mathewhe/aqua_rat huggingface dataset:
Question: If a*b*c=130, b*c*d = 65, c*d*e=1000 and d*e*f=250 the (a*f)/(c*d) = ?
(A) 1/2
(B) 1/4
(C) 3/4
(D) 2/3
(E) None of these
Rationale: Explanation :
a∗b∗c/b∗c∗d= 130/65 => a/d = 2
d∗e∗f/c∗d∗e= 250/1000 => f/c = 14
a/d* f/c = 2 * 1/4 = 1/2
Answer : A
Answer: (A) 1/2
Question: A license plate in the country Kerrania consists of four digits followed by two letters. The letters A, B, and C are used only by government vehicles while the letters D through Z are used by non-government vehicles. Kerrania's intelligence agency has recently captured a message from the country Gonzalia indicating that an electronic transmitter has been installed in a Kerrania government vehicle with a license plate starting with 79. If it takes the police 12 minutes to inspect each vehicle, what is the probability that the police will find the transmitter within three hours?
(A)  18/79
(B)  16/900
(C)  1/25
(D)  1/50
(E)  1/900
Rationale: Everything is correct except that you assumed the letters can't be repeated. It can be repeated.
AA
BB
CC
AB, AC, BC, BA, CA, CB.
Thus; total government vehicles = (10)^2*(3)^2 = 100*9 = 900
Vehicles inspected within 3 hours = 60*3/12 = 16
P = 16/900
Ans:B
Answer: (B)  16/900
Question: Dan’s car gets 32 miles per gallon. If gas costs $4/gallon, then how many miles can Dan’s car go on $54 of gas?
(A) 236
(B) 354
(C) 432
(D) 512
(E) 670
Rationale: 54/4 = 13.5 gallons
13.5*32 = 432 miles
The answer is C.
Answer: (C) 432
Question: Two assembly line inspectors, Lauren and Steven, inspect widgets as they come off the assembly line. If Lauren inspects every fifth widget, starting with the fifth, and Steven inspects every third, starting with the third, how many of the 95 widgets produced in the first hour of operation are not inspected by either inspector?
(A) 50
(B) 43
(C) 45
(D) 55
(E) 60
Rationale: Widgets inspected by Lauren: ((95-5)/5)+1=18+1=19
Widgets inspected by Steven: ((93-3)/3)+1 =31+1 =32
Widgets inspected by both: ((90/15)+1 =6
Total : 19+32 -6=45
hence, widgets not inspected: 95-45=50
Option A
Answer: (A) 50
Question: A shipment of 1500 heads of cabbage, each of which was approximately the same size, was purchased for $600. The day the shipment arrived 2/3 of the heads were sold, each at 25% above the cost per head. The following day the rest were sold at a price equal to 30% less than the price each head sold for on the day before. What was the total gross profit on this shipment.
(A) $100
(B) b $115
(C) c $125
(D) d $130
(E) e $75
Rationale: Purchase cost = 600/1500= $ 0.4
25% above the cost per head = (125/100)*0.4= $ 0.5
2/3 of the heads were sold means 2/3*1500 =1000 ,Selling amount for 1000 cabbage = 1000 * 0.5 = $ 500
Remaining were sold at a price equal to 30% less than the price each head sold for on the day before i.e , (70/100)*0.5 = $ 0.35
Hence selling cost for the remaining cabbage = 500 * 0.35 = $ 175
Total selling cost = 500 + 175 = $ 675
Gross profit = $ 675 - $ 600 = $ 75
Hence Answer is E.
Answer: (E) e $75
Question: Bob bikes to school every day at a steady rate of a miles per hour. On a particular day, Bob had a flat tire exactly halfway to school. He immediately started walking to school at a steady pace of y miles per hour. He arrived at school exactly t hours after leaving his home. How many miles is it from the school to Bob's home?
(A) (a + y) / t
(B) 2(a + t) / ay
(C) 2ayt / (a + y)
(D) 2(a + y + t) / ay
(E) x(y + t) + y(x + t)
Rationale: If we choose for d (distance): 10 miles, for a 10 and for y 5.
t would be 90 minutes or 1,5 hours.
If I try this for answer choice C it fits.
Answer: (C) 2ayt / (a + y)
Question: A company has a job to prepare certain number of cans and there are three machines A, B and C for this job. A can complete the job in 2 days, B can complete the job in 5 days and C can complete the job in 7 days. How many days the company will it take to complete the job if all the machines are used simultaneously?
(A) 71/59 days
(B) 70/59 days
(C) 3 days
(D) 12days
(E) 14 days
Rationale: Let the total number of cans to be prepared be 70.
The number of cans prepared by A in 1 day = 35.
The number of cans prepared by B in 1 day = 14.
The number of cans prepared by C in 1 day = 10.
Thus, the total number of cans that can be prepared by all the machines working simultaneously in a single day = 59.
Therefore, the number of days taken to complete the whole work = 70/59 days.
ANSWER:B
Answer: (B) 70/59 days
Question: An error 4% in excess is made while measuring the side of a square. What is the percentage of error in the calculated area of the square?
(A) 4.05%
(B) 4.02%
(C) 8.16%
(D) 3%
(E) 2%
Rationale: Percentage error in calculated area
=(4+4+(4Ã—4)/100)%
=8.16%
ANSWER:C
Answer: (C) 8.16%
Question: The average of five numbers is 60. If one number is excluded, the average becomes 65. The excluded number is?
(A) 40
(B) 6
(C) 58
(D) 35
(E) 96
Rationale: Excluded number
= (60 * 5) - (65 * 4)
= 300 - 260 = 40
Answer:A
Answer: (A) 40
Question: 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.
(A) 5352
(B) 5355
(C) 2789
(D) 2689
(E) 2688
Rationale: Let the sum lent by Manoj to Ramu be Rs.P.
Amount gained by Manoj = P. 3.9 /100 = 3450.3.6/100
= Rs.824.85
27P = 62100
= 82485
P = (82485 + 62100)/27 = 3055 + 2300
= Rs.5355
Answer: B
Answer: (B) 5355
Question: What is the 100th digit of (3!*5! + 4!*3!)/2?
(A) 4
(B) 3
(C) 2
(D) 7
(E) 6
Rationale: (3!*5! + 4!*3!)/2
=3!(5! + 4!)/2
=6 (120+24)/2
=432
100th digit of the above product will be equal to 4
Answer A
Answer: (A) 4
Question: From a nine-member dance group, five will be chosen at random to volunteer at a youth dance event. If Kori and Jason are two of the nine members, what is the probability that both will be chosen to volunteer?
(A) a) 1/21
(B) b) 35/2
(C) c) 4/21
(D) d) 2/7
(E) e) 3/7
Rationale: Total number of ways to choose 5 out of 9 = 9C5 = 144.
Number of ways to choose 2 (any but Kori and Jason) out of 7 (excluding Kori and Jason) = 7C2 = 2520.
P = favorable/total = 2520/144 = 35/2.
Answer: B.
Answer: (B) b) 35/2
Question: A began business with Rs.45000 and was joined afterwards by B with Rs.5400. When did B join if the profits at the end of the year were divided in the ratio of 2:1?
(A) 6
(B) 9
(C) 7
(D) 5
(E) 1
Rationale: 45*12 : 54*x = 2: 1
x = 5
12 -5 = 7
Answer: C
Answer: (C) 7
Question: W is an even integer greater than 300,000 and smaller than 1,000,000. How many numbers can W be?
(A) 300,000
(B) 349,999
(C) 350,000
(D) 399,999
(E) 400,000
Rationale: W 1,000,000-300,000=700,000 integers
700,000/2= 350,000 even integers.
350,000+1 inclusive. But since 1,000,000 and 300,000 are not included.
350,001-2=349,999
B
Answer: (B) 349,999
Question: A rainstorm increased the amount of water stored in State J reservoirs from 125 billion gallons to 150 billion gallons. If the storm increased the amount of water in the reservoirs to 80 percent of total capacity, approximately how many billion gallons of water were the reservoirs short of total capacity prior to the storm?
(A)  9
(B)  14
(C)  25
(D)  30
(E)  44
Rationale: After the reservoir is filled to 150 gallons the amount of water is at 80% - which means that 20% of the reservoir is empty. To figure out what that 20% is approximate: 150 gallons /80 percent = x gallons /20 percent , therefore, x = 37.5 gallons , answer choices A,B,C,D are below 37.5 . We know that the reservoir must be short more than 37.5 gallons, therefore, the only possible choice is E.
Answer: (E)  44
Question: If the letters of the word PLACE are arranged taken all at a time, find how many do not start with AE
(A) 110
(B) 114
(C) 118
(D) 120
(E) 122
Rationale: Total no'of arrangements 5P5 = 5! = 120
no'of arrangements start with AE = 1 × 6 = 6
no'of arrangements which do not start with AE = 120 - 6 = 114.
B)
Answer: (B) 114
Question: At a recent small town election for mayor a total of 967 votes were cast for the four candidates, the winner exceeding his opponents by 53, 79 and 105 votes, respectively. How many votes were cast for the candidate in fourth place?
(A) 134
(B) 178
(C) 196
(D) 166
(E) 194
Rationale: The number of votes the winning candidate received was
967 + 53 + 79 + 105	/4= 301.
The fourth place received 301 – 105 = 196.
C
Answer: (C) 196
Question: Find the value of x from the below equation? : x^2+5x+4 = 0
(A) 1
(B) -3
(C) 3
(D) 2
(E) 0
Rationale: a = 1, b = 5, c = 4
x1,2 = (-5 Â± âˆš(5^2 - 4Ã—1Ã—4)) / (2Ã—1) = (-5 Â± âˆš(25-16)) / 2 = (-5 Â± 3) / 2
x1 = (-5 + 3)/2 = -2/2 = -1
x2 = (-5 - 1)/2 = -6/2 = -3
B
Answer: (B) -3
Question: In a sequence of 39 numbers, each term, except for the first one, is 7 less than the previous term. If the greatest term in the sequence is 281, what is the smallest term in the sequence?
(A) 2
(B) -2
(C) 0
(D) 18
(E) 6
Rationale: Which term is the greatest? The first or the last? It is given to you that every term is 7 less than the previous term. Hence as you go on, your terms keep becoming smaller and smaller. The first term is the greatest term.
An = 281 + (39- 1)*(-7)
An = 281 - 266 = 15
D
Answer: (D) 18
Question: Arun borrowed a certain sum from Manish at a certain rate of simple interest for 2 years. He lent this sum to Sunil at the same rate of interest compounded annually for the same period. At the end of two years, he received Rs. 2400 as compound interest but paid Rs. 2000 only as simple interest. Find the rate of interest.
(A) 20%
(B) 10%
(C) 40%
(D) 50%
(E) 60%
Rationale: Explanation:
Let the sum be x
Simple interest on x for 2 years = Rs.2000
Simple interest = PRT/100
2000 = x × R × 2100
⇒ xR = 100000 --- (1)
Compound Interest on x for 2 years = 2400
P(1+R/100)T−P=2400
x(1+R/100)2 − x = 2400
x(1+2R/100 + R2/10000) − x = 2400
x(2R/100 + R2/10000) = 2400
2xR/100 + xR2/10000 = 2400 --- (2)
Substituting the value of xR from (1) in (2) ,we get
(2 × 100000)/100 + (100000×R)/10000 = 2400
2000 + 10R = 2400
10R = 400R = 40%
Answer: Option C
Answer: (C) 40%
Question: A man sells a horse for Rs.600 and loses something, if he had sold it for Rs.720 , his gain would have been double the former loss. Find the cost price of the horse?
(A) 27
(B) 98
(C) 27
(D) 40
(E) 71
Rationale: CP = SP + 1CP = SP - g
600 + x = 720 - 2x
3x = 120 => x = 40
Answer:D
Answer: (D) 40
Question: In what ratio must a grocer mix rice worth Rs.60 a kg and Rs.65 a kg.So that by selling the mixture at Rs. 68.20 a kg, He may gain 10%?
(A) 1:2
(B) 3:2
(C) 4:5
(D) 1:3
(E) 1:5
Rationale: S.P of 1kg mix = RS.68.20,
Gain = 10% C.P of 1kg mix =Rs.(100/110 x 68.20) =Rs.62 = 3 : 2
ANSWER B
Answer: (B) 3:2
Question: A and B enter into partnership with capitals in the ratio 3 : 4. At the end of 10 months A withdraws,and the profits now are divided in the ratio of 5 : 4. Find how long B remained in the business?
(A) 9 months
(B) 8 months
(C) 7 months
(D) 6 months
(E) None of these
Rationale: Initially A’s investment = 3x and B’s investment = 4x
Let B remain in the business for ‘n’ months.
⇒ 3x × 10 : 4x × n = 5 : 4
∴ 3x × 10 × 4 = 4x × n × 5
⇒ n = 6
Answer D
Answer: (D) 6 months
Question: A group of hikers is planning a trip that will take them up a mountain using one route and back down using another route. They plan to travel down the mountain at a rate of one and a half times the rate they will use on the way up, but the time each route will take is the same. If they will go up the mountain at a rate of 6 miles per day and it will take them two days, how many miles long is the route down the mountain?
(A) 16
(B) 17
(C) 18
(D) 19
(E) 20
Rationale: On the way down, the rate is 1.5*6 = 9 miles per day.
The distance of the route down the mountain is 2*9 = 18 miles.
The answer is C.
Answer: (C) 18
Question: Peter is a trail runner who decides to take a day off work to run up and down a local mountain. He runs uphill at an average speed of 4 miles per hour and returns along the same route at an average speed of 6 miles per hour. Of the following, which is the closest to his average speed, in miles per hour, for the trip up and down the mountain?
(A)  4.8
(B)  5.8
(C)  6.0
(D)  6.3
(E)  6.5
Rationale: to calculate average of 2 speeds a and b when distance is constant
Formula - 2ab/(a+b)
Here Peter's uphill speed = 4 mph
Peter's downhill speed = 6 mph
2*4*6/(4+6) = 48/10 = 4.8
Correct answer - A
Answer: (A)  4.8
Question: Calculate the different number of ways 7 boys and 2 girls can sit on a bench?
(A) 362881
(B) 362880
(C) 311880
(D) 362280
(E) 362810
Rationale: npn = n!
9p9 = 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 362880
B
Answer: (B) 362880
Question: The population of a town increased from 1,75,000 to 2,10,000 in a decade. The average percent increase of population per year is
(A) 2%
(B) 5%
(C) 6%
(D) 8.75%
(E) None
Rationale: Solution
Increase in 10 years	= (210000 - 175000)
= 35000.
Increase%	= (35000/175000Ã—100)%
= 20%.
Required average	= (20/10)%
= 2%.
Answer A
Answer: (A) 2%
Question: Mysoon collects glass ornaments. Ten more than 1/6 of the ornaments in her collection are handmade, and 1/2 of the handmade ornaments are antiques. If 1/6 of the ornaments in her collection are handmade antiques, how many ornaments are in her collection?
(A) 36
(B) 60
(C) 108
(D) 60
(E) 180
Rationale: The number of ornaments = a
Ten more than 1/6 of the ornaments in her collection are handmade => Handmade = 10+a/6
1/2 of the handmade ornaments are antiques => Handmade ornaments = 1/2*(10+a/6) = 5 + a/12
1/6 of the ornaments in her collection are handmade antiques => Handmade ornaments = a/6
=> 5 + a/12 = a/6 => a = 60
Ans: D
Answer: (D) 60
Question: The smallest 4 digit prime number is?
(A) A)101
(B) B)1003
(C) C)109
(D) D)113
(E) E)None
Rationale: The smallest 3-digit number is 1000, which is divisible by 2.
1000 is not a prime number.
1003< 11 and 101 is not divisible by any of the prime numbers 2, 3, 5, 7, 11.
1003 is a prime number.
Hence 1003 is the smallest 4-digit prime number.
B)
Answer: (B) B)1003
Question: The smallest number which when divided by 20, 25, 35 and 40 leaves a remainder of 14, 19, 29 and 34 respectively is?
(A) 1994
(B) 1494
(C) 1349
(D) 1496
(E) 1596
Rationale: LCM = 1400
1400 - 6 = 1394
ANSWER:C
Answer: (C) 1349
Question: What is the unit digit in (4137)^754?
(A) 1
(B) 3
(C) 7
(D) 5
(E) 9
Rationale: Unit digit in (4137)^754 = Unit digit in {[(4137)^4]^188 x (4137)^2}
Unit digit of 7^4 is 1 and of 4137^2 is 9.
so the required unit digit = 1 x 9 = 9.
Answer E) 9.
Answer: (E) 9
Question: a bank was to give a loan out to a newly married couple for 800,000 with no interest for 2 years and raise the price to 900,000 after 2 years. what is the interest rate?
(A) 17%
(B) 13%
(C) 12%
(D) 7%
(E) 6%
Rationale: for 0 years = (900,000- 800,000) = 100,000.
for 2 years = (100,000 x 2)/2= 100,000
Principal = (800,000 - 100,000) = 700,000.
Hence, rate = (100 x 100,000)/(700,000x2) = 7% ANSWER: D
Answer: (D) 7%
Question: A horse chases a pony 8 hours after the pony runs. Horse takes 12 hours to reach the pony. If the average speed of the horse is 320 kmph, what s the average speed of the pony?
(A) 182kmph
(B) 192kmph
(C) 193kmph
(D) 196kmph
(E) 190kmph
Rationale: pony take 20 hours and horse take 12 hours...then Distance chased by them is 320*12.so speed of pony is (320*12)/20=192kmph.
ANSWER IS B
Answer: (B) 192kmph
Question: The speed of a car is 100 km in the first hour and 80 km in the second hour. What is the average speed of the car?
(A) 12
(B) 75
(C) 88
(D) 54
(E) 90
Rationale: S = (100 + 80)/2
= 90 kmph
Answer: E
Answer: (E) 90
Question: How much time will take for an amount of Rs. 480 to yield Rs. 81 as interest at 4.5% per annum of simple interest?
(A) 8 years
(B) 4 years
(C) 3 years 9 months
(D) 9 years
(E) 5 years
Rationale: Time = (100 * 81) / (480 * 4.5)
= 3 years 9 months
Answer: C
Answer: (C) 3 years 9 months
Question: In a kickball competition of 11 teams, how many possible matches can each team play with each other?
(A)  9
(B)  16
(C)  24
(D)  36
(E)  55
Rationale: 11C2 = 55
Option E
Answer: (E)  55
Question: A, B and C invests Rs.2000, Rs.3000 and Rs.4000 in a business. After one year A removed his money; B and C continued the business for one more year. If the net profit after 2 years be Rs.3200, then A's share in the profit is?
(A) 388
(B) 299
(C) 266
(D) 400
(E) 2871
Rationale: 2*12 : 3*12 : 4*24
1: 3: 4
1/8 * 3200 = 400.Answer: D
Answer: (D) 400
Question: 195,383,575,763,955,___
(A) 1153
(B) 1143
(C) 1243
(D) 1343
(E) 1148
Rationale: 19*1 = 19 5
19*2 = 38 3
19*3 = 57 5
19*4 = 76 3
19*5 = 95 5
19*6 = 114 3
so ans=1143
ANSWER:B
Answer: (B) 1143
Question: Find the number of ways of arranging the letters of the word "MATERIAL" such that all the vowels in the word are to come together?
(A) 1446
(B) 1440
(C) 1444
(D) 1441
(E) 1421
Rationale: In the word, "MATERIAL" there are three vowels A, I, E.
If all the vowels are together, the arrangement is MTRL'AAEI'.
Consider AAEI as one unit. The arrangement is as follows.
M T R L A A E I
The above 5 items can be arranged in 5! ways and AAEI can be arranged among themselves in 4!/2! ways.
Number of required ways of arranging the above letters = 5! * 4!/2!
= (120 * 24)/2 = 1440 ways.
Answer:B
Answer: (B) 1440
Question: In a manufacturing plant, it takes 36 machines 8 hours of continuous work to fill 8 standard orders. At this rate, how many hours of continuous work by 72 machines are required to fill 12 standard orders?
(A) 3
(B) 6
(C) 8
(D) 9
(E) 12
Rationale: the choices give away the answer..
36 machines take 4 hours to fill 8 standard orders..
in next eq we aredoubling the machines from 36 to 72, but thework is not doubling(only 1 1/2 times), = 8*36/72*12/8 = 6
Ans B
Answer: (B) 6
Question: A sum of money deposited at C.I. amounts to Rs.6000 in 6 years and to Rs.7500 in 7 years. Find the rate percent?
(A) 25%
(B) 20%
(C) 15%
(D) 10%
(E) 5%
Rationale: 6000 --- 1500
100 --- ? => 25%
Answer: A
Answer: (A) 25%
Question: Find the fourth proportion to 11,12,66
(A) 80
(B) 120
(C) 90
(D) 25
(E) 72
Rationale: Explanation:
11:12 :: 66:x
=> 11/12 = 66/x
=> x = 792/11
=> x =72
Option E
Answer: (E) 72
Question: In what time will a train 120 m long cross an electric pole, it its speed be 144 km/hr?
(A) 3 sec
(B) 2.9 sec
(C) 3.5 sec
(D) 7.5 sec
(E) 2.4 sec
Rationale: Speed = 144 * 5/18 = 40 m/sec
Time taken = 120/40
= 3 sec.
Answer: A
Answer: (A) 3 sec
Question: The speeds of three motor bikes are in the ratio 6 : 5 : 4. The ratio between the time taken by them to
travel the same distance is :
(A) 10 : 12 : 15
(B) 12 : 10 : 8
(C) 15 : 12: 10
(D) 10 : 15 : 12
(E) None of these
Rationale: Expl : Ratio of time taken : 1/6 :1/5 : 1/4 = 10 : 12 : 15
Answer: A
Answer: (A) 10 : 12 : 15
Question: A sum of money at simple interest amounts to $ 780 in 3 years and to $930 in 4 years. The sum is:
(A) $153
(B) $698
(C) $330
(D) $549
(E) $675
Rationale: C
$330
S.I. for 1 year = $(930 - 780) = $150.
S.I. for 3 years = $(150 x 3) = $450.
Principal = $(780 - 450) = $330.
Answer: (C) $330
Question: A student chose a number, multiplied it by 2, then subtracted 138 from the result and got 102. What was the number he chose?
(A) 240
(B) 120
(C) 150
(D) 200
(E) 100
Rationale: Let x be the number he chose, then
2⋅x−138=102
2x=240
x=120
So answer is B
Answer: (B) 120
Question: In how many ways can the letters {U, R, R, R, R} be arranged?
(A) 5
(B) 20
(C) 120
(D) 720
(E) 840
Rationale: My answer : A
There is 5! ways to arrange those letters in total, however letter U repeats 1! times and letter R repeats 4! times
=> the way to arrange without repeating = 5!/ [1!x4!] = 5
Answer: (A) 5
Question: In how many different ways can the letters of the word ‘JAMELS’ be arranged?
(A) 120
(B) 354
(C) 626
(D) 214
(E) 720
Rationale: E
720
The word SMART has 6 distinct letters.
Number of arrangements = 6!
= 6 x 5 × 4 × 3 × 2 × 1 = 720
Answer is E
Answer: (E) 720
Question: Two trains are running at 40 km/hr and 20 km/hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 9 seconds. What is the length of the fast train?
(A) 23 m
(B) 23 (2/9)m
(C) 27 (7/9)m
(D) 29 m
(E) 50 m
Rationale: Relative speed = (40 - 20) km/hr =	(20 x(5/18))m/sec =	(50/9)m/sec.
Therefore Length of faster train =	((50/9)	x 9) m =	(450/9)m = 50	m.
E
Answer: (E) 50 m
Question: A local elementary school has 1049 students and nine teachers, How many students would have to be added to the school to make sure each teacher has the same amount of students in their classroom?
(A) 4
(B) 6
(C) 5
(D) 1
(E) 2
Rationale: Using the rule on the divisibility of nine, we add the digits of 1049 together to get 14. Since we are doing addition, the next number that is divisible by nine would be 18. Therefore, our answer 4(option A)
Answer: (A) 4
Question: A and B entered into a partnership investing Rs.25000 and Rs.30000 respectively. After 4 months C also joined the business with an investment of Rs.35000. What is the share of C in an annual profit of Rs.47000?
(A) 14028
(B) 14038
(C) 14079
(D) 14000
(E) 14023
Rationale: 25*12: 30*12: 35*8
15:18:14
14/47 * 47000 = 14000
Answer:D
Answer: (D) 14000
Question: If the roots of a quadratic equation are 20 and -7, then find the equation?
(A) x2 + 13x - 140 = 0
(B) x2 - 13x + 140 = 0
(C) x2 - 13x - 140 = 0
(D) x2 + 13x + 140 = 0
(E) None of these
Rationale: Explanation:
Any quadratic equation is of the form
x2 - (sum of the roots)x + (product of the roots) = 0 ---- (1)
where x is a real variable. As sum of the roots is 13 and product of the roots is -140, the quadratic equation with roots as 20 and -7 is: x2 - 13x - 140 = 0.
ANSWER IS C
Answer: (C) x2 - 13x - 140 = 0
Question: 38, 87, 22,76, 31,47, 13, 82
Which of the following numbers is greater than three-fourth of the numbers but less than one-fourth of the numbers in the list above?
(A) a- 55
(B) b- 68
(C) c- 79
(D) d- 81
(E) e- 85
Rationale: Important:- Arrange the numbers in ascending order first.
13, 22, 31, 38, 47, 76, 82, 87
3/4th of the number list represents- 76 (6th number)
remaining 1/4th list represents 82 (7 th number)
79 fits in between above 2
Answer:- C
Answer: (C) c- 79
Question: Find the least number which when divided by 5,6,7, and 8 leaves a remainder 3, but when divided by 9 leaves no remainder .
(A) 1638
(B) 1863
(C) 1683
(D) 1836
(E) None of them
Rationale: L.C.M. of 5,6,7,8 = 840.
Required number is of the form 840k + 3
Least value of k for which (840k + 3) is divisible by 9 is k = 2.
Required number = (840 X 2 + 3)=1683
Answer is C.
Answer: (C) 1683
Question: How many 9-digits number are Palindromic numbers? A Palindromic number reads the same forward and backward, example 123454321.
(A) 100
(B) 610
(C) 729
(D) 900
(E) 90000
Rationale: Take the task of building palindromes and break it intostages.
Stage 1: Select the 9th digit
We can choose 1, 2, 3, 4, 5, 6, 7, 8, or 9
So, we can complete stage 1 in9ways
Stage 2: Select the 8th, 7th, 6th, 5th digit
We can choose 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9
So, we can complete stage 2 in10ways
IMPORTANT: At this point, the remaining digits are alreadylocked in.
Stage 3: Select the 4th, 3rd, 2nd, 1st digit
So, we can complete this stage in1way.
By theFundamental Counting Principle(FCP), we can complete all 5 stages (and thus build a 9-digit palindrome) in(9)(10)(10)(10)(10)(1)(1)(1)(1)ways (= 90000 ways)
Answer: E
Answer: (E) 90000
Question: Tom and John traveled in the same direction along the equal route at their constant speed rates of 15 km per hour and 10 km per hour, respectively. After 15 minutes Tom passed John, Tom reaches a certain Gas station, how many T minutes it takes John to reach the station?
(A) 5 min
(B) 6 min
(C) 7 and 1/2 min
(D) 8 min
(E) 10 min
Rationale: Since the question states “after 15 minutes”, we can say Tom traveled 15/4km for 15 minutes as he can travel 15km per hour. Hence, using the same logic, we can say John traveled 10/4km as he travels 10km per hour. So, John has to travel (15/4)-(10/4)km=5/4km more. Since John’s speed is 10km/hour, which means 1km/6minutes. As he has to travel 5/4km more, it is going to take him 6(5/4) minutes. Hence, T=6(5/4)=15/2 minutes. The correct answer is C.
Answer: (C) 7 and 1/2 min