divelab/Sys2Bench huggingface dataset:
Question: When I was born, my mother was 23 years of age. After 6 years, when my sister was born, my father was 34 years of age. what is the difference between the ages of my parents?
Options:
A)17 years
B)11 years
C)6 years
D)5 years
E)8 years
Rationale: When age of Son=0 ,Mother=23
After 6 years, Son=6 ,Mother=23+6=29 ,Father=34
So difference between ages of Mother & Father=34-29=5
ANSWER:D
Answer: D
Question: On a trip, a cyclist averaged 11 miles per hour for the first 22 miles and 10 miles per hour for the remaining 20 miles. If the cyclist returned immediately via the same route and took a total of 9 hours for the round trip, what was the average speed (in miles per hour) for the return trip?
Options:
A)7.6
B)7.8
C)8
D)8.2
E)8.4
Rationale: The time to go 42 miles was 22/11+20/10=2+2=4 hours.
The average speed for the return trip was 42 miles/5 hours= 8.4 mph.
The answer is E.
Answer: E
Question: Average of five numbers is 27. If one number is excluded the average becomes 25. The excluded number is
Options:
A)35
B)45
C)55
D)65
E)67
Rationale: Explanation:
Number is (5*27) - (4*25) = 135-100 = 35
Answer: Option A
Answer: A
Question: At a certain college, 70 percent of the students taking physical education class who were injured reported their injury, while 20 percent of the students who were injured in physical education class didn't report their injury. What percent of the students taking physical education class were injured?
Options:
A)87.5%
B)60.5%
C)40%
D)75.5%
E)80%
Rationale: Statement: 70% of students taking Pysical Education class (PE) Admitted to being Injured (AI). Of the students who took PE who were Injured (I), 20% declined to admit injury (notAI). [Note: A Venn Diagram is useful to visualize the problem.]
Solution: Sample space is 100%.
PE = 100%
AI/PE = 70%
notAI/I = 20% => 100% - 20% => AI/I = 80%
I/PE = (70)/(80)% = 80%
Answer: A
Answer: A
Question: A train 200 m long is running with a speed of 54 kmph. In what will it pass a car whose speed at 36 kmph in the direction opposite to that in which the train is going
Options:
A)8 sec
B)10 sec
C)12 sec
D)14 sec
E)15 sec
Rationale: Explanation:
Speed of the train relative to man = (54 + 36) kmph
= 90 ×5/18 m/sec = 25 m/sec.
Time taken by the train to cross the car = Time taken by it to cover 200 m
at 25 m / sec = (200 ×1/25) sec = 8 sec
Answer: Option A
Answer: A
Question: If the ratio of ages of two friends is 4:3 and sum of their ages is 70 years then what is the age of older friend?
Options:
A)30 years
B)35 years
C)40 years
D)25 years
E)45 years
Rationale: Sum of thier ages is 70 in ratio 4:3
So 40+30 gives us 70. Wich is 4:3 so, older guy is having 40.
ANSWER:C
Answer: C
Question: In a group of 100 cars, 47 cars do not have air conditioning. If at least 53 cars have racing stripes, what is the greatest number of cars that could have air conditioning but not racing stripes?
Options:
A)45
B)47
C)49
D)51
E)53
Rationale: Lets assume AC=53(includesonly AC carsandcars with AC and racing stripes)
lets assume RS(racing stripes)>=53(includescars with AC and racing stripesandonly racing stripes).
Now since we want to maximize(only AC) we have to see to it thatcars with AC and racing stripesis minimal(assume 0) But since RS>=53.. we have to assign atleast 6 tocars with AC and racing stripes.
Hence AC=53-6=47.
The answer is B
Answer: B
Question: 1,000^2 + 1,001^2 +1,002^2 + 1,003^2 + 1,004^2 =
Options:
A)6,030,053
B)6,030,054
C)6,030,055
D)6,020,030
E)6,030,057
Rationale: Interesting problem.
I think key is to notice that all the given answer choices differs in last two digits. Therefore, our entire focus should be to figure out how the given terms contribute to last two digits of total.
1000^2 -> 00
1001^1 -> 01
.
.
.
1004^2 -> 16
Total -> *30
Answer D.
Answer: D
Question: The simple interest at x% for x years will be Rs. x on sum of:
Options:
A)x
B)100x
C)[100/x]
D)[x/100]
E)None
Rationale: Sol.
Sum = [100 * S.I. / R * T] = Rs. [100 * x / x * x] = Rs. [100/x].
Answer C
Answer: C
Question: The standard deviation of a normal distribution of data is 2, and 3 standard deviations below the mean is greater than 45. What is a possible value for the mean of the distribution?
Options:
A)52
B)47
C)48
D)49
E)50
Rationale: The standard deviation ({SD}) = 2;
3 standard deviations below the mean is greater than 45:
{Mean} - 3*{SD} > 45;
{Mean} - 6 > 45;
{Mean} > 51.
Answer: A.
Answer: A
Question: Four 6 faced dice are thrown together. The probability that all the three show the same number on them is?
Options:
A)1/32
B)1/216
C)1/33
D)1/38
E)1/34
Rationale: The three dice can fall in 6 * 6 *6 * 6 = 1296 ways.
Hence the probability is 6/1296
= 1/216
Answer: B
Answer: B
Question: Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is?
Options:
A)3/7
B)3/2
C)3/5
D)3/4
E)3/1
Rationale: Let the speeds of the two trains be x m/sec and y m/sec respectively. Then, length of the first train = 27 x meters, and length of the second train = 17 y meters. (27 x + 17 y) / (x + y) = 23 ==> 27 x + 17 y = 23 x + 23 y ==> 4 x = 6 y ==> x/y = 3/2.Answer: B
Answer: B
Question: Michele invests 300 of her money in a mutual fund that quickly goes sour, losing 25% of its value each day for a week. Which of the following COULD be the value of Michele’s investment at the close-of-business any day that week?
Options:
A)$40.10
B)$133.00
C)$250.05
D)$1575.00
E)$10000.00
Rationale: Suppose she invests n$ in the starting then in the subesequent days the money left after the day will be
n/2, n/4, n/8, n/16, n/32
So, answer will be A
Answer: A
Question: How many 4 digit numbers can be formed with the digits 0, 1, 2, 3, 4, 5, 6 and 4?
Options:
A)a. 220
B)b. 249
C)c. 432
D)d. 216
E)e. 288
Rationale: Taking Question with it's same language as given
To make number divisible by 5, the unit digit should be either 0 or 5 only
Case 1: If unit digit is fixed as zero
With two6s The choice to fill the remaining three digits = 3C2 x 5 = 15
With all remaining 3 digits different, The choice to fill the remaining three digits = 6 x 5 x 4= 120
Total Such cases = 120+15 = 135
Case 2: If unit digit is fixed as Five
With two6s and one0The choice to fill the remaining three digits = 2 [6605 or 6065]
With two6s and without0The choice to fill the remaining three digits = 3C2 x 4 = 12
With all remaining 3 digits different, and one0The choice to fill the remaining three digits = 2 (ways to place zero) x 5 x 4= 40
With all remaining 3 digits different, and without0The choice to fill the remaining three digits = 3 x 5 x 4= 60
Total Such cases = 2+12+40+60 = 114
Total numbers = 135+114 = 216
ANSWER OPTION D
Answer: D
Question: A man can row 40km upstream and 55km downstream in 13 hours also, he can row 30km upstream and 44km downstream in 10 hours.find the speed of the man in still water and the speed of the current.
Options:
A)1 lmph
B)2 kmph
C)4 kmph
D)5 kmph
E)3 kmph
Rationale: let rate upstream=x km/hr and rate downstream=y km/hr.
Then,40/x +55/y =13â€¦(i) and 30/x +44/y =10
Multiplying (ii) by 4 and (i) by 3 and subtracting ,we get:11/y=1 or y=11.
Substituting y=11 in (i),weget:x=5.
Rate in still water =1/2(11+5)kmph=8kmph.
Rate of current=1/2(11-5)kmph=3kmph
ANSWER E
Answer: E
Question: In a games hour 4 different types of players came to the ground? cricket 11, hokey 15, football 21, softball 15. How many players are present in the ground?
Options:
A)70
B)52
C)62
D)49
E)50
Rationale: total number of players= 11+15+21+15= 62
Answer is C
Answer: C
Question: Sushil got thrice as many marks in English as in Science. His total marks in English, Science and Maths are 180. If the ratio of his marks in English and Maths is 1:2, find his marks in Science?
Options:
A)19
B)77
C)66
D)55
E)31
Rationale: S:E = 1:3
E:M = 1:2
------------
S:E:M = 1:3:6
1/10 * 190 = 19
Answer: A
Answer: A
Question: An automobile parts supplier charges $25 per package of gaskets. When a customer orders more than 10 packages of gaskets, the supplier charges 4/5 the price for each package in excess of 10. During a certain week, the supplier sold 60 packages of gaskets. If 30 percent of the gaskets went to Company X, 15 percent to Company Y, and the rest to Company Z, what was the total amount, in dollars, that the parts supplier received in payment for the gaskets?
Options:
A)1305
B)1375
C)1345
D)1415
E)1455
Rationale: $25 per packet of gasket in case a customer orders less than 10
in case a customer orders > 10 price per gasket = 25*4/5=20
a certain week the supplier sold 60 gasket
1.he sold 30 % of the gaskets to X = 18 gaskets = 25*10 + 20 *8 = 250 + 160 = 410
2.he sold 15 % of the gaskets to Y = 9 gaskets = 25*9= 225
3.he sold remaining 55% to z =33 gaskets = 25*10 =250 + 20*23=710
thus ,total money earned
410+225+710 = 1345
Answer is C
Answer: C
Question: A girl scout was selling boxes of cookies. In a month, she sold both boxes of chocolate chip cookies ($1.25 each) and boxes of plain cookies ($0.75 each). Altogether, she sold 1,585 boxes for a combined value of $1,586.75. How many boxes of plain cookies did she sell?
Options:
A)0
B)233
C)500
D)695
E)789
Rationale: Let #plain cookies sold be X then #chocolate cookies = (total cookies-X)
Equating for X
(0.75)*X +(1.25)*(1585-X)=1586.75
=>x=789
Answer: E
Question: A car going at 20 miles per hour set out on an 80-mile trip at 9:00 A.M. Exactly 10 minutes later, a second car left from the same place and followed the same route. How fast, in miles per hour, was the second car going if it caught up with the first car at 10:30 A.M.?
Options:
A) 40
B) 50
C) 53
D) 55
E) 60
Rationale: Let Car A = car that starts at 9 AM
Car B = car that starts at 9:10 AM
Time for which car A travels at speed of 20 m per hour = 1.5 hours
Distance travelled by Car A = 20 *1.5 = 30 miles
Since Car B catches up Car A at 10:30 , time = 80 mins = 4/3 hour
Speed of Car B = 30/(4/3) = 40 miles per hour
Answer A
Answer: A
Question: A man can row 6 kmph in still water. When the river is running at 2 kmph, it takes him 1 hour to row to a place and black. What is the total distance traveled by the man?
Options:
A)5.32
B)5.7
C)5.76
D)5.74
E)5.71
Rationale: M = 6
S = 2
DS = 8
US = 4
x/8 + x/4 = 1
x = 2.66
D = 2.66 * 2 = 5.32 Answer: A
Answer: A
Question: A is three times as fast as B and working together, they can complete a work in 6 days. In how many days can B alone complete the work?
Options:
A)11 days
B)16 days
C)13 days
D)24 days
E)19 days
Rationale: A= 3B
A + B= 3B+ B= 4B
These 4B people can do the work in 6 days, which means B can alone do the work in 4*6=24 days.
Answer : D
Answer: D
Question: Mr. Thomas invested an amount of Rs. 13,900 divided in two different schemes A and B at the simple interest rate of 14% p.a. and 11% p.a. respectively. If the total amount of simple interest earned in 2 years be Rs. 3508, what was the amount invested in scheme B?
Options:
A)6400
B)2778
C)2699
D)2789
E)1279
Rationale: Let the sum invested in scheme A be Rs. x and that in scheme B be Rs. (13900 - x). Then,
(x * 14 * 2)/100 + [(13900 - x) * 11 * 2]/100 = 3508
28x - 22x = 350800 - (13900 * 22)
6x = 45000 => x = 7500
So, sum invested in scheme B = (13900 - 7500) = Rs. 6400.
Answer:A
Answer: A
Question: A shop keeper marked 30% above the cost price and offered 20% discount then find it's net profit?
Options:
A)2%
B)2.5%
C)3.7%
D)4.6%
E)5%
Rationale: Net profit = 30-20 + (30*(-25)/100) = 2.5%
Answer is B
Answer: B
Question: A person purchased a TV set for Rs. 16000 and a DVD player for Rs. 6250. He sold both the items together for Rs. 34710
. What percentage of profit did he make?
Options:
A)80%
B)49%
C)40%
D)70%
E)56%
Rationale: The total CP = Rs. 16000 + Rs. 6250
= Rs. 22250 and SP = Rs. 34710
Profit(%) = (34710 - 22250)/22250 * 100
= 56%
Answer:E
Answer: E
Question: Martha has the unique talent of being able to guess other people’s height and weight. For every five people that Martha meets, she consistently guesses the people’s correct height four times, and for every seven people that she meets, she consistently guesses the people’s correct weight five times. If Martha meets three people and her success rate remains constant, what is the probability that Martha correctly guesses a person’s weight and height at least once?
Options:
A)8/27
B)2/5
C)49/81
D)98/125
E)316/343
Rationale: Probability that she guesses the height correctly P(h)=4/5
Probability that she guesses the weight correctlyP(w)=5/7
Probability that she guesses both weight and height correctly(P(h)*P(w))=4/5 * 5/7= 20/35
Now the Q asks about the probability of this happening atleast once.
We calculate it by finding the probability of not being able to guess in any of the three occasions.
Probability of not being able to guess any no. of times =1-20/35=15/35=3/7
For all three occasions P(A)=3/7 * 3/7 * 3/7=27/343
Probability of the event happening atleast once=1- P(A)=1-27/343=316/343
Ans should be E
Answer: E
Question: In how many ways can 5 boysand 2 girls be arranged at a table if 2 girls are never together?
Options:
A)230
B)390
C)398
D)470
E)480
Rationale: Total ways of arranging 7 person in a circle = 6! = 720 ways
If we consider two women as one, then we have 5+1=6 persons. Arranging these six persons in circle will take = 5! = 120 ways
And two women can arrange themselves in 2! ways
Total ways in which two women sit together in circle = 5!*2! = 240 ways
Total ways in which two women doesn’t sit together in circle = 6! - 5!*2! = 720 - 240 = 480 ways
E
Answer: E
Question: Each of the positive integers a and c is a four-digit integer. If each of the digits 0 through 8 appears in one of these three integers, what is the minimum possible value of the sum of a and c?
Options:
A)3768
B)3789
C)3850
D)3825
E)3875
Rationale: According to the stem we should use the digits 0 through 8 to construct 2 four-digit integers, so that their sum is as small as possible.
To minimize the sum, minimize the thousands digits of a and c, so make them 1 and 2.
Next, minimize hundreds digits. Make them 3 and 4 .
Next minimize 10's digit place by 5 and 6
Use the remaining digits (7,and 8) for units digits.
So, a would be 1357,and c would be 2468.
1357 + 2468 =3825
Answer: D.
Answer: D
Question: In how many ways can the letters of the CHEATER be arranged
Options:
A)20160
B)2520
C)360
D)80
E)None of these
Rationale: Explanation:
As we can see the letter "E" is twice in given word, so Required Number
=7!/2!=7∗6∗5∗4∗3∗2!/2!=2520
Option B
Answer: B
Question: All of the stocks on the over the counter market are designated by either a 4 letter or a 5 letter code that is created by using the 26 letters of the alphabet. Which of the following gives the maximum number of different stocks that can be designated with these codes?
Options:
A)2 (26)^5
B)26(26)^4
C)27(26)^4
D)26(26)^5
E)27(26)^5
Rationale: In 4-digit code {XXXX} each digit can take 26 values (as there are 26 letters), so total # of 4-digits code possible is 26^4;
The same for 5-digit code {XXXXX} again each digit can take 26 values (26 letters), so total # of 5-digits code possible is 26^5;
Total: 26^4+26^5=26^4(1+26)=27∗26^4
Answer: C.
Answer: C
Question: For any positive integer n, the sum of the first n positive integers equals n(n+1)/2. What is the sum of all the even integers between 99 and 201?
Options:
A)7650
B)9250
C)12,650
D)14,250
E)15,150
Rationale: 100 + 102 + ... + 200 =
100*51 + (2+4+...+100) =
100*51 + 2*(1+2+...+50) =
100*51 + 2(50)(51)/2 =
100*51 + 50*51 = 150(51) = 7650
The answer is A.
Answer: A
Question: If x and y are positive integers such that x/y = 0.875, which of the following numbers could be y?
Options:
A)3
B)2
C)4
D)10
E)8
Rationale: With the given information, we are trying to find the value of y.
To achieve this we must convert the given decimal to a fraction and reduce it to it's lowest integer form.
Take the decimal x/y = 0.875 and because it's in the thousands decimal place, put the given value (x/y = 0.875/1) and multiply it by 1,000.
Take the resulting fraction (x/y = 875/1000) and reduce it to it's lowest form.
Both of the numbers are divisible by 125.
The result is x/y = 7/8.
Thus y = 8.
The correct answer is E.
Answer: E
Question: Find the surface area of a 10 cm x 4 cm x 3 cm brick.
Options:
A)84 sq.c.m.
B)124 sq.cm
C)164 sq.cm.
D)180 sq.cm.
E)None
Rationale: Sol.
Surface area = [2(10 x 4 + 4 x 3 + 10 x 3)] cm2
= (2 x 82) cm2
= 164 cm2.
Answer C
Answer: C
Question: If X boxes of orange juice cost 300 cents, how much will Y boxes cost in dollars?
Options:
A)Y*3/x
B)2Y/x
C)5Y/x
D)Y*4/x
E)Y*6/x
Rationale: X boxes of orange juice cost 300 cents or 3 dollars.
cost of orange juice = 3/x
Cost of Y orange juices = Y*3/x
Hence Answer : A
Answer: A
Question: Two trains of length 350 m and 250 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 36 kmph and 36 kmph. After how much time will the trains meet?
Options:
A)27/7 sec
B)20/7 sec
C)5 sec
D)21/7 sec
E)32/7 sec
Rationale: They are moving in opposite directions, relative speed is equal to the sum of their speeds.
Relative speed = (36 + 36)*5/18 = 4*5 = 20 mps.
The time required = d/s = 100/20 = 5 sec.
Answer : C
Answer: C
Question: Due to 10% decrease in the price of sugar and John can buy 5kg more sugar in Rs100 , then find the CP of sugar?
Options:
A)Rs. 2(1/9)
B)Rs. 2(2/9)
C)Rs. 2(1/7)
D)Rs. 3(2/9)
E)Rs. 3(2/7)
Rationale: Here r = 10 % ,x = 100 and A = 5 kg
Actual price of sugar = 10*100/((100-10 )*5) = Rs. 2(2/9)
B
Answer: B
Question: Find out the wrong number in the series.
7, 8, 18, 57, 228, 1165, 6996
Options:
A)8
B)18
C)57
D)228
E)238
Rationale: The series is
7*1 + 1 = 8
8*2 + 2 = 18
18*3 + 3 = 57
57*4 + 4 = 232
232*5 + 5 = 1165
1165*6 + 6 = 6996
so 228 is wrong
ANSWER:D
Answer: D
Question: A certain car traveled twice as many miles from Town A to Town B as it did from Town B to Town C. From Town A to Town B, the car averaged 10 miles per gallon, and from Town B to Town C, the car averaged 18 miles per gallon. What is the average miles per gallon that the car achieved on its trip from Town A through Town B to Town C?
Options:
A)13
B)13.5
C)14
D)14.5
E)15
Rationale: Ans is D
Given d_ab = 2*d_bc
let d_ab = d and d_bc = x so d=2x
for average miles per gallon = (d+x)/((d/10)+(x/18)) = 14.5 (formula avg speed = total distance/ total time)
Answer: D
Question: Aishwarya’s mom was 28 years of age at the time of her birth, while her mom was 20 years old when her 2 years younger sister was born. The variance between the parents ages is :
Options:
A)10 years
B)11 years
C)15 years
D)9 years
E)4 years
Rationale: A
6 years
Mom’s age when Aishwarya’s sister was born = 20 years.
Dad’s age when Aishwarya’s sister was born = (28 + 2) years = 30 years.
Needed Variance = (30 – 20) years = 10 years.
Answer is A
Answer: A
Question: The difference between C.I. and S.I. on an amount of Rs. 15,000 for 2 years is Rs. 216. What is the rate of interest per annum?
Options:
A)8
B)2
C)9
D)4
E)12
Rationale: Explanation:
[15000 * (1 + R/100)2 - 15000] - (15000 * R * 2)/100 = 216
15000[(1 + R/100)2 - 1 - 2R/100] = 216
15000[(100 + R)2 - 10000 - 200R]/10000 = 216
R2 = (216 * 2)/3 = 144 => R = 12
Rate = 12%
Answer: Option E
Answer: E
Question: Two members of a club are to be selected to represent the club at a national meeting. if there are 91 different possible selections of the 2 members, how many members does the club have?
Options:
A)20
B)14
C)40
D)57
E)95
Rationale: I have done this problem by substituting numbers
We have n!/2!(n-2)! = 91
or n(n-1)/2 = 182 or (n-14)(n+13) =0
n=14 satisfies the equation
B
Answer: B
Question: A circular rim A having a diameter of 36 inches is rotating at the rate of x inches/min. Another circular rim B with a diameter of 84 inches is rotating at the rate of y inches/min. What is the value of y in terms of x, if both the rims reach their starting positions at the same time after every rotation.
Options:
A)3x/7
B)4x/5
C)7x/5
D)5x/7
E)3x/4
Rationale: t = S1/V1 = S2/V2
or, 36/x = 84/y
or, y = 36x/84 = 3x/7 (Answer A)
Answer: A
Question: When positive integer H is divided by positive integer B, the result is 4.35. Which of the following could be the reminder when H is divided by B?
Options:
A) 13
B) 14
C) 15
D) 16
E) 17
Rationale: the remainder will be obtained from the decimal part when H is divided by B i.e. 0.35
0.35 = 35/100 = 7/20 so possible remainders are 7,14,21,28. Only option B-14 satisfies this
PS: for B-14 H=174 and B=40
Answer: B
Question: FEDERAL bank offers an interest of 5% per annum compounded annually on all its deposits. If $10,000 is deposited, what will be the ratio of the interest earned in the 4th year to the interest earned in the 5th year?
Options:
A)1:5
B)625:3125
C)100:105
D)100^4:105^4
E)725:3225
Rationale: Hi Bunuel,
Here is my approach: is this correct?
FEDERAL bank offers an interest of 5% per annum compounded annually on all its deposits
Interest earned in 4 year= 10000(1+0.05)^4
Interest earned in 5 year= 10000(1+0.05)^5
Ratio= {10000(1.05)^4}/{10000(1.05^5)} =>1.05^4/1.05^5 =>1/1.05 Multiplied by 100 in both numerator and denominator gives 100:105
Hence Ans:C
Answer: C
Question: If the length of the sides of two cubes are in the ratio 4:1, what is the ratio of their total surface area?
Options:
A)4:1
B)6:1
C)8:1
D)16:1
E)64:1
Rationale: Let x be the length of the small cube's side.
The total surface area of the small cube is 6x^2.
The total surface area of the large cube is 6(4x)^2=96x^2.
The ratio of surface areas is 16:1.
The answer is D.
Answer: D
Question: What is the leastvalue of x. So that 45x09 is divisible by 3?
Options:
A)0
B)5
C)2
D)6
E)7
Rationale: The sum of the digits of the number is divisible by 3, then the number is divisible by3.
4 + 5 + x + 0+ 9 = 18 + x
Least value of x may be 0
Therefore 18 + 0= 18 is divisible by 3.
A
Answer: A
Question: A basketball coach will select the members of a five-player team from among 8 players, including John and Peter. If the five players are chosen at random, what is the probability that the coach chooses a team that includes both John and Peter?
Options:
A)1/9
B)1/6
C)2/9
D)5/14
E)1/3
Rationale: you can but that will require more cases and will be time consuming.
straight forward way is to group J and P as always present on the team and as order does not matter so we just need to find the total number of ways to select rest three players = 6c3
total number of ways of selecting 5 players out of 8 = 8c5
probability = 6c3/8c5 = 5/14
D
Answer: D
Question: A truck driver drove for 2 days. On the second day, he drove 3 hours longer and at an average speed of 15 miles per hour faster than he drove on the first day. If he drove a total of 900 miles and spent 21 hours driving during the 2 days, what was his average speed on the first day, in miles per hour?
Options:
A)25.0
B)30.3
C)34.2
D)40.5
E)45.4
Rationale: Day 1
2t+3=21
t=9
Day 2
t+3
9+3=12
9r+12(r+15)=900
r=34.2
Answer:C
Answer: C
Question: The ratio of the number of ladies to gents at a party was 1:2 but when 2 ladies and 2 gents left, the ratio became 1:3. How many people were at the party originally?
Options:
A)22
B)18
C)12
D)66
E)99
Rationale: x, 2x
(x-2):(2x-2) = 1:3
3x-6 = 2x-2
x = 4
x+2x = 3x
=> 3*4 = 12
Answer: C
Answer: C
Question: The length of rectangle is thrice its breadth and its perimeter is 56 m, find the area of the rectangle?
Options:
A)432
B)212
C)252
D)992
E)147
Rationale: 2(3x + x) = 56
l = 21 b = 7
lb = 21* 7= 147
Answer:E
Answer: E
Question: On a certain road, 10% of the motorists exceed the posted speed limit and receive speeding tickets, but 30% of the motorists who exceed the posted speed limit do not receive speeding tickets. What percent of the motorists on that road exceed the posted speed limit?
Options:
A)10.5%
B)12.5%
C)14.3%
D)22%
E)30%
Rationale: suppose there are X motorists.
10% of them exceeded the speed limit and received the ticket, i.e. X/10.
Again, suppose total no. of motorists who exceeded the speed limit are Y.
30% of Y exceeded the speed limit but didn't received the ticket, i.e. 3Y/10.
it means 7Y/10 received the ticket.
hence, 7Y/10 = X/10
or Y/X=1/7
or Y/X * 100= 1/7 * 100= 14.3%
C
Answer: C