MU-NLPC/Calc-aqua_rat huggingface dataset:
Of the mutual funds on a “select list,” 1/2 have 5-star ratings, and 2/5 of the remaining funds have 4-star ratings. If the remaining 300 funds on the list have 3-star ratings, how many funds are on the list? Choose the correct choice from the following choices:
A) 500
B) 750
C) 1,000
D) 1,200
E) 1,500

Solution: 1,000   Fraction of 5- and 4-star funds: 1/2 + (2/5)*(1/2) = 1/2 + 1/5 = 7/10   Fraction of 3-star funds = 1 - 7/10 = 3/10   (3/10)*Total = 300   Total = 1000
Answer: C
What will come in place of the x in the following number series? 12, 26, 54, 110, 222, x  Pick.
A) 444 B) 446 C) 448 D) 452 E) 454

Solution: 1212 × 2 + 2 = 2626 × 2 + 2 = 5454 × 2 + 2 = 110110 × 2 + 2 = 222222 × 2 + 2 = 446 446
Answer: B
What approximate value should come in place of the question mark (?) in the following equation?
248.251 ÷ 12.62 × 20.52 = ? Choose the correct choice from the following:
A) 400
B) 450
C) 600
D) 350
E) 375

Solution: 248.251 ÷ 12.62 × 20.52 = ?   or,? ≈ 240 ÷ 12 × 20 = 20 × 20 = 400   400nswer 400
Answer: A
A spike is hammered into a train rail. You are standing at the other end of the rail. You hear the sound of the hammer strike both through the air and through the rail itself. These sounds arrive at your point six seconds apart. You know that sound travels through air at 1100 feet per second and through steel at 16,500 feet per second. How far away is that spike?
Select: A) 7070.25 B) 7080.25 C) 6070.25 D) 8070.25 E) 7170.25

Solution: d = 1100(t + 6 ), d = 16500t, so 1100(t + 6) = 16500t   1100t + 6600 = 16500t, 1100t - 1100t + 6600 = 16500t-1100t, 6600 = 15400t   6600/15400 = 15400t/15400, 0.4285 = t, 1100(.4285 + 6) = 7071.35, 16500(.4285) = 7070.25   7070.25NSWER:7070.25
Answer: A
In a class of 100 students, there are 50 who play soccer, 45 who play
basketball, and 50 who play volleyball. Only 15 of these students play all
three sports. Everyone plays at least one of these sports. How many of
the students play exactly two of these sports? Choices.
A) 15
B) 20
C) 25
D) 30
E) 35

Solution: Let S1 be the number of students who play exactly one of the three sports; S2 - the   number of students who play exactly two of the three sports; and let S3 be the number   of students who play all three sports. We know that S3 = 15 and S1 + S2 + S3 = 100   (the total number of students). Also in the sum 50+45+50 (soccer players + basketball   players + volleyball players), each student who plays exactly one sport is counted once,   the ones who play exactly two sports are counted twice, and those who play all three   sports are counted three times. Thus, 50 + 45 + 50 = S1 + 2S2 + 3S3. Note that   S2 = (S1 + 2S2 + 3S3) − (S1 + S2 + S3) − 2S3 = 15   correct answer 15
Answer: A
Pipes A and B can fill a tank in 2 and 6 hours respectively. Pipe C can empty it in 12 hours. If all the three pipes are opened together, then the tank will be filled in?  Choose the correct choice from the following.
A) 3 9/97 hrs  B) 3 9/77 hrs  C) 3 9/17 hrs  D) 1 5/7 hrs  E) 3 9/19 hrs

Solution: Net part filled in 1 hour = 1/2 + 1/6 - 1/12   = 7/12   The tank will be full in 12/7 hrs, i.e., 1 5/7 hrs.   Answer:1 5/7 hrs
Answer: D
Tom can do a piece of work in 5 days and Ben alone can do it in 10 days. How much time will both take to finish the work ? Choose the correct choice from the following options:	A) A)3.3333	B) B)4.3333	C) C)7.3333	D) D)5.3333	E) E)2.3333

Solution: This question can be solved by different methods. We need to conserve time in exams so solving this problem using equations is the good idea.   Time taken to finish the job = XY / (X + Y)   = 5 x 10 / (5 + 10)   = 50 / 15   = 3.3333 days   3.3333nswer: 3.3333
Answer: A
From the starting point in a boat race, one competitor started to sail north at a speed of 1.5 Km/h, the other competitor started to sail west at a speed of 1.2 Km/h. What is the distance in Km between the two competitors after 5 hours?  Choose the correct choice from the following answers
A) 9.6	B) 12.	C) 12.5.	D) 14.	E) 15.4.

Solution: Both competitors are sailing making angle of 90 degrees.   9.6fter 5 hrs one competitor will cover a distance of = 1.5 *5= 
1.5 *5 = 7.5
7.5 KM   9.6nd, other competitor will cover a distance of= 1.2*5= 
1.2*5 = 6
6KM   distance between them after 5 hrs= (7.5^2+ 6^2)^1/2= 9.6 KM   9.6 is the answer
Answer: A
Which of the following fractions E, if written as a decimal, would have a 2 in the thousandths place ?	Select
A) 3/11  B) 7/9  C) 1/8  D) 4/7  E) 1/6

Solution: (A) E=3/11 = 0.2727272727....   3/11nswer: 3/11
Answer: A
Milk contains 5% water.What quantity of pure milk should be added to 10 litres of milk to reduce this 2%?  Select
A) 15 litres B) 16 litres C) 17 litres D) 25 litres E) 35 litres

Solution: Present Ration of MIlK TO W15 litresTER IS 95:5   15 litresmount of Milk is 10 litres   Hence, Pure milk content is 9.5 litre   and water content is 0.5 litres   Now, we should not disturb the water content   So, 0.5 litres of water is equivalent to 2%   So 100% mixture is :  (0.5/2)*100= 
  (0.5/2)*100 = 25
25litre   Thus, milk should be added=25-10= 
25-10 = 15
15 litres of pure milk   15 litresNSWER:15 litres
Answer: A
A card shop contains 5 birthday cards, 5 holiday cards, and 5 graduation cards. If three cards are purchased at random from the shop, what is the probability that the three cards will be of the same type? Choose the correct choice from the following options:
A) 6/91
B) 5/93
C) 4/95
D) 3/97
E) 2/99

Solution: It might require to be written as "5 different birthday cards, 5 different holiday cards, and 5 different graduation cards" rather than "5 birthday cards, 5 holiday cards, and 5 graduation cards"..   If the cards are same there will be ONLY 1 way to pick from each type and thus overall 3..   so numerator has to be 3, or 1 if 3 cancels out..   If I take all as different cards--   ways to pick 3 cards of same type = 5C3 * 3= 30   ways to pick 3 cards out of 15 = 15C3 = 455   Prob = 30/455 = 6/91   6/91ns: 6/91
Answer: A
The age of the two friends were in the ration of 6:5. If the sum of their ages is 55. Then after how many years their ratio will become 8:7?
Choose the correct choice from the following answers:	A) 11	B) 7	C) 10	D) 12	E) 13

Solution: since given ratio is 6:5 of their ages.   6x+5x=55(given)   11x=55   x=5. so present ages are:  6*5= 
 6*5 = 30
30 and   5*5= 
  5*5 = 25
25   after few yrs ratio becomes 8:5.   so,their ages will become 8x and 7x respectively, ie. 40 and 35 respectively.   nw difference of their current ages and further ages is clear from above... ie. 10 yrs.   ANSWER:10
Answer: C
A certain fraction is equivalent to 2/5. If the numerator of the fraction is increased by 4 and the denominator is doubled, the new fraction is equivalent to 1/4. What is the difference of the numerator and denominator of the original fraction?
Choose the correct choice from the following
A) 49
B) 35
C) 28
D) 24
E) 21

Solution: x/y = 2/5 -> 1   (x+4)/2y = 1/4 -> 2   24ivide 1 by 2 :   => 2x/(x+4) = 8/5   => 5x = 4x + 16   => x = 16   => y = 5/2 *16= 
5/2 *16 = 40
40   so x - y= 24   The answer is 24
Answer: D
The ratio of Male to Female in last week Calvary Church attendance was 4:6. If 60% of the Male and 40% of the Female were Under 35 years, How many people under 35 years of age attended Calvary Church last Sunday. Choices.
A) 51%  B) 50%  C) 48%  D) 54%  E) 46%

Solution: let total no of last week 48%alvary church attendance be 100, Male 40 and Female 60, so total number of last week 48%alvary church attendance below 35 years for both male and female respectively 40* 60/100= 
40* 60/100 = 24
24 and   60* 40/100= 
  60* 40/100 = 24
24   so total 48 48%alvary church attendance last week out of a Total of 100 attendance is under 35 years......so required % is 48%   ANSWER:48%
Answer: C
A man complete a journey in 20 hours. He travels first half of the journey at the rate of 10 km/hr and second half at the rate of 15 km/hr. Find the total journey in km.
Answers:
A) 220 km  B) 240 km  C) 230 km  D) 232 km  E) 234 km

Solution: 0.5x/10 + 0.5x/15 = 20   --> x/10+ x/15= 40   --> 5x = 30x40   --> x = (30x40)/5 = 240 km.   Answer : 240 km.
Answer: B
Sum of 49 odd numbers is?  Choose one:
A) 2398	B) 2399	C) 2400	D) 2401	E) 2402

Solution: sum of 1st n odd no.s = 1+3+5+7+... = n^2   so, Sum of 1st 49 odd numbers = 49^2 = 2401   ANSWER:2401
Answer: D
What is the smallest number K which when increased by 5 is completely divisible by 8, 11 and 24?	Choose the correct choice from the following answers
A) 264 B) 259 C) 269 D) 270 E) 282

Solution: This question includes a number of great Number Property shortcuts that you can take advantage of:   1) The question asks for the SMALLEST number that, when increased by 5 is divisible by 8, 11 and 24. Since the answers are numbers, we can TEST THE ANSWERS.   2) Any number that is divisible by 24 is ALSO divisible by 8, so we really just need to consider the 11 and the 24.   3) To be divisible by 24, the end number MUST be EVEN. Since we're adding 5 to get to that end number, the starting number MUST be ODD.   The last shortcut allows us to eliminate Answers A, D and E. Between Answers B and C, TESTING B first will prove that, when increased by 5, the end sum is divisible by both 11 and 24.   Final Answer:   259
Answer: B
Ayesha's father was 38 years of age when she was born while her mother was 34 years old when her brother four years younger to her was born. What is the difference between the ages of her parents?
Select the correct option
A) 2 years	B) 4 years	C) 6 years	D) 8 years	E) 10 years

Solution: Explanation:   Mother's age when Ayesha's brother was born = 34 years.   Father's age when Ayesha's brother was born = (38 + 4)= 
(38 + 4) = 42
42 years.   Required difference= (42 - 34)= 
(42 - 34) = 8
8 years.   Answer: 8 years
Answer: D
A is a working partner and B is a sleeping partner in a business. A puts in 20,000 and B 90,000. A gets 20% of the profit for managing the business, and the rest is divided in proportion to their capitals. Find the share of B in profit of 11000.
Select:
A) 3500
B) 7200
C) 6800
D) 4800
E) None of these

Solution: The amount A gets for managing   = 20% of Rs. 11000 = 2200   Remaining profit = 11000 – 2200 = 8800   This is to be divided in the ratio 2 : 9.   Share of 7200 = 9/11 of 8800 = 7200   Answer 7200
Answer: B
A bullet train 150 m long is running with a speed of 30 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the bullet train is going?	Choose the correct choice from the following answers:
A) 23 sec
B) 15 sec
C) 12 sec
D) 11 sec
E) 15 sec

Solution: E   15 sec   Speed of the bullet train relative to man = (30 + 6)= 
(30 + 6) = 36
36 *5/18 m/sec= 30/3 m/sec.   Time taken by the bullet train to cross the man = Time taken by it to cover 150 m at (30/3) m / sec   = (150 *3/30)= 
(150 *3/30) = 15
15 sec
Answer: E
99! how many zero's? Choose the correct choice:
A) 20
B) 21
C) 22
D) 23
E) 24

Solution: 99!=99/5=19   =19/5=3   so 99! has (19+3=22 zeroes)   ANSWER:22
Answer: C
A can do a piece of work 30 days. B can do work in 55 days. In how many days they will complete the work together?	Choose the correct choice from the following choices:
A) 15 days	B) 16 days	C) 19.4 days	D) 17.2 days	E) 18 days

Solution: L19.4 daysM = 330, Ratio= 30:45=6:11   No of days= 330/(6+11) = 330/17 = 19.4 days   ANSWER:19.4 days
Answer: C
Raman mixed 24 kg of butter at Rs. 150 per kg with 36 kg butter at the rate of Rs. 125 per kg. At what price per kg should he sell the mixture to make a profit of 40% in the transaction?	Choose the correct choice from the following:	A) 339	B) 278	C) 189	D) 287	E) 211

Solution: CP per kg of mixture = [24(150) + 36(125)]/(24 + 36) = Rs. 135   SP = CP[(100 + profit%)/100]   = 135 * [(100 + 40)/100] = Rs. 189.   Answer: 189
Answer: C
Nitin ranks 18th in a class of 49 students. What is rank from the last ? Choose the correct option.
A) 33  B) 38  C) 32  D) 28  E) 19

Solution: Explanation:   Number students behind the nitin in rank = (49 - 18)= 
(49 - 18) = 31
31   Nitin is 32nd from the last   Answer: 32) 32
Answer: C
Linda and Angela contract to paint a neighbor's house. Even though Linda
spends 30% more time painting the house than Angela, each receives a payment
of m dollars when the work is completed. If Angela decides to pay Linda n
dollars so that they would have received the same compensation per hour
worked, what is n in terms of m?	Choices
A) A)(3/23)m
B) B)(1/3)m
C) C)(1/4)m
D) D)(1/5)m
E) E)(1/6)m

Solution: let angela work for 10hrs and get 1150 rs. (m =1150)   According to question, linda works 30% more time and gets the same amount. so let linda work 13 hrs and get 1150 rs.   so they do a total of  13 +10= 
 13 +10 = 23
23 hrs of work and get 2300 rs together . The question basically asks to equalise their payment. so a total of 2300 rs is received by them and they do 23 hrs work together. average rate will be  2300/23= 
 2300/23 = 100
100 rs per hr. so linda should get 13*100= 
13*100 = 1_300
1300 rs. But she got only 1150. so angela should give 150 rs to linda. answer= 150/1150 =3/23   answer (3/23)m
Answer: A
Three partners A, B, C in a business invested money such that 2(Aâ€™s capital) = 5(Bâ€™s capital) = 10(Câ€™s capital) then, The ratio of their capitals is
Choose the correct choice from the following answers:	A) 63 : 45 : 34	B) 63 : 54 : 34	C) 5 : 2 : 1	D) 63 : 45 : 35	E) None of these

Solution: Explanation:   Let 2(Aâ€™s capital) = 5(Bâ€™s capital) = 10(Câ€™s capital) = Rs.x   Then, Aâ€™s capital = Rs x/2, Bâ€™s capital = Rs. x/5 and Câ€™s capital = Rs. x/10   A : B : 5 : 2 : 1 = x/2 : x/5 : x/10   5 : 2 : 1   Answer: Option 5 : 2 : 1
Answer: C
the walker walking at a constant rate of 4 miles per hour is passed by a cyclist traveling in the same direction along the same path at 20 miles per hour. the cyclist stops to wait for the hiker 5 minutes after passing her, while the walker continues to walk at her constant rate, how many minutes must the cyclist wait until the walker catches up?  Choose one.
A) 16  B) 18  C) 20  D) 22  E) 24

Solution: After passing the hiker the cyclist travels for 5 minutes at a rate of 20 miles/hour.   In those 5 mins the cyclist travels a distance of 5/3 miles.   In those 5 mins the hiker travels a distance of 1/3 miles.   So the hiker still has to cover 4/3 miles to meet the waiting cyclist.   The hiker will need 1/3 hours or 20 mins to cover the remaining 4/3 miles.   So the answer is 20.
Answer: C
Doughnut delivery delivers about 75 orders using 15 fleet bikes in any given day of 15 hours. They need to increase their delivery for Christmas and so they bought 10 more bikes and now work for 4 extra hours. How many more orders will be delivered in the next eight days? Select.
A) 200  B) 225  C) 37.5  D) 16,875  E) 95

Solution: old bikes deliver 75/15= 
75/15 = 5
5 orders per hour, which is  5* (15+4)= 
 5* (15+4) = 95
95 orders in new day time frame.   Total bikes is 25* 95 orders is 225 orders.   Answer is 225.
Answer: B
If the sides of a triangle are 30 cm, 26 cm and 10 cm, what is its area?  Choose the correct choice from the following: A) 120 B) 110 C) 130 D) 140 E) 150

Solution: The triangle with sides 30 cm, 26 cm and 10 cm is right angled, where the hypotenuse is 30 cm.   Area of the triangle = 1/2 * 26 * 10= 
1/2 * 26 * 10 = 130
130 cm2   Answer: Option 130
Answer: C
A bag is filled with pennies and nickels in the ratio of 5 to 3. There are 30 nickles in the bag, how many coins are there in that bag?
Select the correct option: A) 70 B) 65 C) 75 D) 85 E) 80

Solution: A ratio of pennies to nickels of 5 to 3 means that we can write the number of pennies and nickels in the form   number of pennies = 5x and number of nickels = 3x   But we know the number of nickels, 30. Hence   3x = 30   Solve for x   x = 10   The total number of coins is given by   5x + 3x = 8x  5  + 3= 
 5  + 3 = 8
8x= 8 × 10 = 80   80
Answer: E
The L.C.M. of two numbers is 42. The numbers are in the ratio 2 : 3. Then sum of the number is:  Choose the correct choice from the following choices:
A) 28  B) 32  C) 35  D) 53  E) 54

Solution: Let the numbers be 2x and 3x.   Then, their L.C.M. = 6x.   So, 6x = 42 or x = 7.   The numbers are 14 and 21.   Hence, required sum = (14 + 21)= 
(14 + 21) = 35
35.   Answer: Option 35
Answer: C
Kiran has $100 in her piggy bank. How much will she have in her bank 30 weeks from now if she puts $1 in the bank next week, $2 two weeks from now, $3 three weeks from now, and continues to increase the amount that she puts in by $1 each week?
Select:
A) 500  B) 525  C) 535  D) 565  E) 575

Solution: The dollar deposits are in an A.P.   1,2,3,4...30 with common difference 1   Sum of the terms is n(n+1) / 2   i.e 30 * (30+1) /2   = 30 * 31/2= 
30 * 31/2 = 465
465   Total deposit therefore with Chiu-Lihas is 100 + 465= 
100 + 465 = 565
565$
Answer: D
Find the area of a parallelogram with base 24 cm and height 16 cm. Choose the correct choice from the following choices
A) 304 cm2  B) 384 cm2  C) 184 cm2  D) 284 cm2  E) 385 cm2

Solution: Area of a parallelogram = base * height   = 24 * 16= 
24 * 16 = 384
384 cm2   Answer: 384 cm2
Answer: B
A man can row upstream at 7 kmph and downstream at 10kmph.find man’s rate in still water and the rate of current.  Pick:	A) 1.5 km/hr	B) 2.5 km/hr	C) 3.5 km/hr	D) 4.5 km/hr	E) 5.5 km/hr

Solution: Rate in still water=1/2(10+7)km/hr=8.5 km/hr.   Rate of current=1/2(10-7)km/hr=1.5 km/hr.   1.5 km/hrNSWER 1.5 km/hr 1.5 km/hr
Answer: A
A cube of side 5 meter length is cut into small cubes of side 25cm each. How many such small cubes can be obtained? Choices:
A) 10781
B) 1276
C) 1000
D) 8000
E) 5000

Solution: Along one edge, the number of small cubes that can be cut   = 500/25= 
500/25 = 20
20   Along each edge 20 cubes can be cut. (Along length, breadth and height). Total number of small cubes that can be cut=20 *20 * 20= 
20 *20 * 20 = 8_000
8000   Answer:8000
Answer: D
What is the ratio between perimeters of two squares one having 3 times the diagonal then the other? Choose one:
A) 4:8	B) 1:4	C) 6:2	D) 3:1	E) 1:2

Solution: Explanation:   d = 3d d = d   aâˆš2 = 3d aâˆš2 = d   a = 3d/âˆš2 a = d/âˆš2 => 3: 1   ANSWER IS 3:1
Answer: D
A male student must answer 7 out of 10 questions on an examination. If at least 3 of the first 5 questions must be answered, how many possible combinations of 7 questions are available to the student?  Choose the correct choice from the following answers.
A) 120	B) 140	C) 110	D) 150	E) 160

Solution: as there is ONLY one possiblity of choosing 7 out of 10, while choosing less than 3 in first five   choose 2 in first 5 and all 5 from later half..   ways = 5C2 = 10..   total ways = 101103 = 120   ans = 120-10= 
120-10 = 110
110   110
Answer: C
70 is subtracted from 30% of a number, the result is 20. Find the number?  Select the correct option
A) 150  B) 997  C) 266  D) 300  E) 271

Solution: (30/100) * X – 70 = 20   3X = 900   X = 300   Answer:300
Answer: D
Five years ago the average of the ages of A and B was 40 years and now the average of the ages of B and C is 49 years. What will be the age of the B ten years hence?
Choose the correct answer:
A) 22
B) 77
C) 26
D) 98
E) 51

Solution: Let the present ages of A, B and C be a, b and c respectively.   Given, [(a - 5) + (b - 5)] / 2 = 40 => a + b = 90 --- (1)   (b + c)/2 = 49 => b + c = 98 --- (2)   From (1) and (2), we cannot find b.   Answer: 98
Answer: D
A rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered. If the area of the field is 60 sq. feet, how many feet of fencing will be required?
Choose the correct choice from the following choices:
A) 34	B) 40	C) 68	D) 88	E) 26

Solution: We have: l = 20 ft and lb = 60 sq. ft.   So, b = 3 ft.   Length of fencing = (l + 2b) = (20 + 6)= 
(20 + 6) = 26
26 ft.   ANSW26R:26
Answer: E
A bag contains 5 red balls, 5 green balls and 6 white balls. A ball is drawn at
random from the box. What is the probability that the ball drawn is either red or green? Choose the correct choice from the following
A) 2/5	B) 3/5	C) 1/5	D) 7/15	E) 5/8

Solution: Total number of balls = (5 + 5 + 6)= 
(5 + 5 + 6) = 16
16.   Therefore, n(S)= 16.   Let E1 = event of drawing a red ball.   and E2 = event of drawing a green ball.   Then, E1 n E2 = f.   P (E1 n E2) = P(E1) + P(E2) = (5/16 + 5/16) = 5/8.   ANSW5/8R:5/8
Answer: E
A set S = {x, -8, -5, -1, 1, 6, 9, y} with elements arranged in increasing order. If the median and the mean of the set are the same, what is the value of |x|-|y|?	Choose one.
A) -1
B) Cannot be determined
C) 1
D) 0
E) 2

Solution: Median of the set = (-1+1)/2= 
(-1+1)/2 = 0
0   As per statement, Mean of the set= 0   Mean of the set   |y|- |x| +16-14 = 0 (where x is negative n y is positive)   |y|- |x| = -2   So the absolute difference between two numbers is 2   Answer 2
Answer: E
Which of the following are roots of an equation (x^-2)-(2x^-1)-35=0	Choose the correct choice:
A) 1/5 and -1/7 B) -1/5 and 1/7 C) 1/5 and 1/7 D) -1/5 and -1/7 E) -5/2 and -1/7

Solution: Given: (x^-2) - (2x^-1) - 35 = 0   Rewrite as: 1/(x²) - 2/x - 35 = 0   Remove fractions by multiplying both sides by x² to get: 1 - 2x - 35x² = 0   Rearrange to get: 35x² + 2x - 1 = 0   Factor to get: (5x + 1)(7x - 1) = 0   So, EITHER 5x + 1 OR 7x - 1 = 0   If 5x + 1 = 0, then x = -1/5   If 7x - 1 = 0, then x = 1/7   So, the roots (solutions) are -1/5 and 1/7   The answer is -1/5 and 1/7.
Answer: B
In an increasing sequence of 10 consecutive integers, the sum of the first 4 integers is 570. What is the sum of the last 6 integers in the sequence?
Choose one
A) 885	B) 888	C) 889	D) 884	E) 880

Solution: Solution:   In solving this problem we must first remember that when we have 10 consecutive integers we can display them in terms of just 1 variable. Thus, we have the following:   Integer 1: x   Integer 2: x + 1   Integer 3: x + 2   Integer 4: x + 3   Integer 5: x + 4   Integer 6: x + 5   Integer 7: x + 6   Integer 8: x + 7   Integer 9: x + 8   Integer 10: x + 9   We are given that the sum of the first 4 integers is 570. This means that:   x + x+1 + x+2 + x+3 = 570   4x + 6 = 570   4x = 564   x = 141   The sum of the last 6 integers can be expressed and simplified as:   x+4 + x+5 + x+6+ x+7 +x+8 x+9 = 6x + 39   Substituting 141 for x yields:   (6)(141) + 39 = 885   885nswer: 885
Answer: A
P and Q invested in a shop. The profits were divided in the ratio of 4 : 6 respectively. If P invested Rs. 55,000, the amount invested by Q is:  Choices:
A) 48000 B) 40000 C) 35000 D) 60000 E) None

Solution: Suppose Q invested Rs. y. Then, 50000/y = 4/6 or y = [50000 x 6/ 4] = 75000.   Answer None
Answer: E
A vessel of capacity 2 litre has 40% of alcohol and another vessel of capacity 6 litre had 60% alcohol. The total liquid of 8 litre was poured out in a vessel of capacity 10 litre and thus the rest part of the vessel was filled with the water. What is the new concentration of Mixture?
Choose the correct choice from the following choices.
A) 31%.
B) 44%.
C) 49%.
D) 29%.
E) 51%.

Solution: 40% of 2 litres = 0.8 litres   60% of 6 litres = 3.6 litres   Therefore, total quantity of alcohol is 4.4 litres.   This mixture is in a 10 litre vessel. Hence, the concentration of alcohol in this 10 litre vessel is 44%   44%.
Answer: B
A textile worker’s wages are increased by 10% and afterwards decreased by 10 %. Find the change percentage in his wages. Choose the correct answer
A) 2 % increase
B) 4% increase
C) 1% decrease
D) 4% decrease
E) None of these

Solution: Explanation:   Let workers wages = X   A 10% increase would mean new wages   = (110/100) X   A 10% decrease would mean new wages   = (90/100) (110/100 X)   = 99/100 X which means a decrease of 1 %   ANSWER: 1% decrease
Answer: C
Two brothers Ram and Ravi appeared for an exam. The probability of selection of Ram is 3/7 and that of Ravi is 1/5. Find the probability that both of them are selected.
Choose the correct choice from the following
A) 3/35  B) 2/3  C) 7/35  D) 5/7  E) 7/5

Solution: Let A be the event that Ram is selected and B is the event that Ravi is selected.   P(A) = 3/7   P(B) = 1/5   Let C be the event that both are selected.   P(C) = P(3/35) x P(B) as 3/35 and B are independent events:   = 3/7 x 1/5 = 3/35   3/35NSWER:3/35
Answer: A