MU-NLPC/Calc-aqua_rat huggingface dataset:
The cash difference between the selling prices of an article at a profit of 8% and 6% is Rs. 3. The ratio of the two selling prices is?
Choose the correct option:	A) 52:56	B) 52:53	C) 52:50	D) 54:53	E) 52:51

Solution: Let C.P. of the article be Rs. x.   Then, required ratio = 108% of x / 106% of x   = 108/106 = 54/53 = 54:53   Answer: 54:53
Answer: D
For which of the following functions is f(q) = f(−q) for all values of q ?
Choose the most appropriate option.
A) f(x) = x^3 + 3	B) f(x) = −x	C) f(x) = 2x + 3	D) f(q) = −q^2 + 2	E) f(x) = 5x − 4

Solution: f(q) = f(−q)   The above is a property of an even function .   f(q) = f^(n)   f(q) = f(−q) will hold when n is an even integer .   The only case when q is even is option f(q) = −q^2 + 2   Answer f(q) = −q^2 + 2
Answer: D
Last year the price per share of Stock X increased by k percent and the earnings per share of Stock X increased by m percent, where k is greater than m. By what percent did the ratio of price per share to earnings per share increase, in terms of k and m?	Options:
A) k m % B) (k – m) % C) [100(k – m)] / (100 + k) % D) [100(k – m)] / (100 + m) % E) [100(k – m)] / (100 + k + m) %

Solution: Price Per Share (PPS) = x   Earning Per Share(EPS) = y   Increased PPS = x(1+k/100)   Increased EPS = y(1+m/100)   % increase in the ratios (PPS/EPS) = {[x(100+k)]/[y(100+m)] - (x/y)} / (x/y)   On Simplifying, % increase = [100(k-m)] / (100 + m) % , ANSWER:[100(k – m)] / (100 + m) %
Answer: D
A bakery sells 4 varieties of pastries. John buys 10 pastries making sure, he gets at least one of each kind.
In how many ways can John make the purchase ?	Choose the correct choice from the following options:
A) 84	B) 86	C) 88	D) 90	E) 82

Solution: no of 1st variety of pastry: a   no of 2nd variety of pastry: b   no of 3rd variety of pastry: c   no of 4th variety of pastry: d   So, we have a+b+c+d=10 (where a,b,c,d>0)   Remember: Number of positive integer solution of x+y+z+... (r terms) = n is (n-1)C(r-1)   So, the answer to the question would be (10-1)C(4-1) = 9C3 = 84.   84NSWER:84
Answer: A
A certain protective additive increases from 50 days to 60 days the time between required maintenance checks on an industrial vehicle. By what percent is the time between maintenance checks increased by using the additive?  Options.
A) 25% B) 33 1/3% C) 50% D) 66 2/3% E) 20%

Solution: General formula for percent increase or decrease, (percent change):   percent=Change/Original∗100   So, the time between maintenance checks increased by 60−50/50∗100=20   Answer: 20%.
Answer: E
The relationship between quantities m and n is expressed by the equation 30m = 5(n - 42). If the difference between the two chosen values of n is 30, what is the difference in the corresponding values of m?  Pick one.
A) 5  B) 42/11  C) 60/11  D) 150/11  E) 14

Solution: 5nother Simple way   30m=5(n-42)   5ssume n = 42 to make one side equal to 0   then 30m=0   and m = 0   Repeat it by assuming n as 42+30 i.e 72   30m- 5(72-42)   30m=150   m=150/30= 
150/30 = 5
5 - 0= 
5 - 0 = 5
5   5nswer : 5
Answer: A
A sock drawer contains five socks, each one a different solid color. The colors of the socks are yellow, green, blue, indigo, and violet. If the socks are laid next to each other, how many different arrangements of socks could be made? Select:
A) 24
B) 240
C) 1,024
D) 2,520
E) 120

Solution: I see no condition for arrangement.   So 5! ways - IMO option 120 is correct answer..
Answer: E
Two trains started at the same time, one from A to B and the other from B to A . If they arrived at B and A respectively 16 hours and 25 hours after they passed each other the ratio of the speeds of the two trains was Answers:
A) 2:1
B) 3:2
C) 4:3
D) 5:4
E) 1:2

Solution: Explanation:   Note : If two trains (or bodies) start at the same time from points A and B towards each other and after crossing they take a and b sec in reaching B and A respectively, then: (A's speed) : (B's speed) = (b : a)   Therefore, Ratio of the speeds of two trains = = 5 : 4. Answer: 5:4
Answer: D
At a certain university, the ratio of the number of teaching assistants to the number of students in any course must always be greater than 4:85. At this university, what is the maximum number of students possible in a course that has 5 teaching assistants?  Choices:  A) 106  B) 107  C) 108  D) 109  E) 110

Solution: (5/4)*85=106 plus remainder   The answer is 106.
Answer: A
A, B, and C working alone can finish constructing a house in 6, 12, and 18 hours respectively. A starts alone and works for 1 hour. He is then joined by B and they work together for 1 hour. Finally C joins them and they all work together to finish the work. If they start working at 9 am, at what time will they finish?  Choose the correct choice:  A) 12:05 pm  B) 12:15 pm  C) 12:35 pm  D) 12:55 pm  E) 1:15 pm

Solution: A completes 1/6 of the job each hour.   B completes 1/12 of the work each hour.   C completes 1/18 of the work each hour.   A completes 1/6 of the work in the first hour.   Working together, A and B complete another 3/12 for a total of 5/12.   Working together, A, B, and C can complete 11/36 of the work each hour.   To complete 7/12, the time required is (7/12) / (11/36) = 21/11 hours.   The work will be completed at 12:00 plus 10*60/11 minutes which is about 12:55 pm.   The answer is 12:55 pm.
Answer: D
If |20x-10| = 150, then find the product of the values of x? Select:  A) -45  B) 56  C) -62  D) 35  E) -30

Solution: |20x-10| = 150   20x-10 = 150 or 20x-10 = -150   20x = 160 or 20x = -140   x = 8 or x = -7   product = -7*8 = -56   Answer is 56
Answer: B
Jack has two dice, one has six equally probable sides, labeled 1, 2, 3, 4, 5, 6, and the other has seven equally probable sides, labeled 1, 2, 3, 4, 5, 6, 7. If Jack rolls both dice what is the probability that both of the numbers will be even? Choose the correct choice.
A) 3/14  B) 2/7  C) 1/3  D) 1/2  E) 12/21

Solution: Probability that the number on first die is even = 3/6 [Because 3 out of 6 faces are even]   Probability that the number on Second die is even = 3/7 [Because 3 out of 7 faces are even]   Probability that Both Dice result in odd numbers = (3/6)*(3/7) = 3/14   3/14nswer: Option 3/14
Answer: A
If the average cost of a house was $70,000 in 1965 and was x in 2005, what was the average increase in home prices per year over this period?
Choose the correct choice:
A) A)(x+50,000)/40 B) C)(50,000/40)+x C) B)(x-50,000)/40 D) D)(50,000-x)/40 E) E)x/40

Solution: Average house price in 2005: x   Average house price in 1965: 50,000   2005-1965= 
2005-1965 = 40
40   Average increase per year: (x-70,000)/40   Answer is B)(50,000/40)+x
Answer: C
A loan has a variable interest rate that fluctuates between 5% and 10% of the base payment per month. If base payments remain at $200 each month and an additional monthly surcharge of 1% is added to the combined (base + interest), what would be the greatest possible payment due in any given month?  Pick one:
A) $220.00
B) $222.20
C) $224.20
D) $224.40
E) $225.60

Solution: The maximum interest in one month is 10%*$200=$20.   The combined payment (base plus interest) is $200 + $20 = $220.   The greatest possible payment is: 1.01*$220  200 +  20= 
  200 +  20 = 220
$220.   The greatest possible payment is: 1.01*$220=$222.20.   The answer is $222.20.
Answer: B
If the original mass of an element, in grams, is a whole number and the element has decayed by exactly 93 percent in some time period, which of the following could be the final mass of that element? Choose the correct answer:	A) 27 grams	B) 28 grams	C) 29 grams	D) 42 grams	E) 32 grams

Solution: Let original mass be 100   The final mass of that element will be 7   So whatever option we have it will be divisible by 7   Check for the options the one that doesn't produce non terminating decimal is our answer   A. 27 grams   27/7 = 3.857...   B. 25 grams   25/7 = 3.571...   C. 29 grams   29/7 = 4.142.......   D. 42 grams   42/7= 
42/7 = 6
6   E. 32 grams   32/7= 4.571....   Hence our answer will be (42 grams)
Answer: D
Five people are planning to share equally the cost of a rental car. If one person withdraws from the arrangement and the others share equally the entire cost of the car, then the share of each of the remaining persons increased by:
Choose the correct choice from the following choices:  A) 7/8  B) 1/8  C) 1/4  D) 1/7  E) 1/9

Solution: Original share of 1 person =1/5   New share of 1 person =1/4   Increase =1/4 -	1/5 =1/20   Required fraction =	(1/20)/(1/5)=1/4   Answer is 1/4.
Answer: C
In a certain boys camp, 20% of the total boys are from school A and 30% of those study science. If there are 42 boys in the camp that are from school A but do not study science then what is the total number of boys in the camp?  Answers:
A) 70
B) 245
C) 150
D) 300
E) 350

Solution: Since 30% of the boys from school A study science, then 70% of the boys from school A do NOT study science and since 20% of the total number of boys are from school A, then 0.2*0.7= 
0.2*0.7 = 0.14
0.14, or 14% of the boys in the camp are from school A and do not study science.   We are told that this number equals to 42, so 0.14*{total}= 42 --> {total} = 300.   Answer: 300.
Answer: D
A can have a piece of work done in 8 days, B can work three times faster than the A, C can work five times faster than A. How many days will they take to do the work together ?	Answers:	A) 3 days	B) 8/9 days	C) 4 days	D) can't say	E) none

Solution: A's 1 day work is 1/8   8/9 days's 1 day work is 3/8   C's 1 day work is 5/8   (A+8/9 days+C)'s 1 day work(1/8+3/8+5/8) is 9/8   so, they can finish the work in 8/9 days   ANSWER:8/9 days
Answer: B
Calculate the sum of first 28 natural numbers. Select the correct option.
A) 426
B) 406
C) 401
D) 409
E) 405

Solution: Solution   We know that(1+2+3+.....+28)	= n(n+1)/2   Therefore (1+2+3+....+28)	=(28×29 / 2)   = 406.   Answer 406
Answer: B
The average age of 15 students of a class is 15 years. Out of these, the average age of 5 students is 14 years and that of the other 9 students is 16 years. The age of the 15th student is Answers:
A) 9 years
B) 11 years
C) 14 years
D) 21 years
E) 25 years

Solution: Solution   Age of the 15th student	=[15x15-(14x5+16x9)]   = (225 - 214)= 
(225 - 214) = 11
11 years.   Answer 11 years
Answer: B
The average of seven numbers is 26. The average of first three numbers is 14 and the average of last three numbers is 19. What is the middle number? Choose the most appropriate option: A) 25 B) 83 C) 29 D) 32 E) 34

Solution: The total of seven numbers = 7X26 = 182   The total of first 3 and last 3 numbers is = 3 X 14+3 X 19 = 99   So, the middle number is  (182 - 99 )= 
 (182 - 99 ) = 83
83   83
Answer: B
How many figures are required to number the pages the pages of a book containing 709 pages?
Choose the correct choice from the following answers
A) 2020
B) 2019
C) 1019
D) 2029
E) 2039

Solution: 1 to 9 = 9 * 1= 
9 * 1 = 9
9   10 to 99= 90 * 2= 
90 * 2 = 180
180   100 to 709= 610 * 3= 
610 * 3 = 1_830
1830   -----------   2019   ANSWER:2019
Answer: B
If k is an integer, which of the following must be an even integer? Select the correct option.
A) k^2-k-1  B) k^2-4k+6  C) k^2-5k+5  D) k^2+3k+8  E) k^2+2k+10

Solution: Check the options by plugging in some values ( Preferably smaller integers like 1 and 2 )   A: k^2-k-1 = -1 { If k = 1 }   B: k^2-4k+6 = 3 { If k = 1 }   C: k^2-5k+5 = 1 { If k = 1 }   k^2+3k+8: k^2+3k+8 = 12 { If k = 1 }k^2+3k+8 = 18 { If k = 2 }   E: k^2+2k+10 = 13 { If k = 1 }   Thus the only possible answer is (k^2+3k+8)
Answer: D
A trained covered x km at 40 kmph and another 2x km at 20 kmph. Find the average speed of the train in covering the entire 3x km.	Answers
A) 22  B) 99  C) 24  D) 66  E) 887

Solution: Total time taken = x/40 + 2x/20 hours   = 5x/40 = x/8 hours   Average speed = 3x/(x/8) = 24 kmph   Answer: 24
Answer: C
Three unbiased coins are tossed. What is the probability of getting 2 Tails?	Choose one
A) 3/4
B) 1/4
C) 3/8
D) 7/8
E) 1/8

Solution: Let, H --> Head , T --> Tail   Here S = {TTT, TTH, THT, HTT, THH, HTH, HHT, HHH}   Let E = event of getting 2 Tails   Then E = {TTH, THT, HTT}   P(E) = n(E)/n(S) =3/8   Answer is 3/8
Answer: C
The average age of a group of n people is 15 years old. One more person aged 37 joins the group and the new average is 17 years old. What is the value of n?
Choose the correct choice: A) 10 B) 12 C) 14 D) 16 E) 18

Solution: 15n + 37 = 17(n+1)   2n = 20   n = 10   The answer is 10.
Answer: A
The sum of ages of 5 children born at the intervals of 2 years each is 55 years. What is the age of the youngest child?	Options:
A) 4
B) 7
C) 6
D) 9
E) 8

Solution: Let the ages of children be x, (x + 2), (x + 4), (x + 6) and (x + 8) years.   Then, x + (x + 2) + (x + 4) + (x + 6) + (x + 8) = 50   5x = 55-20= 
55-20 = 35
35   x= 7.   Age of the youngest child = x = 7 years.   Answer:7
Answer: B
Out of 15 consecutive numbers, 2 are chosen at random. The probability that they are both odds or both primes is ?  Choose one
A) 10/17
B) 10/19
C) 46/105
D) 11/15
E) Cannot be determined

Solution: Explanation:   There is no definite formula for finding prime numbers among 15 consecutive numbers. Hence the probability cannot be determined.   Cannot be determined)
Answer: E
A train 400 m long can cross an electric pole in 20 sec and then find the speed of the train? Choose the correct choice from the following answers: A) 35 Km/hr B) 48 Km/hr C) 57 Km/hr D) 72 Km/hr E) 83 Km/hr

Solution: Length = Speed * time   Speed = L/T   S = 400/20= 
400/20 = 20
20 M/Sec   Speed= 20*18/5 (To convert M/Sec in to Km/hr multiply by 18/5)   Speed = 72 Km/hr   ANSWER:72 Km/hr
Answer: D
A electricity company charges $3 for the first 500 units consumption plus $0.05 for each additional unit. What would this company charge for a consumption of 800 units ?
Choose the correct choice from the following answers:	A) $10	B) $12	C) $15	D) $16	E) $18

Solution: first 500 units harges = $3   rest of the units = 800 - (500)= 
800 - (500) = 300
300   charge for the rest of the units= 300 *05 = 15   total charge = 3 + 15= 
3 + 15 = 18
18   Answer is $18
Answer: E
If b can complete the work in n days and if a and b can work together then they will complete in y days. what will be time to complete the work a alone?	Select the correct option:
A) (n-y)/yn	B) 1/yn	C) yn/(n-y)	D) 2^(yn/(n-y))	E) cannot be determined

Solution: option C is answer.   one day work of b =1/n.   a+b=1/y(one day work)   a=(1/y)-b   =(1/y)-1/n   =(n-y)/yn(one day work of a)   No of days =yn/(n-y)
Answer: C
A trader marks his product 40% above its cost. He sells the product on credit and allows 10% trade discount. In order to ensure prompt payment, he further gives 10% discount on the reduced price. If he makes a profit of Rs. 67 from the transaction, then the cost price of the product is  Choose the correct answer
A) Rs. 300
B) Rs. 400
C) Rs. 325
D) Rs. 500
E) Rs. 600

Solution: M.P = C.P *1.4   Profit = S.P - C.P = C.P ( 1.4 ) ( 0.9 ) ( 0.9 ) – C.P = 67   C.P ( 1.134 – 1 ) = 67,   C.P = 500   ANSWER:Rs. 500
Answer: D
If 638521 is to be divisible by 5, what is the least whole number that should be added to? Choose the correct choice from the following: A) 8 B) 7 C) 5 D) 4 E) 3

Solution: A number is divisible by 5 if the last digit is either 0 or 5.   Here, 638521=1(last digit is neither 0 or 5).   the next multiple of 5 i.e to make the last digit 0 or 5 add 4   4 must be added to 638521 to make it divisible by 5   4
Answer: D
A, B and C can do a piece of work in 6,8 and 12 days respectively. In how many days would all of them complete the same job working together? Choose the correct choice from the following options
A) 2 3/4 days.  B) 2 2/3 days.  C) 2 3/2 days.  D) 3 1/2 days.  E) 3 3/4 days.

Solution: Explanation:   In this type of questions we first get the finishing of work in 1 day for A,B,C then we will add them to get the result, as:   Part finished by A in 1 day= 1/6   Part finished by B in 1 day = 1/8   Part finished by C in 1 day =1/12   Part finished by (A+B+C) in 1 day = 9/24   = 9/24 Remaining work =1-9/20=11/20. Number days to finish the work by A+B+C =2 2/3 days.   Option 2 2/3 days.
Answer: B
The food in a camp lasts for 10 men for 20 days. If 30 more men join, how many days will the food last? Options:
A) 8 days
B) 4 days
C) 5 days
D) 10 days
E) 17 days

Solution: one man can consume the same food in 10*20= 
10*20 = 200
200 days.   30 more men join, the total number of men= 40   The number of days the food will last = 200/40= 
200/40 = 5
5 days.   Answer:5 days
Answer: C
A sequence consists of 16 consecutive even integers written in increasing order. The sum of the first 8 of these even integers is 456. What is the sum of the last 8 of the even integers?  Choose the correct answer:
A) 580 B) 584 C) 588 D) 592 E) 596

Solution: The sum of the first 8 numbers is: x + (x+2) +...+ (x+14) = 456   The sum of the next 8 numbers is: (x+16) + (x+2+16) +...+ (x+14+16) =   456 + 8(16) = 456 + 128= 
456 + 128 = 584
584   The answer is 584.
Answer: B
The perimeter of one square is 48 cm and that of another is 20 cm. Find the perimeter and the diagonal of a square which is equal in area to these two combined?  Pick.
A) 13√6 B) 13√2 C) 13√0 D) 13√2 E) 13√1

Solution: 4a = 48 4a = 20   a = 12 a = 5   a2 = 144 a2 = 25   Combined area = a2 = 169 => a = 13   d = 13√2 Answer:13√2
Answer: B
In a recent election, Ms. Robinson received 8000 voters cast by independent voters, that is, voters not registered with a specific political party. She also received 40 percent of the votes cast by those voters registered with a political party. IF N is the total number of votes cast in the election and 40 percent of the votes cast were cast by independent voters, which of the following represents the number of votes that Mrs. Robbins received?  Choose the correct choice:
A) 0.06N+3200
B) 0.1N+7200
C) 0.24N+8000
D) 0.1N+8000
E) 0.06N+8000

Solution: 40% of N are independent voters, hence 60% of N are not independent voters. From this group she received 40% votes so, 0.4*0.6*N plus 8,000 votes from independents: total=0.4*0.6*N+8,000=0.24*N+8,000.   Answer: 0.24N+8000.
Answer: C
David invested certain amount in three different schemes. A, B and C with the rate of interest 10% p.a., 12% p.a. and 15% p.a. respectively. If the total interest accrued in one year was Rs. 3200 and the amount invested in scheme C was 150% of the amount invested in scheme A and 240% of the amount invested in scheme B, what was the amount invested in scheme B?
Options.
A) Rs. 5000
B) Rs. 6500
C) Rs. 8000
D) Cannot be determined
E) None of these

Solution: Let x, y and z be the amount invested in schemes A, B and C respectively. Then,   (x * 10 * 1)/100 + (y * 12 * 1)/100 + (z * 15 * 1)/100 = 3200   10x + 12y + 15z = 320000   Now, z = 240% of y = 12/5 y   And, z = 150% of x = 3/2 x   x = 2/3 z = ( 2/3 * 12/5) y = 8/5 y   16y + 12y + 36y = 320000   y = 5000   Sum invested in scheme B = Rs. 5000   Rs. 5000NSWER:Rs. 5000
Answer: A
In a partnership between A, B and C. A's capital is Rs.5000. If his share of a profit of Rs.800 is Rs.200 and C's share is Rs.130, what is B's capital?  Pick.
A) 11719 B) 11710 C) 11712 D) 11750 E) 11751

Solution: 200 + 130= 
200 + 130 = 330
330   800 - 330= 
800 - 330 = 470
470   200 ---- 5000   470 ---- ?=> 11750   Answer:11750
Answer: D
There are 16 balls in a jar: 8 red, 6 blue and 2 green. If a single ball is drawn from the jar, what is the probability of that it is either blue or red?  Choose the correct option.
A) 1/12	B) 1/4	C) 7/8	D) 2/3	E) 3/4

Solution: Blue + Red =14   Total number of balls is  8+6+2= 
 8+6+2 = 16
16   So the answer is 14/16=7/8   Answer 7/8
Answer: C
By selling an article at Rs.800, a shopkeeper makes a profit of 25%. At what price should he sell the article so as to make a loss of 40%?	Choose the correct choice from the following answers:
A) 228
B) 384
C) 267
D) 288
E) 276

Solution: SP = 800   Profit = 25%   CP = (SP)*[100/(100+P)]   = 800 * [100/125]   = 640   Loss 800 *  100/125= 
800 *  100/125 = 640
640   Loss= 40% = 40% of 640 = Rs.256   SP = CP - Loss = 640 - 256 = Rs.384   Answer: 384
Answer: B
If x, y, and z are positive integers, and 4x = 5y = 8z, then the least possible value of x + y + z is  Choose the correct choice from the following answers:
A) 15
B) 23
C) 37
D) 42
E) 60

Solution: Take LCM of 4,5 and 8 = 40   Now 4x = 40 => x =10   5y = 40 => y = 8   8z = 40 => z =5   10+8+5= 
10+8+5 = 23
23.   Option 23.
Answer: B
Twelve years ago, P was half of Q's age. If the ratio of their present ages is 3:4 what will be the total of their present ages?  Select the correct option.
A) 33  B) 37  C) 29  D) 31  E) 42

Solution: E   Let present age of P and Q be 3x3x and 4x4x respectively.   Twelve years ago, P was half of Q's age   â‡’(3xâˆ’12)=1/2(4xâˆ’12)   â‡’6xâˆ’24=4xâˆ’12   â‡’2x=12   â‡’x=6   Total of their present ages   =3x+4x=7x3 +4= 
3 +4 = 7
7x=7Ã—6=42
Answer: E
1. The simple interest on a sum of money is Rs. 50. What is the sum?
I. The interest rate is 10% p.a.
II. The sum earned simple interest in 10 years
Choose the most appropriate option.
A) I alone sufficient while II alone not sufficient to answer  B) II alone sufficient while I alone not sufficient to answer  C) Either I or II alone sufficient to answer  D) Both I and II are necessary to answer  E) None of these

Solution: Explanation:   Given : S.I. = Rs. 50.   I gives, R = 10% p.a.   II gives, T = 10 years.   Sum = (100 x S.I)/(t x r ) = Rs.(100 x 50)/(10 x 10) = Rs.50   ANSWER IS Both I and II are necessary to answer
Answer: D
(6)6.5 × (36)4.5 ÷ (216)4.5 = (6)?
Options
A) 1	B) 2	C) 4	D) 6	E) 8

Solution: Explanation :   (6)6.5 × (36)4.5 ÷ (216)4.5   = (6)6.5 × [(6)2]4.5 ÷ [(6)3]4.5   = (6)6.5 × (6)9 ÷ (6)13.5   = (6)(6.5 + 9 - 13.5)   = (6)2   Answer : Option 2
Answer: B
A train 200 m long is running at a speed of 68 kmph. How long does it take to pass a man who is running at 8 kmph in the same direction as the train?	Choices
A) 5 sec	B) 9 sec	C) 12 sec	D) 15 sec	E) 18 sec

Solution: Speed of the train relative to man = (68 - 8) kmph   = (60* 5/18) m/sec = (50/3)m/sec   Time taken by the train to cross the man   = Time taken by It to cover 200 m at 50/3 m / sec   = 200 *3/ 50= 
200 *3/ 50 = 12
12sec   Answer : 12 sec
Answer: C
What inequality represents the condition 1<x<7?  Pick:  A) |x|<3  B) |x+5|<4  C) |x-1|<9  D) |-4+x|<3  E) |3+x|<5

Solution: 1<x<7 represents segment with   length:   7-1= 
  7-1 = 6
6   center:   (7+1)/2= 
  (7+1)/2 = 4
4   For any |x-a|<b a is a center and b is a half of length. So, |x-4|<6/2 represents our inequality (answer |-4+x|<3)
Answer: D
Free notebooks were distributed equally among children of a class. The number of notebooks each child got was one-eighth of the number of children. Had the number of children been half, each child would have got 16 notebooks. Total how many notebooks were distributed?
Choose the correct choice from the following options.
A) 502
B) 512
C) 523
D) 521
E) 500

Solution: Let n be the total number of children.   More children, less notebooks(Indirect proportion)   If the number children = n, number of books each child will get = n/8   If the number children = n/2, number of books each child will get = 16   Hence we can write as   children n:n/2}::16:n/8   ⇒n×n/8=n/2×16   ⇒n8=16/2= 
16/2 = 8
8   ⇒n=8×8=64   Then, total number of notebooks those were distributed = n×n/8=(64×64)/8=64×8=512   Answer is 512.
Answer: B
Vijay sells a cupboard at 16% below cost price. Had he got Rs.1200 more, he would have made a profit of 16%. What is the cost price of the cupboard?  Choices:
A) 3750	B) 3600	C) 7400	D) 7500	E) None of these

Solution: Explanation:   Cost price = 1200/(0.16 + 0.16) = 1200/0.32   = Rs.3750   3750NSWER 3750
Answer: A
The total marks obtained by a student in Physics, Chemistry and Mathematics is 150 more than the marks obtained by him in Physics. What is the average mark obtained by him in Chemistry and Mathematics?	Choose the correct option:
A) 75 B) 28 C) 279 D) 271 E) 27

Solution: Let the marks obtained by the student in Physics, Chemistry and Mathematics be P, C and M respectively.   P + C + M = 150 + P   C + M = 150   Average mark obtained by the student in Chemistry and Mathematics   = (C + M)/2 = 150/2= 
150/2 = 75
75.   75nswer:75
Answer: A