MU-NLPC/Calc-aqua_rat huggingface dataset:
Laura took out a charge account at the General Store and agreed to pay 5% simple annual interest. If she charges $35 on her account in January, how much will she owe a year later, assuming she does not make any additional charges or payments?  Choose the correct option: A) $2.10 B) $36.75 C) $37.16 D) $38.10 E) $38.80

Solution: Principal that is amount taken by Laura at year beginning = 35$   Rate of interest = 5%   Interest = (5/100)*35= 
(5/100)*35 = 7/4 = around 1.75
1.75$   Total amount that Laura owes a year later= 35+1.75= 
35+1.75 = 36.75
36.75 $   Answer $36.75
Answer: B
Sheik Abdullah decides to buy 4 new cars for his collection. If he has to choose between nine different cars, what is the number of purchasing possibilities he has?  Options:
A) A)106  B) B)116  C) C)126  D) D)136  E) E)146

Solution: Sheik Abdullah decides to buy 4 new cars for his collection. He has to choose between nine different cars   81263= 9*8*7*6/(4*3*2*1)= 
9*8*7*6/(4*3*2*1) = 126
126 ANS:126
Answer: C
There were five baskets of apples on the table. Each basket had one more apple in it than the basket before it. The average number of apples in the baskets A, B, C, D and E is 220. What percent is E of C ?
Choices
A) 99.1  B) 99.2  C) 99.3  D) 99.4  E) 99.5

Solution: Explanation :   In such a case the middle number (C) is the average   ∴ C = 220 and E = 222   Required percentage = 220/222 x 100 = 99.1   99.1nswer : Option 99.1
Answer: A
Find the average of the first 20 natural numbers?	Choose the correct choice from the following options
A) 10.9
B) 10.8
C) 10.2
D) 10.5
E) 10.4

Solution: Average of the first 'n' natural numbers = (n + 1)/2   We get  (20 + 1)/2= 
 (20 + 1)/2 = 21/2 = around 10.5
10.5   Answer:10.5
Answer: D
A car traveling at a certain constant speed takes 15 seconds longer to travel 1 kilometer than it would take to travel 1 kilometer at 48 kilometers per hour. At what speed, in kilometers per hour, is the car traveling?	Choices
A) 39	B) 40	C) 41	D) 42	E) 43

Solution: 48 * T = 1 km => T = 1/48 km/h   V*(T+15/3600) = 1   V (1/48 + 15/3600) = 1   V (90/3600) = 1   V = 40 km/h   The answer is 40.
Answer: B
Jennifer had $180 to spend on herself. She spent 1/5 of the money on a sandwich, 1/6 for a ticket to a museum, and 1/2 of it on a book. How much money does Jennifer have left over? Choices:
A) $4
B) $14
C) $5
D) $15
E) $24

Solution: 1/5 x $180 = $36 for sandwich   1/6 x $180 = $30 for museum   1/2 x $180 = $90 for book   $36 + $30 + $90 = $156 spent   $180 - $156  36 +  30 +  90= 
 36 +  30 +  90 = 156
$156 spent   $180 - $156 = $24 left over   correct answer $24 180 -  156= 
 180 -  156 = 24
$24 left over   correct answer $24
Answer: E
Of the 200 stamps in a collection, 90 are foreign and 60 are more than 10 years old. If 20 stamps are both foreign and more than 10 years old, how many stamps are neither foreign nor more than 10 years old?	Choose the most appropriate option:
A) 50  B) 70  C) 100  D) 130  E) 150

Solution: 20 stamps are both foreign and more than 10 years old.   70 stamps are foreign only.   40 stamps are 10 years old only.   The number of remaining stamps is  200 - (20+70+40)= 
 200 - (20+70+40) = 70
70   The answer is 70.
Answer: B
Read the following three equations:
5 ~ 4 ~ 3 ~ 9 = 4215
6 ~ 9 ~ 2 ~ 6 = 3816
4 ~ 7 ~ 3 ~ 3 = 1122
Now based on the rule that has been used, solve the following equation:
4 ~ 2 ~ 7 ~ 4 = ____
Pick:
A) 1416 B) 2910 C) 2940 D) 3749 E) 4470

Solution: 1416   1416   1416   The rule that is being followed here is   P ~ Q ~ R ~ S = [first digit of (P * S)] [last digit of (Q * R)] [first digit of (Q * R)] [last digit of (P * S)]   Using the same rule in the incomplete equation,   4 ~ 2 ~ 7 ~ 4 = [first digit of (4 * 4)] [last digit of (2 * 7)] [first digit of (2 * 7)] [last digit of (4 * 4)]   = 1416   Thus 1416 is the missing number.
Answer: A
Of the 800 employees of Company X, 80 percent have been with the company for at least ten years. If y of theselong-termmembers were to retire and no other employee changes were to occur, what value of y would reduce the percent oflong-termemployees in the company to 60 percent ?  Answers:
A) 400
B) 160
C) 112
D) 80
E) 56

Solution: The # oflong-termemployees is 80%*800=640.   After y of them retire new # oflong-termemployees would become 640-y.   Total # of employees would become 800-y.   We want 640-y to be 60% of 800-y --> 640-y=(800 -y)*60% --> y = 400.   400nswer: 400.
Answer: A
In how many ways can a group of 6 men and 3 women be made out of a total of 7 men and 4 women?
Select the correct option.
A) 63 B) 29 C) 70 D) 74 E) 28

Solution: We need to select 7 men from 6 men and 4 women from 3 women. Number of ways to do this= 7C6 × 4C32828)
Answer: E
Suraj has a certain average of runs for 9 innings. In the 10th innings he scores 200 runs thereby increasing his average by 8 runs. What is his average after the 10th innings?	Choose the correct choice from the following answers.
A) 149 B) 190 C) 128 D) 178 E) 190

Solution: To improve his average by 8 runs per innings he has to contribute 9 x 8 = 72 runs for the previous 8 innings.   Thus, the average after the 9th innings   = 200 - 72= 
200 - 72 = 128
128.   ANSWER:128
Answer: C
If x is 25 percent greater than 88, then x =	Pick
A) 110  B) 70.4  C) 86  D) 105.6  E) 108

Solution: x=88*1.25= 
88*1.25 = 110
110   So the answer is 110.
Answer: A
On a certain day, orangeade was made by mixing a certain amount of orange juice with an equal amount of water. On the next day, orangeade was made by mixing the same amount of orange juice with four times the amount of water. On both days, all the orangeade that was made was sold. If the revenue from selling the orangeade was the same for both days and if the orangeade was sold at $0.40 per glass on the first day, what was the price per glass on the second day? Answers:
A) $0.16
B) $0.20
C) $0.30
D) $0.40
E) $0.45

Solution: On the first day 1 unit of orange juice and 1 unit of water was used to make 2 units of orangeade;   On the second day 1 unit of orange juice and 4 units of water was used to make 5 units of orangeade;   So, the ratio of the amount of orangeade made on the first day to the amount of orangeade made on the second day is 2 to 5. Naturally the ratio of the # of glasses of orangeade made on the first day to the # of glasses of orangeade made on the second day is 2 to 5.   We are told thatthe revenue from selling the orangeade was the same for both daysso the revenue from 2 glasses on the first day equals to the revenue from 5 glasses on the second day.   Say the price of the glass of the orangeade on the second day was $x then 2*0.4=5*x --> x=$0.16.   $0.16nswer: $0.16.
Answer: A
In a games hour 4 different types of players came to the ground? cricket 11, hockey 15, football 21, softball 15. In these 4 people play both cricket and hockey, 3people play both softball and football. 4 people play both cricket and football. How many people play only cricket?
Pick:
A) 11 B) 3 C) 5 D) 7 E) 9

Solution: people play only cricket = total players in cricket- both cricket and football- both cricket and hockey.   people play only cricket = 11-4-4= 
11-4-4 = 3
3   Answer is 3
Answer: B
A discount electronics store normally sells all merchandise at a discount of 10 percent to 30 percent off the suggested retail price. If, during a special sale, an additional 20 percent were to be deducted from the discount price, what would be the lowest possible price of an item costing $260 before any discount?	Choices.
A) $130.00	B) $145.60	C) $163.80	D) $182.00	E) $210.00

Solution: Original price : 260 $   Max first discount = -30%   Thus : 260∗(1−30/100)=182   Second discount on the discounted price = -20%   Thus : 182∗(1−20/100)=145,6   Answer $145.60.
Answer: B
8 litres are drawn from a cask full of wine and is then filled with water. This operation is performed three more times. The ratio of the quantity of wine now left in cask to that of the water is 16 : 65. How much wine the cask hold originally ?	Choose the correct choice from the following options.
A) 18 litres
B) 24 litres
C) 32 litres
D) 42 litres
E) None

Solution: Solution   Let the quantity of the wine in the cask originally be x litres   then, quantity of wine left in cask after 4 operations   = [x(1- 8/x)4] litres.   Therefore x(1- 8/x)4 / x = 16/81 =› (1- 8/x)4 = (2/3)2   =› (x - 8 / x) = 2/3 =› 3x - 24 = 2x =› x = 24.   Answer 24 litres
Answer: B
In a kilometer race, A beats B by 50 meters or 10 seconds. What time does A take to complete the race?	Select the correct option:
A) 167 sec
B) 190 sec
C) 176 sec
D) 716 sec
E) 123 sec

Solution: Time taken by B run 1000 meters   = (1000 * 10)/50= 
(1000 * 10)/50 = 200
200 sec.   Time taken by A= 200 - 10= 
200 - 10 = 190
190 sec.   Answer:190 sec
Answer: B
To apply for the position of photographer at a local magazine, a photographer needs to include two or three photos in an envelope accompanying the application. If the photographer has pre-selected seven photos representative of her work, how many choices does she have to provide the photos for the magazine? Choose the correct choice from the following choices:
A) 42
B) 48
C) 56
D) 60
E) 64

Solution: 7562 + 7563 = 21 + 35= 
21 + 35 = 56
56   The answer is 56.
Answer: C
A man counted his animals, 80 heads and 240 legs (ducks and goats). how many goats are there?
Choose the correct choice from the following choices:
A) 30
B) 40
C) 50
D) 60
E) 70

Solution: let no of ducks=d and no of goat=g   d+g=80(heads)----------> eq 1   each duck has 2 legs and goat has 4 legs   2d+4g=240 and divide 2d+4g=240 by 2 we get d+2g=120 -----------> eq2   subtract eq1 from eq2   we get no of goats=40   ANSWER:40
Answer: B
There are some rabbits and peacocks in a zoo. The total number of their heads is 60 and total number of their legs is 192. Find the number of total rabbits?  Choices
A) 36	B) 77	C) 88	D) 99	E) 22

Solution: Let the number of rabbits and peacocks be 'r' and 'p' respectively. As each animal has only one head, so r + p = 60 --- (1)   Each rabbit has 4 legs and each peacock has 2 legs. Total number of legs of rabbits and peacocks, 4r + 2p = 192 --- (2)   Multiplying equation (1) by 2 and subtracting it from equation (2), we get   => 2r = 72 => r = 36.   36nswer: 36
Answer: A
How many seconds will a train 200 meters long take to cross a bridge 150 meters long if the speed of the train is 36 kmph?	Options:
A) 22 sec	B) 35 sec	C) 25 sec	D) 18 sec	E) 17 sec

Solution: D = 200 + 150= 
200 + 150 = 350
350   S= 36 * 5/18= 
36 * 5/18 = 10
10 mps   T= 350/10= 
350/10 = 35
35 sec   Answer:35 sec
Answer: B
A shopkeeper sold 10 articles at the cost price of 12 articles. Then find the profit% or lost%  Choose the most appropriate option
A) -10%
B) 10%
C) 15%
D) 20%
E) 25%

Solution: here 10 articles selling price = 12 articles cost price   so the difference = 12-10= 
12-10 = 2
2   % of profit= 2*100/10= 
2*100/10 = 20
20%   correct option is 20%
Answer: D
What is the perimeter of a regular polygon with sides of length 12 cm and internal angles measuring 84° each?	Choose the most appropriate option.
A) 45 cm B) 108 cm C) 120 cm D) 132 cm E) 144 cm

Solution: Sum of all interior angles is given by:   180(n-2) = n is number of sides   180(n-2) = 84*n   from here   n = 3.75   So perimeter becomes 12*3.75= 
12*3.75 = 45
45   answer 45 cm
Answer: A
a^3 - b^3 - 3ab = 1,
a^3 - b^3 + ab = x! + 1,
where a,b,x are positive integers,x is least.
Find (a + b) ?	Choose the correct choice from the following answers: A) 2 B) 3 C) 4 D) 5 E) 6

Solution: a^3 - b^3 + ab = x! + 1,   a^3 - b^3 - 3ab = 1,   subtracting,   ab+3ab =x!   4ab=x!   if x=4   a=3   b=2   a+b=3+2= 
3+2 = 5
5 and x=4.   ANSWER:5
Answer: D
Which of the following CANNOT be a value of 8/(x–8)?	Choose the correct choice from the following choices: A) -1 B) -1/2 C) 0 D) 2 E) 8

Solution: The question doesn't ask for the value of x here, but for the possible results of the equation.   If 8/(x-8) = 0, then the numerator must be 0. But since the numerator is 8, the fraction can not be equal to 0.   The answer is 0.
Answer: C
Alok ordered 16 chapatis, 5 plates of rice, 7 plates of mixed vegetable and 6 ice-cream cups. The cost of each chapati is Rs.6, that of each plate of rice is Rs.45 and that of mixed vegetable is Rs.70. The amount that Alok paid the cashier was Rs.1021. Find the cost of each ice-cream cup?  Options:
A) 35 B) 66 C) 77 D) 99 E) 91

Solution: Let the cost of each ice-cream cup be Rs.x   16(6) + 5(45) + 7(70) + 6(x) = 1021   96 + 225 + 490 + 6x = 1021   6x = 210 => x = 35.   35nswer: 35
Answer: A
If green means red, red means yellow, yellow means blue, blue means orange and orange means green, what is the colour of sun ? Choose the correct choice from the following choices.
A) Blue B) Red C) Yellow D) Orange E) Pink

Solution: Explanation:   The colour of sun is 'yellow' and as given 'red' means 'yellow'.   so, the colour of sun is 'red'.   Answer: Red
Answer: B
Before leaving home for the town of Madison, Pete checks a map which shows that Madison is 5 inches from his current location, Gardensquare. Pete arrives in Madison 6.5 hours later and drove at an average speed of 60 miles per hour. At what scale, in inches per mile, is the map drawn?	Choose one:	A) 1/3	B) 1/30	C) 1/10	D) 1/78	E) 30

Solution: Pete covered 6.5*60= 
6.5*60 = 390
390 miles which correspond to 5 inches on the map --> scale in inches per mile is 5/390=1/78.   Answer: 1/78.
Answer: D
How many times digit 2 is used while writing numbers from 400 to 700? Choices:
A) 150 B) 190 C) 250 D) 80 E) 130

Solution: in 400 to 500 there are 50 two's   in 500 to 600 there are 50 two's   in 600 to 700 there are 50 two's   so total is 150 two's   CORRECT OPTION :150
Answer: A
A trader bought a car at 10% discount on its original price. He sold it at a 80% increase on the price he bought it. What percent of profit did he make on the original price? Choose the correct option.
A) 17%  B) 62%  C) 12%  D) 19%  E) 22%

Solution: Original price = 100   CP = 90   S = 90*(180/100)= 
90*(180/100) = 162
162   100 - 162= 62%   Answer: 62%
Answer: B
A car traveled 45% of the way from Town A to Town B at an average speed of 45 mph.
The car traveled at an average speed of v mph for the remaining part of the trip.
The average speed for the entire trip was 50 mph. What is v in mph? Pick:
A) 45	B) 55	C) 65	D) 43	E) 42

Solution: Assume total distance = 100miles   Time taken for 45 miles = 45/45= 
45/45 = 1
1 hour   Time taken for the rest of the 55 miles= 55/v hours.   Average speed = 50   Therefore the total time needed = 2 hours.   2 = 1 + 55/v   Hence v = 55 mph   Answer : 55
Answer: B
One-sixth of the attendees at a certain convention are female students, two-thirds of the attendees are female, and one-third of the attendees are students. If 100 of the attendees are neither female nor students, what is the total number of attendees at the convention?
Pick:
A) 600	B) 700	C) 800	D) 900	E) 1000

Solution: Let no. of Attendee are A.   Now As per the condition of the problem stated above .   We have following population in the convention as Attendee.   Total no. of females = [2/3]*A   Total no. of females as student : [1/6]*A   Total no. of students = [1/3]*A   Total no. of male as student = [1/6]*A   Total no. of males = A - [2/3]*A = [1/3]A   No. of males which are not student = [1/3]600 - [1/6]*600 = 100   Hence 600 = 600   So 600nswer is 600
Answer: A
Length of a rectangular plot is 14 mtr more than its breadth. If the cost of fencing the plot at 26.50 per meter is Rs. 5300, what is the length of the plot in mtr?  Options.
A) 50 m  B) 57 m  C) 80 m  D) 82 m  E) 84 m

Solution: Let breadth = x metres.   Then, length = (x + 14) metres.   Perimeter = 5300 m = 200 m.   26.50   2[(x + 14) + x] = 200   2x + 14 = 100   2x = 86   x = 43.   Hence, length = x + 14 = 57 m   57 m
Answer: B
A car traveling at a certain constant speed takes 10 seconds longer to travel 1 km than it would take to travel 1 km at 80 km/hour. At what speed, in km/hr, is the car traveling? Choose the correct choice from the following choices: A) 70 B) 72 C) 74 D) 65 E) 78

Solution: Time to cover 1 kilometer at 80 kilometers per hour is 1/80 hours = 3,600/80 seconds = 45 seconds;   Time to cover 1 kilometer at regular speed is  45 + 10= 
 45 + 10 = 55
55 seconds= 55/3,600 hours = 1/65 hours;   So, we get that to cover 1 kilometer 1/65 hours is needed --> regular speed 65 kilometers per hour (rate is a reciprocal of time or rate=distance/time).   Answer: 65
Answer: D
A room 5m 55cm long and 3m 74cm broad is to be paved with square tiles. Find the least number of square tiles required to cover the floor? Choose the most appropriate option.
A) 176  B) 175  C) 185  D) 188  E) None

Solution: Solution   Area of the room	= (544 x 374)cm ²   Size of largest square tile	= H.C.F of 544 & 374cm   = 34 cm   Area of 1 tile	= (34 x 34)cm²   Number of tiles required	= [544 x 374 / 34 x 34]   = 176.   176nswer 176
Answer: A
On Sunday morning, Pugsley and Wednesday are trading pet spiders. If Pugsley were to give Wednesday two of his spiders, Wednesday would then have nine times as many spiders as Pugsley does. But, if Wednesday were to give Pugsley six of her spiders, Pugsley would now have six fewer spiders than Wednesday had before they traded. How many pet spiders does Pugsley have before the trading game commences?	Choose the correct choice
A) 4 B) 6 C) 8 D) 10 E) 20

Solution: If Pugsley were to give Wednesday two of his spiders, Wednesday would then have nine times as many spiders as Pugsley does:   (w + 2) = 9(p - 2)   If Wednesday were to give Pugsley six of her spiders, Pugsley would now have six fewer spiders than Wednesday had before they traded:   p + 6 = w - 6   Solving gives p = 4 and w = 16.   4nswer: 4.
Answer: A
The average of the marks of 25 students in a class is 70. If the marks of each student are doubled, find the new average?
Choose the correct choice from the following answers.
A) 140  B) 100  C) 85  D) 160  E) 190

Solution: Sum of the marks for the 25 students   = 25 * 70= 
25 * 70 = 1_750
1750. The marks of each student are doubled, the sum also will be doubled.   The new sum= 1750 * 2= 
1750 * 2 = 3_500
3500. So, the new average= 3500/25= 
3500/25 = 140
140.   140nswer:140
Answer: A
If A and B get profits of Rs.60,000 and Rs.6,000 respectively at the end of year then ratio of their investments are  Choose the most appropriate option
A) 4:1 B) 10:1 C) 3:2 D) 2:3 E) 2:5

Solution: Ratio = 60000/6000= 
60000/6000 = 10
10 : 1   Answer : 10:1
Answer: B
A horse is tethered to one corner of a rectangular grassy field 42 m by 26 m with a rope 16 m long. Over how much area of the field can it graze? Pick
A) 154 cm2 B) 308 m2 C) 201 m2 D) 205 m2 E) None of these

Solution: Area of the shaded portion   = 1⁄4 × π × (16)2 = 201 m2   Answer 201 m2
Answer: C
The speed of a boat in upstream is 60 kmph and the speed of the boat downstream is 80 kmph. Find the speed of the boat in still water and the speed of the stream?  Options:
A) 70, 10 kmph
B) 35, 27 kmph
C) 50, 60 kmph
D) 45, 55 kmph
E) 45, 65 kmph

Solution: Speed of the boat in still water = (60+80)/2= 
(60+80)/2 = 70
70 kmph. Speed of the stream= (80-60)/2= 
(80-60)/2 = 10
10 kmph   70, 10 kmphNSWER:70, 10 kmph
Answer: A
Two dice are tossed. The probability that their product is a prime number is:	Select:	A) 1/12	B) 1/6	C) 1/4	D) 2/9	E) 2/2

Solution: Explanation :   Number of possible outcomes = 6x6 = 36.   Favourable outcomes = {1x2,1x3,1x5,2x1,3x1,5x1}   Number of favourable outcomes = 6.   Hence, probability of the event = 6/36 = 1/6.   Answer : 1/6
Answer: B
In a rectangular coordinate system, if a line passes through the points (-12,-18), (18,22) and (x,2) then what is the value of x?
Choose the correct answer:
A) 2
B) 3
C) 4
D) 5
E) 6

Solution: The slope of the line m is rise/run = 22-(-18) / 18-(-12) = 4/3   4/3 = 22-2 / 18-x   72-4x = 66-6   x = 3   The answer is 3.
Answer: B
hat should come in place of question mark (?) in the following equation ?
197 × ? + 16(2) = 2620	Answers
A) 22  B) 12  C) 14  D) 16  E) None of these

Solution: ? = 2620−256 /197=12   Answer 12
Answer: B
A man took loan from a bank at the rate of 12% p.a. S.I. After 10 years he had to pay Rs. 1500 interest only for the period. The principal amount borrowed by him was?  Choose the correct choice from the following choices:
A) 1502	B) 1900	C) 1250	D) 1750	E) 2000

Solution: Principal = (100 * 1500) / (12 * 10)   = Rs.1250   Answer: 1250
Answer: C
Consider a lady took a loan from a bank at the rate of 12% p.a. simple interest. After 3 years she had to pay Rs. 7200 interest only for the period. The principal amount borrowed by her was Answers
A) Rs. 2000
B) Rs. 10000
C) Rs. 15000
D) Rs. 20000
E) None of these

Solution: Explanation :   Principal = Rs. (100×7200 / 12×3)   => Rs. 20,000.   Answer : Rs. 20000
Answer: D
What annual payment will discharge a debt of Rs. 1025 due in 2 years at the rate of 5% compound interest?  Select the correct option.
A) Rs. 550 B) Rs. 551.25 C) Rs. 560 D) Rs. 560.75 E) Rs. 660.75

Solution: Let each installment be Rs. x. Then,   x/(1 + 5/100) + x/(1 + 5/100)2 = 1025   820x + 1025 * 441   x = 551.25   So, value of each installment = Rs. 551.25   ANSWER:Rs. 551.25
Answer: B
Anil invested a sum of money at a certain rate of simple interest for a period of five years. Had he invested the sum for a period of eight years for the same rate, the total intrest earned by him would have been sixty percent more than the earlier interest amount. Find the rate of interest p.a.
Pick.
A) 8PR/108	B) 8PR/100	C) 8PR/102	D) 8PR/100	E) 8PR/101

Solution: Let the sum be Rs.P. Let the rate of interest be R% p.a.   (P)(8)(R)/100 = [1 + 6/100][ (P)(5)(R) /100] = 1.6{5PR/100]   8PR/100 = 8PR/100   Answer: 8PR/100
Answer: D
When positive integer x is divided by 11, the quotient is y and the remainder is 4. When 2x is divided by 8, the quotient is 3y and the remainder is 1. What is the value of 13y – x ? Choose the correct choice from the following
A) 2 B) 3 C) 4 D) 5 E) 6

Solution: (1) x = 11y + 4   (2) 2x = 24y + 1   Let's subtract equation (1) from equation (2).   13y - 3 = x   13y - x = 3   The answer is 3.
Answer: B
If x is a positive integer, f(x) is defined as the number of positive integers which are less than x and do not have a common factor with x other than 1. If x is prime, then f(x) =?	Choose the correct option
A) x-2
B) x-1
C) (x+1)/2
D) (x-1)/2
E) 2

Solution: x is a prime, all positive numbers less than x have no common factors with x (except common factor 1). So there would be x-1 such numbers (as we are looking number of integers less than x).   If we consider x=7 how many numbers are less than 7 having no common factors with 7: 1, 2, 3, 4, 5, 6 --> 7-1=6.   Answer: x-1.
Answer: B
If q and y are positive integer and q/y is an even integer, which of the following can be an odd integer?
Choose one.
A) x  B) xy  C) x−y  D) x+2y  E) q/3

Solution: C q-Y   Let says q =12 Y=3 iT BECOMES q-Y =9 This is odd True   q = 12 Y = 6 THEN q-Y = 2, Which is even hence this is False.   so both Yes and NO situations are exists for this Option. C can't be the correct answer same logic goes for E. I believe this question is incomplete b'coz of Irrelevant Options.
Answer: E
Cheese, bologna, and peanut butter sandwiches were made for a picnic in a ratio of 4 to 5 to 11. If a total of 120 sandwiches were made, how many bologna sandwiches
were made? Choose the correct choice from the following answers: A) 15 B) 30 C) 38 D) 42 E) 48

Solution: For deciding such task we should calculate all parts 4 + 5 + 11= 
4 + 5 + 11 = 20
20 parts   and we should calculate how many sandwiches holds 1 part:   120 / 20= 
120 / 20 = 6
6 sandwiches in one part   For bologna we have 7 parts so:    5* 6= 
 5* 6 = 30
30   Answer is 30
Answer: B