MU-NLPC/Calc-aqua_rat huggingface dataset:
A certain no. when divided by 65 leaves a remainder 25, what is the remainder if the same no.be divided by 15? Pick one.
A) 2 B) 4 C) 6 D) 8 E) 9

Solution: Explanation:   65 + 25= 
65 + 25 = 90
90/15= 
90/15 = 6
6 (Remainder)   6
Answer: C
Kateys mom has $137 to pay 12 kids to clean up her backyard. How much more money does she need to be able to pay each of the 12 kids $12?	Choose the correct choice from the following answers.
A) 8  B) 7  C) 9  D) 11  E) 4

Solution: 12*12= 
12*12 = 144
144, not 137.   144-137= 
144-137 = 7
7   Kateys mom needs 7 more dollars to be able to pay each kid $12   Therefore 7 is correct
Answer: B
A car averages 35 miles per hour for the first 4 hours of a trip and averages 53 miles per hour for each additional hour of travel time. If the average speed for the entire trip is 50 miles per hour, how many hours long is the trip?  Choose one: A) 16 B) 18 C) 20 D) 22 E) 24

Solution: Let T be the total time of the trip.   35*4 + 53(T-4) = 50T   3T = 212-140   T = 24   The answer is 24.
Answer: E
How many liters of a 40% iodine solution need to be mixed with 35 liters of a 20% iodine solution to create a 32% iodine solution?
Choose the correct choice from the following choices
A) 35 B) 49 C) 100 D) 102 E) 140

Solution: Solution 1:   Assume the iodine solution to be mixed = x lts.   Iodine = 0.4x lts, Water = 0.6x lts.   Solution 2: 35 liters of a 20% iodine solution   Iodine = 7 lts, Water = 28 lts.   Total iodine = 0.4x + 7   Total water = 0.6x + 28   The resultant is a 35% idoine solution.   Hence (0.4x + 7) / (x + 35) = 32/100   40x + 700 = 32x + 1120   8x = 820   x = 102 lts   Correct Option: 102
Answer: D
For which of the following “n” is the number 2^74 +2^2058+2^2n is a perfect square? Choose one
A) 22777 B) 2686 C) 8667 D) 2020 E) 99771

Solution: 2^74 +2^2058+2^2n = K2K2   2^74 +2^2058+2^2n = (237)2+22058+(2n)2(237)2+22058+(2n)2   We try to write this expression as (a+b)2=a2+2ab+b2(a+b)2=a2+2ab+b2   Now a = 237237, 2ab = 2205822058 and b = 2n2n   Substituting the value of a in 2ab, we get b = 2020   Ans: 2020
Answer: D
A teacher will pick a group of 5 students from a group of 9 students that includes Bart Lisa and john. If one of all the possible 5-student groups is picked at random, what is the probability of picking a group that includes john Bart and Lisa? Choose the correct choice from the following options:
A) 5/97  B) 3/41  C) 7/41  D) 5/42  E) 2/21

Solution: Probability = Favorable Outcomes / Total Outcomes   Total Outcomes= Total No. of ways of Picking Group of 5 out of 9 = 9C5 = 9! / (5! * 4!) = 126   Favorable Outcomes= Total No. of ways of Picking Group of 5 out of 9 such that J, B and L are always in the group (i.e. we only have to pick remaining 2 out of remaining 6 as J, B and L must be there is group) = 6C2 = 15   Hence,Probability=15/126=5/42   Answer: Option 5/42
Answer: D
Which of these must the factor F of the product of four consecutive even integers:-
1) 48
2) 64
3) 96
4) 192
5) 80  Pick:
A) 1,2 only
B) F=2,3 only
C) F=1,2,3 only
D) F=1,2,3,4 only
E) All of them

Solution: Let the four variables be a< b< c< d.   Assume a worst case scenario where the a equal to a prime number (hence odd).   therefore   a = divisible by 1   b = a + 1 (divisible by 2)   c = a + 3 (divisible by 3)   d = a + 4 (divisible by 4)   therefore   each answer choice must be divisible by 2 x 3 x 4 = 24   only 80 is not divisible. Therefore answer = F=1,2,3,4 only
Answer: D
If x is to be chosen at random from the set {5,6,7,8} and y is to be chosen at random from the set {1,2,3}, what`s the probability that xy will be even?  Choose the correct choice from the following:	A) 1/6	B) 1/3	C) 2/3	D) 1/2	E) 5/6

Solution: The product to be even either one or both must be even, so:   P(x=even OR y=even)=P(x=even)+P(y=even)-P(x=even AND y=even)=2/4+1/3-2/4*1/3=2/3;   Or: P(xy=even)=1-P(xy=odd)=1-2/4*2/3=2/3, so basically we find the probability of the product to be odd (which happens when both x and y are odd) and subtract it from 1.   Answer: 2/3.
Answer: C
A candidate who gets 30% of the marks fails by 30 marks. But another candidate who gets 45% marks gets 15 marks more than necessary for passing. Find the number of marks for passing?
Pick
A) 100 Marks
B) 200 Marks
C) 280 Marks
D) 371 Marks
E) 120 Marks

Solution: 30% ------------ 30   45% ------------ 15   ----------------------   15% ------------- 45   30% -------------- ?     90 + 30= 
  90 + 30 = 120
120 Marks   Answer:120 Marks
Answer: E
A ladder learning against a wall makes an angle of 60° with the ground. If the length of the ladder is 19 m, find the distance of the foot of the ladder from the wall.	Choose the most appropriate option.
A) 9 m  B) 9.5 m  C) 10.5 m  D) 12 m  E) None

Solution: Let AB be the wall and BC be the ladder.   Then, < ABC	= 60°   and, BC	= 19 m.;   AC = x metres   AC/BC	= cos 60°   = x / 19   =1 / 2   x= 19/2= 
19/2 = 19/2 = around 9.5
9.5 m.   Answer 9.5 m
Answer: B
A family made a down payment of $75 and borrowed the balance on a set of encyclopedias that cost $300. The balance with interest was paid in 23 monthly payments of $12 each and a final payment of $3. The amount of interest paid was what percent of the amount borrowed?	Choose the correct choice from the following options.
A) 23%	B) 20%	C) 25%	D) 26%	E) 24%

Solution: borrowings = 300-75= 
300-75 = 225
225   total pmt= 23x12 + 3 = 279   so int = 279 - 225= 
279 - 225 = 54
54   interest in terms of borrowing= 54/225 = 24%   Answer is 26%
Answer: D
The average of 9 observations was 4, that of the 1st of 5 being 10 and that of the last 5 being 8. What was the 5th observation? Pick one:  A) 54  B) 12  C) 15  D) 17  E) 18

Solution: Explanation:   1 to 9 = 9 * 4= 
9 * 4 = 36
36   1 to 5= 5 * 10= 
5 * 10 = 50
50   5 to 9= 5 * 8= 
5 * 8 = 40
40   5th= 50 + 40= 
50 + 40 = 90
90 – 36= 54   Option 54
Answer: A
What is the square root of 225?	Options:  A) 6  B) 9  C) 12  D) 45  E) 15

Solution: 15X15 = 225   ANSW15R 15
Answer: E
The average of 11 results is 55, if the average of first six results is 49 and that of the last six is 52. Find the sixth result?
Options:	A) A)46	B) B)1	C) C)66	D) D)76	E) E)74

Solution: 1 to 11 = 11 * 55= 
11 * 55 = 605
605   1 to 6= 6 * 49= 
6 * 49 = 294
294   6 to 11= 6 * 52= 
6 * 52 = 312
312   6th= 294 + 312 –605= 1   Answer:1
Answer: B
Total number of men, women and children working in a factory is 18. They earn Rs. 4000 in a day. If the sum of the wages of all men, all women and all children is in ratio of 18: 10: 12 and if the wages of an individual man, woman and child is in ratio 6: 5: 3, then how much a woman earn in a day? Choose the correct choice from the following choices
A) Rs. 120
B) Rs. 150
C) Rs. 250
D) Rs. 400
E) None of these

Solution: Solution: Ratio of number of men, women and children,   = (18/6): (10/5):(12/3) = 3:2:4   Total (Men +Women +Children) = 18   3X +2X +4X = 18   9X = 18   X = 2   Hence, number of women = 2X = 2*2= 
2*2 = 4
4   Share of all women= (10*4000)/40 = Rs. 1000 [18+10+12 =40]   Thus, share of each woman = 1000/4 = Rs. 250.   Answer: Option Rs. 250
Answer: C
A man swims downstream 30 km and upstream 20 km taking 5 hours each time, what is the speed of the man in still water?
Choose the correct choice from the following answers
A) 7 B) 8 C) 2 D) 5 E) 4

Solution: 30 --- 5 5S = 6   ? ---- 1   20 ---- 5 US = 4   ? ---- 1 M = ?   M = (6 + 4)/2= 
(6 + 4)/2 = 5
5   Answer:5
Answer: D
A computer store offers employees a 30% discount off the retail price. If the store purchased a computer from the manufacturer for $1500 dollars and marked up the price 30% to the final retail price, how much would an employee save if he purchased the computer at the employee discount (30% off retail price) as opposed to the final retail price.	Select:
A) 525 B) 545 C) 565 D) 575 E) 585

Solution: Cost price=1500   Profit=30% =30% of 1500=450   selling price=CP+ Profit   SP=1950   a Discount of 30% to employees means 30% off on 1950   so 30% of 1950= 585   Ans 585
Answer: E
What will be the ratio between the area of a rectangle and the area of a triangle with one of the sides of the rectangle as base and a vertex on the opposite side of the rectangle ? Select:
A) 1:1	B) 1:2	C) 2:3	D) 2:1	E) None of these

Solution: Explanation:   As far as questions of Area or Volume and Surface area are concerned, it is all about formulas and very little logic. So its a sincere advice to get all formulas remembered before solving these questions.   Lets solve this,   Area of rectangle =l∗b   Area of triangle =1/2l∗b   Ratio =l∗b:1/2l∗b   =1:1/2   =2:1   Option 2:1
Answer: D
The average age of three boys is 20 years and their ages are in proportion 3:5:7. What is the age in years of the youngest boy? Choose the correct answer
A) 6	B) 9	C) 8	D) 4	E) 12

Solution: 3x + 5x + 7x = 60   x =4   3x = 12   Answer:12
Answer: E
the average age of 56 employees in a company is 35. An employee aged 60 is retired and a fresher of age 20 is taken in. What is the new age average of employees?
Answers.
A) 25.45  B) 32.26  C) 33.13  D) 34.28  E) 35.55

Solution: The sum of age of the employees when the age average is 35 = 35x56 =1960   The sum of ages of the employees of new group= (1960-60)+20= 
(1960-60)+20 = 1_920
1920   The average age of the new group= 1920/56 = 34.28   Answer: 34.28
Answer: D
A part-time employee whose hourly wage was decreased by 20 percent decided to increase the number of hours worked per week so that the employee's total income did not change. By what percent R should the number of hours worked be increased?	Choose the correct option
A) 12.5%	B) 20%	C) 25%	D) 50%	E) 100%

Solution: Correct Answer: C   Solution: C. We can set up equations for income before and after the wage reduction. Initially, the employee earns W wage and works H hours per week. After the reduction, the employee earns .8W wage and works X hours. By setting these equations equal to each other, we can determine the increase in hours worked: WH = .8WX (divide both sides by .8W) 1.25H = X We know that the new number of hours worked R will be 25% greater than the original number. The answer is 25%.
Answer: C
The average age of 6 boys is 25 years and their ages are in the proportion 3:5:7. The age of the youngest boy is?	Choose the correct choice from the following answers:
A) 10years
B) 15years
C) 20years
D) 25years
E) 30years

Solution: Total age of 6 boys = 25*6= 
25*6 = 150
150   ratio of their ages= 3:5:7   Age of the youngest = 150*3/15= 
150*3/15 = 30
30 years   Answer is 30years
Answer: E
Twenty percent of Country Y's yearly exports come from fruit exports. One-sixth of all fruit exports from Country Y are orange exports. If country Y generates $5 million from its orange exports, how much money does it generate from its yearly total of exports?  Choose the correct choice from the following choices:
A) $21.25m  B) $25.5m  C) $106.25m  D) $127.5m  E) $150m

Solution: 2/10*1/6*(total) = 5   1/30*(total) = 5   (total) = 5*30= 
5*30 = 150
150   Answer: $150m.
Answer: E
When 10 per cent of a number is added to another number the second number increases to its 140 per cent. What is the ratio between the first and the second number?	Choose the correct choice from the following options:
A) 3 : 4  B) 4 : 1  C) 3 : 2  D) Data inadequate  E) None of these

Solution: Let the first and the second numbers be x and y respect then   y + 10% of x = 140% of y   or, y + 0.1x = 1.4y   or, 0.1x = 0.4y   ∴ x : y = 0.4 : 0.1 = 4 : 1   Answer 4 : 1
Answer: B
If a train, travelling at a speed of 270 kmph, crosses a pole in 5 sec, then the length of train is?	Pick:
A) 281 m B) 325 m C) 117 m D) 375 m E) 350 m

Solution: 375 m   375 m = 270 * 5/18 * 5= 
270 * 5/18 * 5 = 375
375 m
Answer: D
Difference between two numbers is 6, six times of the smaller lacks by 6 from the four times of the greater. Find the numbers?  Choose the correct option
A) 5,6 B) 7,9 C) 9,15 D) 11,12 E) 13,14

Solution: Explanation:   x – y = 6   4x – 6y = 6   x = 15 y = 9   9,15)
Answer: C
If r and y are integers, then ry(r + y) is Pick
A) Always positive
B) Always negative
C) Positive when r is positive
D) Negative when r is negative
E) It cannot be determined by the information given

Solution: Given r and y are integers, then ry(r + y)   Let's take even as 2 / -2 and odd as 3 / -3..we get the following.. and IMO option D is correct answer..   I presume its Option E if am not missing anything.   r=-3 and y=1   ry(r + y) is positive = 6
Answer: E
What number has a 20:1 ratio to the number 10?	Choose the correct answer:
A) 130  B) 100  C) 200  D) 150  E) 120

Solution: 20:1 = x: 10   x = 10*20   x=150   ANSWER:200
Answer: C
How many terms are there in 2,4,8,16,………..1024?  Choose one
A) 10 B) 6 C) 9 D) 8 E) 7

Solution: Let the number of terms be n. Then,   2 * 2 ^n – 1 = 1024 ,   2^ n-1 = 512 = 2^ 9   n – 1 = 9, n = 10   10NSWER:10
Answer: A
A man's regular pay is $3 per hour up to 40 hours. Overtime is twice the payment for regular time. If he was paid $174, how many hours overtime did he work? Choose the correct choice from the following answers
A) 8 B) 5 C) 9 D) 6 E) 10

Solution: At $3 per hour up to 40 hours, regular pay = $3 x 40 = $120 If total pay = $168, overtime pay = $174 - $120 = $54 Overtime rate (twice regular) 174 -  120= 
174 -  120 = 54
$54 Overtime rate (twice regular)= 2 x $3 = $6 per hour => number of overtime hours = $54/$6 = 9   Ans is 954/ 6= 
54/ 6 = 9
9   Ans is 9
Answer: C
If x > 0.8, which of the following could be the value of x? Choose the correct choice from the following choices
A) √0.03 B) √0.8 C) √0.07 D) √0.06 E) √0.05

Solution: Answer : √0.8
Answer: B
The average age of 15 men of a group is 17 years. Out of these, the average age of 5 men is 14 years and that of the other 9 men is 16 years. The age of the 15th man is?  Choose the most appropriate option.
A) 11 years	B) 17 years	C) 41 years	D) 14 years	E) 12 years

Solution: Age of the 15th student   =[15 * 17 - (14 * 5 + 16 * 9)]   = (255 - 214)= 
(255 - 214) = 41
41 years.   Answer:41 years
Answer: C
In a fort, there are 1200 soldiers. If each soldier consumes 3 kg per day, the provisions available in the fort will last for 30 days. If some more soldiers join, the provisions available will last for 25 days given each soldier consumes 2.5 kg per day. Find the number of soldiers joining the fort in that case? Choose one: A) 288 B) 528 C) 299 D) 277 E) 200

Solution: Assume X soldiers join the fort. 1200 soldiers have provision for 1200(days for which provisions last them)(rate of consumption of each soldier)   = 1200(30)(3) kg   Also provisions available for (1200 + x) soldiers is (1200 + x)(25)(2.5) kg   As the same provisions are available   => 1200(30)(3) = (1200 + x)(25)(2.5)   x = [1200(30)(3)]/[(25)(2.5)] - 1200   x = 528   Answer: 528
Answer: B
How many seconds will a 500 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr? Select
A) 22  B) 30  C) 99  D) 88  E) 11

Solution: Speed of train relative to man = 63 - 3= 
63 - 3 = 60
60 km/hr.= 60 * 5/18 = 50/3 m/sec.   Time taken to pass the man = 500 * 3/50= 
500 * 3/50 = 30
30 sec.   Answer: 30
Answer: B
If a, b, and c are consecutive positive integers and a < b < c, which of the following must be true?
I. b - a = 1
II. abc is an even integer.
III. (a + b + c)/3 is an integer.
Choose the correct choice from the following answers:
A) I only  B) II only  C) I and II only  D) II and III only  E) I, II, and III

Solution: Since a, b, and c are consecutive positive integers and a < b < c, then b = a + 1, from which it follows that b - a = 1. So, I is true.   Next, out of 3 consecutive integers at least 1 must be even, thus abc=even. II is true.   Finally, since b = a + 1, and c = a + 2, then (a + b + c)/3 = (a + a + 1 + a + 2)/3 = a + 1 = integer. III is true as well.   Answer: I, II, and III.
Answer: E
If 20 honey bees make 20 grams of honey in 20 days, then 1 honey bee will make 1 gram of honey in how many days?	Choose the correct choice from the following options.
A) 1  B) 3.5  C) 20  D) 49  E) 30

Solution: Explanation :   Let the required number days be x.   Less honey bees, More days (Indirect Proportion)   Less honey, Less days (Direct Proportion)   Honey bees 1 : 20 :: 20 : x   Honey 20 : 1   => 1 x 20 x x = 20 x 1 x 20   => x = 20.   Answer : 20
Answer: C
there is a set of 52 card.1 card fall down.then we take 2 cards from the rest.that 2 cards are spade.what is the probablity of that fallen card is spade?
Choose the correct choice from the following options:
A) 11/50 B) 13/50 C) 11/20 D) 13/20 E) 17/50

Solution: there are total 13 spades card in a pack if we have drawn 2 spade cards from the pack then out of 13 cards only 11 cards are left.   and out 52 card only 50 cards are left in hand.   p(fallen card is spade)=11C1/50C1=11/50   11/50NSWER:11/50
Answer: A
By selling 150 mangoes, a fruit-seller gains the selling price of 30 mangoes. Find the gain percent?  Choose the correct choice from the following options:
A) 98%	B) 25%	C) 29%	D) 35%	E) 12%

Solution: SP = CP + g   150 SP = 150 CP + 30 SP   120 SP = 150 CP   120 --- 30 CP   100 --- ? => 25%   Answer:25%
Answer: B
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.
Choose the correct choice from the following answers
A) 33
B) 77
C) 24
D) 55
E) 88

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
If $650 is deposited into a savings account at an annual interest rate of 5% that compounds monthly, what is the value of the investment after 7 years?	Choose the correct choice from the following answers:  A) $750.00  B) $823.50  C) $973.25  D) $921.75  E) $110.00

Solution: Using CI Formula:   A=P(1+r/n)^n*t   A=650(1+5/7)^5*7   A=921.75   Option: $921.75
Answer: D
If in a book a total of 3209 digits are used for numbering, then find out the total number of pages in the book.	Choose one.
A) 1079 B) 1000 C) 1100 D) 1075 E) None of these

Solution: Explanation:   Number of digits used in 1 digit numbers = 1*9= 
1*9 = 9
9   Number of digits used in 2 digit numbers= 2*90= 
2*90 = 180
180   Number of digits used in 3 digit numbers= 3*900= 
3*900 = 2_700
2700   Number of digits used in 1 digit numbers= 3209 – (9+180+2700) = 320   Hence, number of pages with 4 digit number = 320/4= 
320/4 = 80
80   Total number of pages= 1079   1079NSWER: 1079
Answer: A
A train 441 m long can cross an electric pole in 21 sec and then find the speed of the train?	Choose the correct choice:
A) 88 Kmph
B) 89 Kmph
C) 76 Kmph
D) 16 Kmph
E) 18 Kmph

Solution: Length = Speed * time   Speed = L/T   S = 441/21= 
441/21 = 21
21 M/Sec   Speed= 20*18/5 (To convert M/Sec in to Kmph multiply by 18/5)   Speed = 76 Kmph   Answer: 76 Kmph
Answer: C
On July 1 of last year, total employees at company E was decreased by 10 percent. Without any change in the salaries of the remaining employees, the average (arithmetic mean) employee salary was 10 percent more after the decrease in the number of employees than before the decrease. The total of the combined salaries of all the employees at Company E after July 1 last year was what percent T of thatbeforeJuly 1 last year? Choose one.
A) 90% B) 99% C) 100% D) 101% E) 110%

Solution: the total number of employees = n   the average salary = x   total salary to all emplyoees = xn   after   the total number of employees = n - 0.1n = 0.9n   the average salary = x + 10% of x = 1.1x   total salary to all emplyoees = 0.9n (1.1x)   total salary after as a % of total salary before T= [0.9n (1.1x)]/xn= 0.99 or 99%.99%
Answer: B
What is the probability of tossing a coin five times and having heads appear at least two times? Options:
A) 1/32 B) 1/16 C) 15/16 D) 13/16 E) 7/8

Solution: If 'n' coins are tossed there will   nc0 outcomes in which n coins will show head   nc1 outcomes in which 1 head will appear   and so on   Here 5 coins are tossed so the total outcomes = 2 ^5 = 32   Outcomes in which at least 2 heads will appear = 32 - 5c0 - 5c1 = 26   Prob at least two heads will appear = 26/32 = 13/16   ANSWER:13/16
Answer: D
In a party there are 5 couples. Out of them 5 people are chosen at random. Find the probability that there are at the least two couples? Choose the correct option:
A) 5/21 B) 5/22 C) 5/20 D) 5/18 E) 5/19

Solution: Number of ways of (selecting at least two couples among five people selected) = (⁵C₂ * ⁶C₁)   As remaining person can be any one among three couples left.   Required probability = (⁵C₂ * ⁶C₁)/¹⁰C₅   = (10 * 6)/252 = 5/21   5/21nswer: 5/21
Answer: A
The radius of a circle is increased by 1%. Find how much % does its area increases?	Choose the correct choice from the following answers: A) 1.01% B) 5.01% C) 3.01% D) 2.01% E) 4.01%

Solution: r = 100 r = 101   r2 = 10000 r2 = 10201   10000 ---- 201   100 ---- ? => 2.01%   ANSWER:2.01%
Answer: D
There are 100 boxes numbered from 1 to 100. Either a red ball or a green ball will be placed in each box in such a way that at least 1 box contains a green ball and the boxes containing green balls are consecutively numbered. How many different ways can this be done?	Choose the correct choice from the following options:
A) 4650 B) 4750 C) 4850 D) 4950 E) 5050

Solution: 1 green ball: 100 ways   2 green balls: 99 ways   3 green balls: 98 ways   4 green balls: 97 ways   etc...   95 green balls: 6 ways   96 green balls: 5 ways   97 green balls: 4 ways   98 green balls: 3 ways   99 green balls: 2 ways   100 green balls: 1 way   The total number of ways is   100*101/2= 
  100*101/2 = 5_050
5050   The answer is 5050.
Answer: E
Playing kick-ball, 6 people are standing in a circle. two standing positions are considered different only when the position of the people are different relative to each other. what is the total number of possible standing positions in the group?
Select.
A) a.5	B) b.10	C) c.24	D) d.32	E) e.120

Solution: for 6 people seating arrangement around a circular table = (6-1)!   = 4!   = 5*4*3*2*1= 
5*4*3*2*1 = 120
120   OA is e.120
Answer: E
All prime numbers are odd numbers Choose the correct choice from the following answers:
A) True  B) False  C) All of these  D) Cannot be determined  E) None of these

Solution: Explanation :   2 is even prime number. Answer : Option False
Answer: B
A man can row downstream at 35 kmph and upstream at 25 kmph. Find the speed of the man in still water and the speed of stream respectively?	Choose the correct option.
A) 35, 3  B) 25, 5  C) 35, 4  D) 5, 30  E) 30, 5

Solution: Let the speed of the man in still water and speed of stream be x kmph and y kmph respectively.   Given x + y = 35 --- (1)   and x - y = 25 --- (2)   From (1) & (2) 2x = 60 => x = 30, y = 5.   Answer:30, 5
Answer: E
Which of the following values of x do not satisfy the inequality x2 - 3x + 2 > 0 at all ?	Choose the correct choice from the following answers:
A) 1 ≤ x ≤2 B) -1 ≥ x ≥ -2 C) 0 ≤ x ≤ 2 D) 0 ≥ x ≥ -2 E) None of these

Solution: Explanation :   On solving x2 - 3x + 2 > 0 , we get ( x - 1 )( x - 2 ) > 0.   That is the roots are x = 1 or x = 2.   The equation assumes a positive value for all values which belong to the interval less than 1 and greater than 2   For x = 1 and x = 2, it becomes zero and for any value of x between 1 and 2 it becomes negative.   1 ≤ x ≤2nswer : 1 ≤ x ≤2
Answer: A
By selling 12 pencils for a rupee a man loses 20%. How many for a rupee should he sell in order to gain 20%?	Choose the correct choice from the following choices:
A) 8  B) 6  C) 5  D) 3  E) 1

Solution: 80% --- 12   120% --- ?     80/120 * 12= 
  80/120 * 12 = 8
8   8nswer:8
Answer: A
3, 7, 15, 27, 43, ? Choose one: A) 63 B) 56 C) 74 D) 57 E) 32

Solution: The pattern is + 4, + 8, + 12, + 16, +20   63nswer : 63.
Answer: A
The total number of digits used in numbering the pages of a book having 356 pages is Select.
A) 732  B) 990  C) 1098  D) 960  E) 1405

Solution: Total number of digits   = (No. of digits in 1- digit page nos. + No. of digits in 2-digit page nos. + No. of digits in 3- digit page nos.)   = (1 x 9 + 2 x 90 + 3 x 257) = (9 + 180 + 771)= 
(9 + 180 + 771) = 960
960.   ANSWER:960
Answer: D