MU-NLPC/Calc-aqua_rat huggingface dataset:
A certain car averages 25 miles per gallon of gasoline when driven in the city and 35 miles per gallon when driving on the highway. According to these rates, which of the following is closest to the number of miles per gallon that the car averages when it is driven 10 miles in the city and then 50 miles on the highway?
Choose the correct choice from the following choices: A) 28 B) 30 C) 33 D) 36 E) 38

Solution: 10*1/25 gpm+50*1/35 gpm=1.82 total gallons   60 total miles/1.82 total gallons=32.9 average mpg   C. 33
Answer: C
A train crosses a platform of 150 m in 15 sec, same train crosses another platform of length 200 m in 18 sec. then find the speed of the train?
Choices:
A) 40/3 m/sec	B) 37/3 m/sec	C) 50/3 m/sec	D) 41/3 m/sec	E) 55/3 m/sec

Solution: Length of the train be ‘X’   (X + 150)/15 = (X + 200)/18   6X + 900 = 5X + 1000   X = 100m   Speed = (100+150)/15 = 50/3 m/sec   Answer: 50/3 m/sec
Answer: C
Timothy drove at an average speed of 10 mph for some time and then at an average speed of 50 mph for the rest of the journey. If he made no stops during the trip and his average speed for the entire journey was 40 mph, for what fraction of the total time did he drive at 50 mph? Choose the correct answer
A) 1/5 B) 1/3 C) 2/5 D) 3/4 E) 3/5

Solution: We don't need to get into calculations for solving this question. We can use the concept of weighted averages.   We know that if the average speed for the entire journey was 40 mph, then he drove at 50 mph for a longer duration of time.   10 30   10--40------50   This shows that you can divide the entire journey into 4 equal parts. Thus, 3/4 part he drove at 50 mph and 1/4 part he drove at 10 mph.   Answer: 3/4
Answer: D
A rectangular lawn of dimensions 80 m * 60 m has two roads each 10 m wide running in the middle of the lawn, one parallel to the length and the other parallel to the breadth. What is the cost of traveling the two roads at Rs.2 per sq m?	Answers: A) 2288 B) 2779 C) 2779 D) 3900 E) 2600

Solution: Area = (l + b â€“ d) d   (80 + 60 â€“ 10)10 => 1300 m2   1300 * 2 = Rs.2600   Answer:2600
Answer: E
The mass of 1 cubic meter of a substance is 500 kilograms under certain conditions. What is the volume, in cubic centimeters, of 1 gram of this substance under these conditions? (1 kilogram = 1,000 grams and 1 cubic meter = 1,000,000 cubic centimeters)
Choose the correct choice from the following answers
A) 0.8
B) 1.25
C) 2.0
D) 2.5
E) 80.0

Solution: Density is mass divided by volume. So density of the given substance will be mass/volume=500kg/1m^3=800 kg/m^3 or 1g/1.5cm^3=0.5 g/cm^3.   Next, ask yourself if 500,000 g is equivalent to 1,000,000 cubic centimeters then 1 g is equivalent to how many cubic centimeters? --> 1 g - 1,000,000/500,000 = 10/5= 
10/5 = 2
2.0 cubic centimeters.   Answer is 2.0
Answer: C
In May, the grounds keeper at Spring Lake Golf Club built a circular green with an area of 25 square feet. In August, he doubled the distance from the center of the green to the edge of the green. What is the total area of the renovated green? Choose the correct option.
A) 100PI  B) 80  C) 70  D) 60  E) 50

Solution: 100PIRE100PI OF CIRCLE 25PI SQ FEET =PI R^2 THEREFORE R =5   NOW GREEN R100PIDI DOUBLED I.E R =10 100PIRE100PI =100 PI   100PI
Answer: A
A man performs 1/2 of the total journey by rail, 1/3 by bus and the remaining 4km on foot. His total journey is
Choose the correct choice
A) 16km B) 10km C) 12km D) 24km E) 25km

Solution: Explanation:   Let the journey be x km   Then, 1x/2 + 1x/3 +4 =x   5x +24 =6x   X = 24km   Answer: Option 24km
Answer: D
The product of all the prime numbers less than 40 is closest to which of the following powers of 10 ?	Pick one:	A) 10^9	B) 10^8	C) 2*10^7	D) 10^6	E) 10^5

Solution: 2*3*5*7*11*13*17*19   2*19*3*17*5*13*7*11   38*51*65*77   By approximation   40*50*70*70   2000*4900   By approximation   4000*5000   20,000,000   2*10^7
Answer: C
If a and b are the roots of the equation x2 - 6x + 6 = 0, then the value of a2 + b2 is:	Choose the most appropriate option:	A) 36	B) 24	C) 17	D) 6	E) 5

Solution: Sol.(b) The sum of roots = a+ b = 6   Product of roots = ab = 6   Now, a2 + b2 = (a + b)2 - 2ab = 36 - 12= 
36 - 12 = 24
24   Answer 24
Answer: B
The value of x + x(xx) when x = 5	Choose one:
A) A) 120	B) B)130	C) C) 110	D) D) 316	E) E) 164

Solution: x + x(xx)   Put the value of x = 5 in the above expression we get,   5 + 5(55)   = 5 + 5(5 Ã— 5)   = 5 + 5(25)   = 5 + 125= 
5 + 125 = 130
130 The answer is (130)
Answer: B
Find the value of a/b + b/a, if a and b are the roots of the quadratic equation x2 + 9x + 4 = 0? Choose the correct option
A) 17
B) 88
C) 14
D) 65
E) 89

Solution: a/b + b/a = (a2 + b2)/ab = (a2 + b2 + a + b)/ab   = [(a + b)2 - 2ab]/ab   a + b = -9/1 = -9   ab = 4/1= 
4/1 = 4
4   Hence a/b + b/a= [(-9)2 - 2(4)]/4 = 73/4 = 18.25.   88)
Answer: B
The average of five numbers is 27. If one number is excluded, the average becomes 25. The excluded number is?	Select the correct option:  A) 8  B) 6  C) 58  D) 35  E) 96

Solution: Excluded number   = (27 * 5) - (25 * 4)   = 135 - 100= 
135 - 100 = 35
35.   Answer:35
Answer: D
A train crosses a post in 15 seconds and a platform 100 m long in 25 seconds. Its length is Choose the correct option
A) 150 m  B) 300 m  C) 400 m  D) 180 m  E) 160 m

Solution: Explanation:   150 mssume x is the length of the train and v is the speed   x/v = 15 => v = x/15   (x+100)/v = 25 => v = (x+100)/25   Ie, x/15 = (x+100)/25   => 5x = 3x+ 300   => x = 300/2= 
300/2 = 150
150   150 mnswer: Option 150 m
Answer: A
A reduction of 20% in the price of salt enables a lady to obtain 10kgs more for Rs.100, find the original price per kg? Pick one.
A) Rs.3.2 B) Rs.2.9 C) Rs.2.5 D) Rs.5.2 E) Rs.2.1

Solution: 100*(20/100)= 
100*(20/100) = 20
20 --- 10   ? --- 1=> Rs.2   100 --- 80   ? --- 2 => Rs.2.5   Answer:Rs.2.5
Answer: C
In a kilometer race, A beats B by 50 meters or 10 seconds. What time does A take to complete the race? Choose the correct choice: A) 238 B) 190 C) 127 D) 279 E) 211

Solution: Explanation:   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
Answer: B
The sum of two numbers is 45. Their difference is 5. The bigger number is
Choose the correct choice from the following answers.
A) 20 B) 25 C) 30 D) 35 E) 45

Solution: X + Y = 45   X - Y = 5   Adding 2X = 50 ==> X = 25 and Y = 45 - 25= 
45 - 25 = 20
20   25igger number is X= 25   Answer 25.
Answer: B
The population of a town is 8000. It decreases annually at the rate of 10% p.a. What will be its population after 1 years? Pick:  A) 5100  B) 5120  C) 7200  D) 5400  E) 5500

Solution: Formula :   ( After =100 denominator   Ago = 100 numerator)   8000 Ã— 90/100= 7200   Answer : 7200
Answer: C
A soft drink company had 6000 small and 14000 big bottles in storage. If 20% of small 23% of big bottles have been sold, then the total bottles remaining in storage is
Choose the correct option:	A) 15360	B) 15720	C) 15060	D) 14930	E) 16075

Solution: 6000 + 14000 - (0.2*6000 + 0.22*14000)= 
6000 + 14000 - (0.2*6000 + 0.22*14000) = 15_720
15720.   Answer: 15720.
Answer: B
Find the odd man out
4, 10, 22, 40, 84, 94
Select the correct option.
A) 22
B) 40
C) 94
D) 84
E) 10

Solution: 84iffernce is multiple of 6   4 and 10 diff is 6   10 and 22 diff is 12   22 and 40 diff is 18   40+24= 
40+24 = 64
64 but in series it is mentioned as 84   64+30= 
64+30 = 94
94   ANSWER:84
Answer: D
Three times the first of three consecutive odd integers is 3 more than twice the third. The third integer is :  Choose the correct choice from the following choices.
A) 9	B) 11	C) 13	D) 15	E) 21

Solution: let the three integers be x, x+2, x+4   3x = 2(x+4) + 3 ==> 3x = 2x + 8 +3 ==> x = 11   so the third integer is x+4 = 15.   so the correct option is 15.
Answer: D
A train running at the speed of 60 km/hr crosses a pole in 12 seconds. What is the length of the train?	Choices.
A) 120 metres	B) 180 metres	C) 324 metres	D) 200 metres	E) 180 metres

Solution: Speed=(60 x 5/18)/m/sec	=	50/3	m/sec.   Length of the train = (Speed x Time).   Length of the train =	50 x 12/3 m = 200 m.   ANSWER : OPTION 200 metres
Answer: D
A person covered one-fourth of the total distance at 26 kmph and remaining distance at 24 kmph. What is the average speed for the total distance?
Choose the correct choice from the following answers: A) 21 (1/3)kmph B) 22 (1/3)kmph C) 24 (1/3)kmph D) 26 (1/3)kmph E) 26 (1/3)kmph

Solution: 21 (1/3)kmph   21 (1/3)kmph   Let the total distance be x km   total time taken = (x/4)/16 + (3x/4)/24 = x/64 + x/32 = 3x/64   21 (1/3)kmphverage speed = x/(3x/64) = 64/3kmph = 21 (1/3)kmph.
Answer: A
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? Select: A) 122 B) 123 C) 828 D) 122 E) 176

Solution: Area of the room=(544 * 374)   size of largest square tile= H.C.F of 544 & 374 = 34 cm   Area of 1 tile = (34 x 34)   Number of tiles required== [(544 x 374) / (34 x 34)] = 176   Answer: 176
Answer: E
The ratio of incomes of two person P1 and P2 is 5 : 4 and the ratio of their expenditures is 3 : 2. If at the end of the year, each saves Rs.1200, then what is the income of P1?	Choose the correct choice from the following.
A) s.800
B) s.2400
C) s.3000
D) s.3200
E) s.4200

Solution: Let the income of P1 and P2 be Rs. 5x and Rs.4x respectively and let their   expenditures be Rs.3y and 2y respectively.   Then, 5x – 3y = 1200 …(i) and 4x – 2y = 1200 ……..(ii)   On multiplying (i) by 2, (ii) by 3 and subtracting, we get : 2x = 1200 -> x = 600   P1’s income = Rs 5*600 = Rs.3000   ANSWER:s.3000
Answer: C
If x : y = 4 : 7, find the value of (6x + 2y) : (5x – y)  Pick: A) 7:13 B) 38:7 C) 3:13 D) 2:3 E) 38:13

Solution: 38:13xplanation:   Given: X/Y = 4/7   (6x + 2y) : (5x – y)   = (6*4 + 2*7) : (5*4 – 7)   38:13   ANSW38:13R: 38:13
Answer: E
If w/x = 1/3 and w/y = 2/3, then (x + y)/y =  Choose the correct answer:
A) 2 B) 4 C) 5 D) 3 E) 7

Solution: Ratio 1:   3w = x   Ratio 2:   3w = 2y   x = 2y   (x+y)/y = (2y+y)/y = y(2+1)/y = 3   Answer is 3
Answer: D
Mike, Jim and Bob are all professional fisherman. Mike can catch 15 fish in one hour, Jim can catch twice as much and Bob can catch 50% more than Jim. If the three started to fish together and after 40 minutes Mike and Bob left, how many fish did the three fishermen catch in one hour? Pick one
A) 64
B) 70
C) 85
D) 98.
E) 112.

Solution: All of them catch fishes in relation to number 15....   2/3*15+2*15+2*1.5*15*2/3= 
2/3*15+2*15+2*1.5*15*2/3 = 70
70   Answer is 70
Answer: B
A train running at the speed of 60 km/hr crosses a pole in 9 sec. What is the length of the train?
Choose one:
A) 120 m  B) 180 m  C) 324 m  D) Cannot be determined  E) None of these

Solution: Speed = 60 * 5/18 = 50/3 m/sec   Length of the train = speed * time = 50/3 * 9= 
50/3 * 9 = 150
150 m   ANSWNone of theseR:None of these
Answer: E
Two tailors P and Q are paid a total of Rs. 550 per week by their employer. If P is paid 120 percent of the sum paid to Q, how much is Q paid per week?  Choose the correct choice from the following answers:
A) 200 B) 300 C) 150 D) 100 E) 250

Solution: Consider x   x+120 Of x =550   11/5x=550   x=550*5/11= 
550*5/11 = 250
250   ANSW250R 250
Answer: E
Choose the missing terms out of the given alternatives.
QPO, SRQ, UTS, WVU, ? Choose the correct choice from the following options:  A) XVZ  B) ESD  C) ZYA  D) VWX  E) YXW

Solution: E   YXW   Each term consists of three consecutive letters in reverse order. The first letter and the last letter of the next term are the same.
Answer: E
If a*b*c=130, b*c*d = 65, c*d*e=1000 and d*e*f=150 the (a*f)/(c*d) = ?
Choices
A) 1/2
B) 1/4
C) 3/4
D) 1/3
E) None of these

Solution: Explanation :   aâˆ—bâˆ—c/bâˆ—câˆ—d= 130/65 => a/d = 2   dâˆ—eâˆ—f/câˆ—dâˆ—e= 150/1000 => f/c = 1/4   a/d* f/c = 2 * 15/10 = 1/3   Answer : 1/3
Answer: D
Two unbiased coin are tossed .what is the probability of getting atmost one head?	Choose the correct answer
A) 1/3
B) 3/4
C) 5/7
D) 8/9
E) 2/3

Solution: Here S={HH,HT,TH,TT}   Let Ee=event of getting one head   E={TT,HT,TH}   P(E)=n(E)/n(S)=3/4   Ans: 3/4
Answer: B
Anne bought doughnuts for a class breakfast party. She bought 9 chocolate doughnuts, 7 coconut doughnuts, and 9 jam-filled doughnuts. How many doughnuts did Anne buy in all?  Choose one
A) 25 B) 36 C) 39 D) 21 E) 11

Solution: Add the numbers of doughnuts.   9 + 7 + 9= 
9 + 7 + 9 = 25
25.   25nswer is 25.
Answer: A
Four people are to be seated on a bench. How many different sitting arrangements are possible if Erik must sit next to Joe?
Pick one
A) 4	B) 6	C) 8	D) 12	E) 16

Solution: Consider E and J one. But, in this arrangement they can sit in two different combinations.   E first and J second or J first and E second.   Total we have (E and J) and the two other persons= 4 arrangements to do.   Total arrangements= 4*2= 
4*2 = 8
8   8 is the answer
Answer: C
If the sides of a rectangle are increased by 25%, what is the percentage increase in the area?  Choose one:
A) 54.25%
B) 56.25$
C) 53.25%
D) 55.25%
E) 58.25%

Solution: If sides are a and b, after increase sides would be 1.25a and 1.25 b.   Percentage increase in area = (1.25a*1.25b - ab) *100/ab = 56.25%   Answer : 56.25$
Answer: B
The set S consists of 5 numbers: {1,2,3,4,5}. If all possible subsets including the null set are created and one subset is chosen at random, what is the probability that the subset has 3 as its largest number?  Choose the correct choice from the following answers:
A) 1/2
B) 1/4
C) 1/8
D) 1/16
E) 1/32

Solution: The set S has 2^5 = 32 subsets.   The number 5 is in half of these subsets.   Of the remaining 16 subsets, 4 is an element in 8 of them.   Of the remaining 8 subsets, 3 is an element in 4 of them.   Thus 3 is the largest number in 4 subsets of S.   The probability that 3 is the largest number is 4/32 = 1/8.   The answer is 1/8.
Answer: C
The age of father 10 years ago was thirce the age of his son.Ten years hence,father’s age will be twice that of his son.The ration of their present ages is : Choose the correct choice from the following choices:  A) 5:2  B) 7:3  C) 9:2  D) 13:4  E) None of these

Solution: Solution   Let the ages of father and son 10 year ago be 3x and x years respectively.   Then,(3x + 10)+10 = 2[(x +10)+10 ⇔ 3x + 20 = 2x + 40 ⇔ x =20.   ∴ Required ratio =(3x +10) : (x + 10) = 70 : 30 : 7 : 3. Answer 7:3
Answer: B
Mary’s annual income is $15,000 and John’s annual income is $16,000. By how much must Mary’s annual income increase so that it constitutes 50% of Mary and John’s combined income?  Choose the correct choice from the following options:  A) $1,000  B) $4,000  C) $7,000  D) $11,000  E) $25,000

Solution: Let Mary's income increase by x, then the equation will be   15,000 + x= (50/100)* (15,000 + x + 16000 )   15,000 + x = (1/2) * (31,000 + x)   30,000 + 2x = x + 31,000   x =1,000   So, $1,000nswer will be $1,000
Answer: A
The area of the largest circle that can be drawn inside a square of side 28 Cm in length is:
Choose the most appropriate option:
A) 600  B) 646  C) 616  D) 636  E) 606

Solution: Radius of required circle = 14 616m   its area = 22/7 × 14 × 14   44 × 14 = 616 616m(power)2   Answer is 616.
Answer: C
Find the curved surface area, if the radius of a cone is 7 m and slant height is 14 m? Choose the correct choice from the following answers:  A) 308  B) 369  C) 434  D) 476  E) 513

Solution: Cone curved surface area = Ï€rl   22/7 Ã— 7 Ã— 14 = 22 Ã— 14 = 308 m(power2)   308nswer is 308.
Answer: A
Two brothers took the GMAT exam, the higher score is U and the lower one is V. If the difference between the two scores is equal to their average, what is the value of V/U ? Choose the correct choice from the following answers:
A) 3 B) 2 C) 1/2 D) 1/3 E) There isn't enough data to answer the question.

Solution: Answer is 1/3 : 1/3   U - V = (U + V)/2   Solving for V/U = 1/3   1/3
Answer: D
The sale price bags listed for Rs.2000 after successive discount is 25% and 15% is? Choose the correct choice.
A) 415  B) 425  C) 435  D) 445  E) 455

Solution: 2000*(75/100)*(85/100)   = 425   Answer: 425
Answer: B
The perimeters of two squares are 36 cm and 32 cm. Find the perimeter of a third square whose area is equal to the difference of the areas of the two squares?	Choose the correct choice from the following answers.
A) 16.4 cm
B) 24 cm
C) 88 cm
D) 55 cm
E) 34 cm

Solution: We know perimeter of square = 4(side)   So Side of first square = 40/4= 
40/4 = 10
10 cm   Side of second square= 36/4= 
36/4 = 9
9 cm   16.4 cmrea of third Square= 9*9 - 8*8= 
9*9 - 8*8 = 17
17 cm   So side of third square= 4.1 [because area of square = side*side]   Perimeter = 4*Side = 4*4.1= 
4*4.1 = 16.4
16.4 cm   16.4 cmnswer:16.4 cm
Answer: A
In a class of 28 students in an examination in maths 4 students scored 95 marks each, 3 get zero each and the average of the rest was 45. What is the average of the whole class?
Choices:
A) A)47.3	B) B)45.6	C) C)44	D) D)48	E) E)49

Solution: Explanation:   Total marks obtained by a class of 25 students   = 4*95 + 3*0 + 21 * 45= 
4*95 + 3*0 + 21 * 45 = 1_325
1325   47.3verage marks of whole class= 1325/28 =47.3   47.3nswer: Option 47.3
Answer: A
Find the average marks of all the students in classes A and B, if :
classes A = 43 students (average marks of students is 65)
classes B = 54 students (average marks of students is 72)  Choose the correct choice:	A) 41.9	B) 68.9	C) 65.9	D) 61.9	E) 62.9

Solution: Sum of the marks for the class of 43 students = 43 * 65= 
43 * 65 = 2_795
2795   Sum of the marks for the class of 54 students= 54 * 72= 
54 * 72 = 3_888
3888   Sum of the marks for the class of 97 students=   2795 + 3888= 
2795 + 3888 = 6_683
6683   Average marks of all the students= 6683/97   = 68.9   Answer:68.9
Answer: B
Amar takes as much time in running 18 meters as a car takes in covering 48 meters. What will be the distance covered by Amar during the time the car covers 1.2 km?	Choose the correct option.
A) 600 m  B) 200 m  C) 300 m  D) 400 m  E) 100 m

Solution: 300 m   300 m   Distance covered by Amar = 18/4.8 (1.6km) = 3/8(1200) = 300 m   Answer is 300 m
Answer: C
Danny and Steve are running towards each other, each one from his own house. Danny can reach Steve's house in 35 minutes of running, which is half the time it takes Steve to reach Danny's house. If the two started to run at the same time, how much time longer will it take Steve to reach the halfway point between their houses than Danny to reach the halfway point between their houses?  Choose the correct choice from the following
A) 17.5 minutes.	B) 35 minutes.	C) 52.5 minutes.	D) 70 minutes.	E) 105 minutes.

Solution: Danny's time is 35 minutes. The time to reach halfway is 17.5 minutes.   Steve's time is 70 minutes. The time to reach halfway is 35 minutes.   The time difference is   35 - 17.5= 
  35 - 17.5 = 17.5
17.5 minutes   The answer is 17.5 minutes..
Answer: A
Pipes A and B can fill a tank in 5 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? Answers
A) 3	B) 3 9/11	C) 3 9/17	D) 4	E) 4 1/7

Solution: Net part filled in 1 hour 1	+	1	-	1 =	17	.   5	6	12	60   The tank will be full in	60/17	hours i.e., 3 9/17	hours.   3 9/17)
Answer: C
The telephone company wants to add an area code composed of 2 letters to every phone number. In order to do so, the company chose a special sign language containing 24 different signs. If the company used 22 of the signs fully and two remained unused, how many additional area codes can be created if the company uses all 24 signs?	Choose the correct choice from the following.
A) 246  B) 248  C) 92  D) 15,128  E) 30,256

Solution: # of 2-letter codes possible from 24 different signs = 24*24.   # of 2-letter codes possible from 22 different signs = 22*22.   The difference = 24^2 - 22^2 = (24 - 22)(24 + 22) = 92.   Answer: 92.
Answer: C
Company T produces two kinds of stereos: basic and deluxe. Of the stereos produced by Company T last month, 2/3 were basic and the rest were deluxe. If it takes 7/5 as many hours to produce a deluxe stereo as it does to produce a basic stereo, then the number of hours it took to produce the deluxe stereos last month was what fraction of the total number of hours it took to produce all the stereos?  Choose the correct answer: A) 5/17 B) 7/17 C) 4/17 D) 3/17 E) 5

Solution: # of basic stereos was 2/3 of total and # of deluxe stereos was 1/3 of total, let's assume total=15, then Basic=10 and Deluxe=5.   Now, if time needed to produce one Deluxe stereo is 1 unit than time needed to produce one Basic stereo would be 7/5 units. Total time for Basic would be  10*1= 
 10*1 = 10
10 and total time for Deluxe would be 5*7/5= 
5*7/5 = 7
7 --> total time for both of them would be 10+7= 
10+7 = 17
17 --> deluxe/total=7/17.   7/17
Answer: B
If a is a positive integer, then 2^a + 2^(a + 1)+ 2^(a + 2)+ 2^(a + 3)+ 2^(a + 4)+ 2^(a + 5) =	Select:
A) 3^(a + 1)  B) 2^(a + 1)  C) 2a  D) 2a^(a + 1)  E) 63(2^a)

Solution: If a is a positive integer, then 2^a + 2^(a + 1)+ 2^(a + 2)+ 2^(a + 3)+ 2^(a + 4)+ 2^(a + 5) =   2^a(1+2+4+8+16+32)   2^a(63)   E. 63(2^a)
Answer: E
Andrew purchased 10kg of grapes at the rate of 82 per kg and 6 kg of mangoes at the rate of 62 per kg. How much amount did he pay to the shopkeeper?
Choose the correct choice from the following options: A) 1000 B) 1055 C) 1378 D) 1075 E) 1080

Solution: Cost of 10 kg grapes = 82 × 10 = 820.   Cost of 6 kg of mangoes = 62 × 6 = 558.   Total cost he has to pay = 820 + 558= 
820 + 558 = 1_378
1378   1378
Answer: C
If log10 2 = 0.3010, then log2 10 is equal to:  Options
A) 1000/301  B) 0.301  C) 600/301  D) 0.6992  E) 0.7254

Solution: log2 10 = 1/log10 2 = 1/0.3010 = 10000/3010 = 1000/301   1000/301NSWER 1000/301
Answer: A
Lionel left his house and walked towards Walt's house, 48 miles away. Two hours later, Walt left his house and ran towards Lionel's house. If Lionel's speed was 2 miles per hour and Walt's 6 miles per hour, how many miles had Lionel walked when he met Walt? Choose the correct choice from the following choices:  A) 12  B) 15  C) 20  D) 24  E) 28

Solution: In the first 2 hours Lionel at the rate of 2 miles per hour covered distance=rate*time=2*2= 
2*2 = 4
4 miles. So, the distance between him and Walt was 48-4= 
48-4 = 44
44 miles when Walt left his house. Now, their combined rate to cover this distance was 2+6= 
2+6 = 8
8 miles per hour, hence they will meet (they will cover that distance) in time=distance/rate=44/8= 
44/8 = 11/2 = around 5.5
5.5 hours. Total time that Lionel was walking is 2+5.5= 
2+5.5 = 7.5
7.5 hours, which means that he covered in that time interval distance=rate*time=2*7.5= 
2*7.5 = 15
15 miles.   Answer: 15.
Answer: B
If pq = 3(p+ 1) + q and p and q are integers, p could be any of the following values EXCEPT:  Options
A) 2  B) 4  C) 3  D) 7  E) 9

Solution: pq = 3(p + 1) + q   pq - q = 3(p + 1)   q = 3(p + 1)/(p-1)   q won't be an integer only if p = 8 (from the options).   Answer: 9
Answer: E
If by selling 110 apples, the cost price of 120 apples is realised. The gain % is?	Choose the correct choice from the following answers:
A) 9%
B) 10%
C) 11%
D) 12%
E) 13%

Solution: 1 apple=1 rup   cp of 110 app=110 rs   sp of 110 app=120 rs   gain=120-110= 
120-110 = 10
10   gain%=10/100*110= 
10/100*110 = 11
11%   ANSWER:11%
Answer: C
If a:b=3:1 and b:c=1:4 find a:b:c?	Select
A) 1:6:2	B) 3:1:4	C) 2:3:4	D) 2:3:3	E) 1:4:2

Solution: a:b = 3:1, b:c = 1:4   3:1   1:4   (a = a × b, b = b × b and c = b × c)   a:b:c = 3:1:4   3:1:4
Answer: B
Anne earned $3 an hour baby-sitting, and $4 an hour working in the garden. Last week she did
baby-sitting for 5 hours and garden work for 3 hours. How much more money does she need to
buy a game that costs $35?  Choose the most appropriate option
A) $8 B) $12 C) $6 D) $21 E) $10

Solution: 5 x $3 = $15 for baby-sitting   3 x $4 = $12 for garden work   $15 + $12 = $27 she has   $35 - $27   15 +  12= 
  15 +  12 = 27
$27 she has   $35 - $27 = $8 more needed to   buy the game   correct answer $835 -  27= 
35 -  27 = 8
$8 more needed to   buy the game   correct answer $8
Answer: A