 students respectively. The pass percentage of these classes are 20%, 30%, 60% and 100% respectively. Find the pass % of the entire school.  Choose the correct choice from the following choices.
A) 56% B) 76% C) 34% D) 66% E) None of these

Solution: Solution: The number of pass candidates are 2+6+18+40= 
2+6+18+40 = 66
66 out of total 100.   Hence,   Pass pecentage= 66%.   Answer: Option 66%
Answer: D
Today is Jack's birthday. One year, from today he will be twice as old as he was 13 years ago. How old is Jack today ? Choose the correct choice from the following options
A) 23 years B) 24 years C) 25 years D) 26 years E) 27 years

Solution: let Jack's age=xx+1=2(x-13)x=27ANSW27 yearsR:27 years
Answer: E
Peter brought a scooter for a certain sum of money. He spent 10% of the cost on repairs and sold the scooter for a profit of $ 1100. How much did he spend on repairs if he made a profit of 20%?	Choose the correct choice from the following choices.
A) 100  B) 200  C) 300  D) 400  E) 500

Solution: E   500   Let the C.P. be $ x. Then, 20% of x = 1100   20/100 * x = 1100 => x = 5500   C.P. = $ 5500, expenditure on repairs = 10%   Actual price = $ (100 * 5500)/110= 
(100 * 5500)/110 = 5_000
$ 5000   500xpenditures on repairs= (5500 - 5000)= 
(5500 - 5000) = 500
$ 500.
Answer: E
Find the odd man out
4, 16, 25, 36, 42, 64  Choose the correct answer:
A) 36	B) 25	C) 42	D) 95	E) 4

Solution: 2^2 = 4   4^2 = 16   5^2 = 25   6^2 = 36   7^2 = 49   8^2 = 64   ANSWER:42
Answer: C