divelab/Sys2Bench huggingface dataset:
Question: A set of numbers has an average of 50. If the largest element is 3 greater than 3 times the smallest element, which of the following values cannot be in the set?
Options:
A) 85
B) 90
C) 123
D) 150
E) 155
Rationale: Ans: E
Solution: we are given the relation between smallest and the largest term. so let the smallest a and largest be 3a+3
so the avg = 50
which tells us that any value of a must be less than 50
so a<50 means, largest value 3a+3 <(3*50)+3
=largest value must be <153
so 155 can not be the value in the set.
Answer: E
Question: A focus group is currently made up of x men and y women. If 2 men and 4 women are added to the group, and if one person is selected at random from the larger focus group, then what is the probability that a man is selected?
Options:
A)x/(x + 2)
B)x/(x + y)
C)(x + 2)/(x + y + 2)
D)(y + 4)/(x + y + 6)
E)(x + 2)/(x + y + 6)
Rationale: x men
y women
x+2+y+4 is the total
=x+y+6
x+2 is the number of men
so (x + 2)/(x + y + 6)
E. (x + 2)/(x + y + 6)
Answer: E
Question: A train is running with a speed of 60 kmph and its length is 110 metres. Calculate the time by which it will pass a man running opposite with speed of 6 kmph
Options:
A)2 second
B)4 second
C)6 second
D)8 second
E)10 second
Rationale: Explanation:
From the given question,
we will first calculate the speed of train relative to man,
=> ( 60 + 6 ) = 66 km/hr ( we added 6 because man is running opposite )
Convert it in metre/second
=66Ã—5/18
=55/3m/sec
Time it will take to pass man
=110Ã—3/55
=6 seconds
ANSWER IS C
Answer: C
Question: A driver covers a certain distance by car driving at 50 km/hr and returns back to the starting point riding on a scooter at 10 km/hr. What was the average speed for the whole journey?
Options:
A)12.5 km/h
B)14.8 km/h
C)16.7 km/h
D)17.5 km/h
E)18.9 km/h
Rationale: time 1 = d / 50
time 2 = d / 10
total time = d/50 + d/10 = 3d/25
average speed = total distance / total time = 2d / (3d/25) = 16.7 km/h
The answer is C.
Answer: C
Question: When 20 is subtracted from a number, it reduces to seven-twelve of the number. What is the sum of the digit of the number
Options:
A)40
B)44
C)46
D)48
E)45
Rationale: Explanation:
Let the number be x. Then,
x - 20 = 7x/12 => x - 7x/12 = 20
5x/12 = 20 => x = 48
Answer: Option D
Answer: D
Question: A student earned a grade of 80% on a math test that had 20 problems. How many problems on this test did the student answer correctly? (round to the nearest whole number)
Options:
A)36 problems
B)53 problems
C)27 problems
D)16 problems
E)18 problems
Rationale: Multiply the opposites:
80/100=x/20
80 x 20 = 1600
Divide by the remaining number:
16/1600
*100
16 problems
correct answer D
Answer: D
Question: A train 500 meters long is running with a speed of 44 kmph. The time taken by it to cross a tunnel 230 meters long is?
Options:
A)287 sec
B)288 sec
C)48 sec
D)61 sec
E)17 sec
Rationale: D = 500 + 230 = 730
S = 44 * 5/18 = 12 mps
T = 730/12 = 61 sec
Answer: D
Answer: D
Question: A man rides at the rate of 50km/hr. But stops 20minutes to change horses at the end of every 25th kilometer. How long will he take to go a distance of 100 kilometers?
Options:
A)3hr
B)6hr 30min
C)8hr 10min
D)7hr 20min
E)9hr
Rationale: speed of man = 50km/hr
number of rests = (100/25)-1 = 3
time taken for the man = (100/50)+3*(20/60) = 3 hr
Answer is A
Answer: A
Question: Consider there is an elevator and you are at the upside and coming down using elevator. You walk 20 steps and then you stop, then you reach to the ground in 10 minutes. If you walk 10 steps and then stop, then you reach to the ground in 20 minutes. What is the speed of the elevator and How many steps are there??
Options:
A)1 step/min
B)2 step/min
C)3 step/min
D)4 step/min
E)5 step/min
Rationale: Let e be the speed of the elevator, n be the no. of steps
n = 20 + 10*e = 10+20*e
e=1
n=30
No. of steps : 30
Speed : 1 step/min
ANSWER:A
Answer: A
Question: In a division sum, the divisor is ten times the quotient and five times the remainder. If the remainder is 44, the dividend is:
Options:
A)5330
B)5336
C)4884
D)5345
E)5350
Rationale: Divisor = (5 * 44) = 220
= 10 * Quotient = Divisor
=> Quotient = 220/10 = 22
Dividend = (Divisor * Quotient) + Remainder
Dividend = (220 * 22) + 42 = 4884.
C
Answer: C
Question: Two taps can separately fill a cistern 10 minutes and 15 minutes respectively and when the waste pipe is open, they can together fill it in 42 minutes. The waste pipe can empty the full cistern in?
Options:
A)8 min
B)7 min
C)5 min
D)9 min
E)4 min
Rationale: 1/10 + 1/15 - 1/x
= 1/42
x = 7
Answer: B
Answer: B
Question: The radius of the wheel of a bus is 175 cms and the speed of the bus is 66 km/h, then the r.p.m. (revolutions per minutes)of the wheel is
Options:
A)100
B)250
C)300
D)330
E)None of these
Rationale: Radius of the wheel of bus = 175 cm. Then,
circumference of wheel = 2Ï€r = 350Ï€ = 1100 cm
Distance covered by bus in 1 minute
= 66â„60 Ã— 1000 Ã— 100 cms
Distance covered by one revolution of wheel
= circumference of wheel
= 1100 cm
âˆ´ Revolutions per minute = 6600000/60Ã—1100 = 100
Answer A
Answer: A
Question: There are three departments having students 72,58,24 .In an exam they have to be seated in rooms such that each room has equal number of students and each room has students of one type only (No mixing of departments). Find the minimum number of rooms required?
Options:
A)73
B)74
C)75
D)76
E)77
Rationale: WE NEED TO TAKE GCD WHICH IS 2
THUS ALL THE ROOMS WILL HAVE 2 STUDENTS OF THE SAME DEPT
1) 72/2 = 36
2) 58/2 = 29
3) 24/2 = 12
TOTAL NO. OF MIN ROOMS REQD = 36+12+29 = 77
ANSWER:E
Answer: E
Question: Tough and Tricky questions: Mixture Problems.
A drink holding 6 ounces of an alcoholic drink that is 1 part rum to 2 parts coke is added to a jug holding 30 ounces of an alcoholic drink that is 1 part rum to 3 parts coke. What is the ratio of rum to coke in the resulting mixture?
Options:
A)2:5
B)5:14
C)3:5
D)4:7
E)14:5
Rationale: Answer = E) 5:10
........................ Rum ..................... Coke ................. Total
First Drink ........... 2 ............................ 4 ..................... 6 (Ratio 1:2)
Second Drink ....... 8 ............................. 24 ................... 32 (Ratio 1:3)
Total .................. 10 ............................. 28 .................... 38
Ratio = 10:20 = 5:10
E
Answer: E
Question: A candidate got 35% of the votes polled and he lost to his rival by 2250 votes. How many votes were cast?
Options:
A)7500
B)2327
C)2997
D)2662
E)7121
Rationale: 35%-----------L
65%-----------W
------------------
30%----------2250
100%---------? => 7500
Answer: A
Answer: A
Question: 12 men take 18 days to complete a job whereas 12 women in 18 days can complete 3⁄4 of the same job. How many days will 10 men and 8 women together take to complete the same job?
Options:
A)6
B)13 1⁄2
C)12
D)Data inadequate
E)None of these
Rationale: 12 M × 18 = 12 W × 18 × 4⁄3
\ w = 3/4 M
10M + 8W = 10M + 8 × 3⁄4M = 16 M
\16 men can complete the same work
in 12×18/16=27/2=13 1/2days
Answer B
Answer: B
Question: Three small cruise ships, each carrying 10 passengers, will dock tomorrow. One ship will dock at Port A, another at Port B, and the third at Port C. At Port A, two passengers will be selected at random; each winner will receive one gift certificate worth $50. At Port B, one passenger will be selected at random to receive a gift certificate worth $35, and at Port C, one passenger will be selected at random to receive a gift certificate worth $25. How many different ways can the gift certificates be given out?
Options:
A)270
B)450
C)2,700
D)4,500
E)27,000
Rationale: Number of ways 3 ships can go to 3 ports = 3! =6
Let ship A goes to dock A . Thus, the number of ways of selecting 2 winners out of 10 passengers = 10C2 = 45
Let ship B goes to dock B . Thus, the number of ways of selecting 1 winner out of 10 passengers = 10C1 = 10
Let ship C goes to dock C . Thus, the number of ways of selecting 1 winner out of 10 passengers = 10C1 = 10
Thus the total number of arrangements possible = 6*45*10*10 = 27000, thus E is the correct answer.
Answer: E
Question: What is the square root of 121?
Options:
A)11
B)12
C)16
D)18
E)25
Rationale: 11X11 = 121
ANSWER A
Answer: A
Question: A bag of P peanuts can be divided into 9 smaller bags with 6 peanuts left over. Another bag of m peanuts can be divided into 12 smaller bags with 4 peanuts left over. Which of the following is the remainder when Pm is divided by 18?
Options:
A)6
B)4
C)2
D)8
E)5
Rationale: P = 9x + 6
m = 12y + 4
Pm = (9x + 6)*(12y + 4) = 108xy + 36x + 72y + 24
Remainder of nm/18 = (108xy + 36x + 72y + 24)/18
Observe that the first three terms are a multiple of 18
24 when divided by 18 leaves remainder 6
Hence mn/18 will leave remainder 6
A
Answer: A
Question: 1 boy forgot the last digit of a 7 digit telephone no. If he randomly dial thefinal 3 digits after correctly dialing the 1st four, then what is the chance of dialing the correct no.?
Options:
A)2/989
B)3/456
C)1/1000
D)1/2314
E)2/2315
Rationale: it is given that last 3 digits are randomly dialed
Then, each of the digit can be selected out of 10 digits in 10 ways. Hence, required probability
= 1/(10)3 = 1/1000
C
Answer: C
Question: In how many different ways can the letters of the word ‘ARMOUM’ be arranged?
Options:
A)230
B)250
C)260
D)300
E)360
Rationale: ARMOUR = 6 letter whereas R repeated twice 6! 6xSx4x3x2x1 => 360
E
Answer: E
Question: A cube with its sides numbered 1 through 6 is rolled twice, first landing on a and then landing on b. If any roll of the cube yields an equal chance of landing on any of the numbers 1 through 6, what is the probability R that a + b is prime?
Options:
A) 0
B) 1/12
C) 5/12
D) 7/18
E) 4/9
Rationale: Total # of outcomes is 6*6=36;
Favorable outcomes:
a-b --> prime
1-1 --> 2;
1-2 --> 3;
2-1 --> 3;
1-4 --> 5;
4-1 --> 5;
2-3 --> 5;
3-2 --> 5;
1-6 --> 7;
6-1 --> 7;
2-5 --> 7;
5-2 --> 7;
3-4 --> 7;
4-3 --> 7;
6-5 --> 11;
5-6 --> 11.
Total of 15 favorable outcomes
R=15/36.
Answer: C.
Answer: C
Question: A popular website requires users to create a password consisting of digits only. If no digit may be repeated and each password must be at least 9 digits long, how many passwords are possible?
Options:
A)9! + 10!
B)2 x 10!
C)9! x 10!
D)19!
E)20!
Rationale: If we choose the 10 different digits then they can be arranged (permutations) in 10! ways.
But the question asks at least 9 digits. So we have the possibility of choosing only 9 digits for the password ( but digit shouldn't repeat), so we can have a total of 10 different combinations and each combination can be arranged in 9! ways.
Therefore
10 x 9! + 10!
= 10! + 10!
= 2 x 10!
Therefore B
Answer: B
Question: Two cars cover the same distance at the speed of 60 and 64 kmps respectively. Find the distance travelled by them if the slower car takes 1 hour more than the faster car.
Options:
A)980 km
B)860 km
C)960 km
D)460 km
E)660 km
Rationale: B
60(x + 1) = 64x
X = 15
60 * 16 = 960 km
Answer: B
Question: Sonika deposited Rs.14500 which amounted to Rs.12200 after 3 years at simple interest. Had the interest been 3% more. She would get how much?
Options:
A)13505
B)12004
C)15003
D)14500
E)16400
Rationale: (14500*3*3)/100 = 1305
12200
--------
13505
Answer: A
Answer: A
Question: A train 310 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?
Options:
A)40 sec
B)50 sec
C)44 sec
D)36 sec
E)60 sec
Rationale: Speed = 45 * 5/18 = 25/2 m/sec
Total distance covered = 310 + 140 = 450 m
Required time = 450 * 2/25 = 36 sec
Answer:D
Answer: D
Question: An arithmetic Sequence is a number sequence which has a constant difference between terms. Considering this definition which of the following is an arithmetic sequence?
I. e^2, f^2, g^2, h^2, i^2
II. e-6, f-3, g-5, h-3, i-3
III. 2e, 2f, 2g, 2h,2i
Options:
A)II and III
B)III only
C)I and III
D)I and II
E)II only
Rationale: lets look at the three choices...
I. e^2, f^2, g^2, h^2, i^2
since the difference is not constant, it is not an arithmetic sequence...
II. e-6, f-3, g-5, h-3, i-3
since the difference is not constant, it is not an arithmetic sequence
III. 2e, 2f, 2g, 2h,2i
since the difference is constant it is an arithmetic sequence...
The answer B)
Answer: B
Question: Tough and Tricky questions: Ratios
1/6 of a certain class left on a field trip. 1/3 of the students who stayed behind did not want to go on the field trip (all the others did want to go). When another vehicle was located, 1/2 of the students who did want to go on the field trip but had been left behind were able to join. What fraction of the class ended up going on the field trip?
Options:
A)1/2
B)2/3
C)11/15
D)23/30
E)4/9
Rationale: let total no. of students be 30
students left on a field trip =1/6(30) =5
thus 25 students left behind
1/3(25) students did not want to go. thus 50/3 students want to go on the trip
1/2(50/3)=25/3 were able to join the other students on the field trip.
thus total number of students that went on a field trip =5+ 40/3
thus required fraction = 4/9
E
Answer: E
Question: A carpenter worked alone for 1 day on a job that would take him 6 more days to finish. He and another carpenter completed the job in 7 more days. How many days would it have taken the second carpenter to do the complete job working alone?
Options:
A)4.5
B)7.5
C)9.5
D)14.5
E)24.5
Rationale: A carpenter worked only 1 day on something that takes him 6 MORE days.
Means;
Carpenter finishes his work in 7 days.
Let his buddy finish the same task in x days.
Respective rates per day:
1/7 AND 1/x
To complete 1 work:
First guy worked for 5 days @ rate=1/7 per day.
Second one worked for 7 days @ rate=1/x per day
Expression:
Days*Rate=Work
5*1/7+7*1/x=1
5x+49=7x
2x=49
x=24.5 days.
Ans:E
Answer: E
Question: A person borrows Rs. 4000 for 2 years at 4% p.a. simple interest. He immediately lends it to another person at 6 p.a for 2 years. Find his gain in the transaction per year.
Options:
A)100 rs
B)80 rs
C)160 rs
D)180 rs
E)200 rs
Rationale: Gain in 2 years =
[(4000*6*2)/100]-[(4000*4*2)/100]
480-320=160
Gain in 1 year =(160/2)=80 rs
ANSWER:B
Answer: B
Question: A rectangular garden has a fence along three sides and a wall along the fourth side. The fenced side opposite the wall is twice the length of each of the other two fenced sides. If the area of the rectangular garden is 1800 square feet, what is the total length of the fence, in feet?
Options:
A)60
B)100
C)120
D)200
E)300
Rationale: two sides EACH = x the third = 2x and the wall length is thus 2x too
x*2x = 2x^2 = 1800 ie x^2 = 900 ie x = 30
L = 60 W= 30
TOTAL LENGHT OF FENCE = 2*30+60 = 120
MY ANSWER IS C
Answer: D
Question: Gasoline varies in cost from $0.98 to $1.18 per gallon. If a car’s mileage varies from 16 to 24 miles per gallon, what is the difference between the most and least that the gasoline for a 480-mile trip will cost?
Options:
A)$15.10
B)$15.30
C)$15.50
D)$15.75
E)$15.80
Rationale: Solution:
We know that the per gallon cost of gasoline varies from $0.98 - $1.18.
Now we want to find the MAXIMUM difference between the least amount of money spent on gasoline and the largest amount of money spent i.e. to calculate max. trip cost - min. trip cost.
Mileage is given to be 16 to 24 miles per gallon, thus to travel 480 miles you will need gasoline in the range 480/24 to 480/16 which is 20 to 30 gallons.
So, for these 20 gallons and 30 gallons of gasoline the cost is as follows: (divide this task into 2 parts, 1 for 30 gallons and 2nd one for 20 gallons).
Case 1: for 30 gallons the cost is 30*0.98 to 30*1.18 which is $29.40 to $35.40
Case 2: for 20 gallons the cost is 20*0.98 to 20*1.18 which is $19.60 to $23.60
Thus, the maximum cost of the 480 mile trip is $35.40 and minimum is $19.60
so the difference is $35.40 - $19.60 = $15.80
Answer: E
Answer: E
Question: Find the average of first 40 natural numbers?
Options:
A)20.5
B)22
C)30.5
D)35
E)25
Rationale: Sum of first 100 natural numbers = 40*41/2 = 820Required average = 820/40 = 20.5Answer is A
Answer: A
Question: Each of the 38 members in a high school class is required to sign up for a minimum of one and a maximum of three academic clubs. The three clubs to choose from are the poetry club, the history club, and the writing club. A total of 12 students sign up for the poetry club, 20 students for the history club, and 19 students for the writing club. If 3 students sign up for exactly two clubs, how many students sign up for all three clubs?
Options:
A)2
B)3
C)4
D)5
E)6
Rationale: The total number in the three clubs is 12+20+19=51.
All 38 students signed up for at least one club.
3 of those students signed up for exactly one more club.
51 - 41 = 10 so 5 students must have signed up for exactly three clubs.
The answer is D.
Answer: D
Question: A heap of coconuts is divided into groups of 2, 3 and 5 and each time one coconut is left over. The least number of Coconuts in the heap is?
Options:
A)31
B)42
C)50
D)22
E)60
Rationale: LCM = 30 => 30 + 1 = 31
ANSWER A
Answer: A
Question: If k^2 is divisible by 240 what is the least possible value of integer K?
Options:
A)60
B)30
C)12
D)90
E)120
Rationale: 240 can be written as (2^4)*3*5.
For k^2 to be divisible by 240 it should contain at least 2^4 and 3 and 5 in its factors. We can leave out option C because 12 doesnt have 5 as one of its factor. Now if we check for option B, 30 can be written as 2*3*5, hence 30^ 2 will have 2 as the maximum power of 2, so we can leave out this option too.
Option C is the right answer if we follow the same method as we followed for other two previous options.
60 = (2^2)*3*5; 60^2 = (2^4)*(3^2)*(5^2). So it shows that 60^2 is divisible by 240 and hence the answer.
Answer : A
Answer: A
Question: If the cost price is 99% of selling price then what is the profit percentage.
Options:
A)1
B)1.11
C)1.01
D)1.1
E)1.21
Rationale: selling price=Rs100 : then cost price=Rs 99:profit =Rs 1.
Profit={(1/99)*100}%=1.01%
Answer is C.
Answer: C
Question: What is the sum of two consecutive even numbers, the difference of whose squares is 84?
Options:
A)42
B)44
C)48
D)56
E)none
Rationale: Sol.
Let the numbers be x and x + 2.
then, (x + 2)² - x² = 84 ⇔ 4x + 4 = 84 ⇔ 4x = 80 ⇔ x=20.
∴ Required sum = x + (x + 2) = 2x + 2 = 42.
Answer A
Answer: A
Question: The set S has 36 different subsets each of which contains exactly two elements. How many subsets of S could contain exactly seven elements each?
Options:
A)81
B)63
C)54
D)36
E)90
Rationale: nC2 = 36
=> n*(n-1)/2 = 36 by middle term factor and n cannot be negative
=> n = 9
nC7 = 9C7 = 9!/7!*(9-7)!= 9*8*7!/7!*2 =36
So, Answer is D.
Answer: D
Question: The average of the marks of 12 students in a class is 36. If the marks of each student are doubled, find the new average?
Options:
A)72
B)88
C)15
D)10
E)12
Rationale: Sum of the marks for the 12 students = 12 * 36 = 432. The marks of each student are doubled, the sum also will be doubled.
The new sum = 432 * 2 = 864. So, the new average = 864/12 = 72.
Answer: A
Answer: A
Question: Car A runs at the speed of 65km/hr & reaches its destination in 8hr. Car B runs at the speed of 70 km/h & reaches its destination in 4h. What is the respective ratio of distances covered by Car A & Car B?
Options:
A)11 : 5
B)11 : 8
C)13 : 7
D)15 : 7
E)16 : 9
Rationale: Sol. Distance travelled by Car A = 65 × 8 = 520 km
Distance travelled by Car B = 70 × 4 = 280 km
Ratio = 520/280 = 13 : 7
C
Answer: C
Question: After a mathematics exam, 20 percent of the students reported that they didn't study, while 20 percent of the students who didn't study refused to admit they hadn't studied. What percent of the students didn't study?
Options:
A)15%
B)50%
C)35%
D)20%
E)25%
Rationale: Statement: 20% of Students (S) Reported they Didn't Study (RDS). Of the students who didn't study (DS) 20% refused to admit they didn't study (notRDT). [Note: A Venn Diagram is useful to visualize the problem.]
Solution: Sample space is 100%.
S = 100%
RDS/S = 20%
notRDS/DS = 20% => 100% - 20% => RDS/DS = 80%
DS/S = (20)/(80)% = 25%
Answer: E
Answer: E
Question: A train covers a distance of 12 km in 10 min. If it takes 9 sec to pass a telegraph post, then the length of the train is?
Options:
A)177 m
B)189 m
C)120 m
D)178 m
E)180 m
Rationale: Speed = (12/10 * 60) km/hr = (72 * 5/18) m/sec
= 20 m/sec.
Length of the train = 20 * 9
= 180 m.
Answer: E
Answer: E
Question: If the price of an article went up by 40%, then by what percent should it be brought down to bring it back to its original price?
Options:
A)2/3%
B)28.57%
C)2/1%
D)1/3%
E)2/7%
Rationale: Let the price of the article be Rs. 100.
40% of 100 = 40.
New price = 100 + 40 = Rs. 140
Required percentage = (140 - 100)/140 * 100
= 40/140 * 100= 28.57%.
Answer:B
Answer: B
Question: If n is the product of the integers from 1 to 13, inclusive, how many different prime factors greater than 1 does n have?
Options:
A)Four
B)Five
C)Six
D)Seven
E)Eight
Rationale: n = 1*2*3*4*5*6*7*8*9*10*11*12*13
The prime factors of n are 2, 3, 5, 7, 11, and 13.
There are 6 prime factors.
The answer is C.
Answer: C
Question: If m=9^(x−1), then in terms of m, 3^(4x−1) must be which of the following?
Options:
A)m/3
B)9m
C)27m^2
D)m^2/3
E)m^2/9
Rationale: m = 9 ^ (X-1)
m = 3 ^ (2x-2)
m^2 = 3 ^ (4x-4)
27m^2 = 3 ^ (4x-1)
Answer C
Answer: C
Question: The average of 1st 3 of 4 numbers is 16 and of the last 3 are 15. If the sum of the first and the last number is 13. What is the last numbers?
Options:
A)4
B)7
C)5
D)9
E)3
Rationale: A + B + C = 48
B + C + D = 45
A + D = 13
A – D = 3
A + D = 13
2D = 10
D = 5
Answer:C
Answer: C
Question: On a certain date, Pat invested $7,000 at x percent annual interest, compounded annually. If the total value of the investment plus interest at the end of 10 years will be $28,000, in how many years total will the total value of the investment plus interest increase to $56,000?
Options:
A)15
B)16
C)18
D)20
E)24
Rationale: 28,000 = 7,000(1 + x)^10
4 = (1+x)^10 = 2^2
(1+x)^10 = ((1+x)^5)^2 = 2^2
Therefore, (1+x)^5 = 2
56,000 = 7,000(1 + x)^n
(1+x)^n = 8
(1+x)^n = 2^3
(1+x)^n = ((1+x)^5)^3 = (1+x)^15
Therefore, n = 15.
The answer is A.
Answer: A
Question: On a Saturday night, each of the rooms at a certain motel was rented for either $40 or $60. If 10 of the rooms that were rented for $60 had instead been rented for $40, then the total rent the motel charged for that night would have been reduced by 50 percent. What was the total rent the motel actually charged for that night ?
Options:
A) $400
B) $800
C) $1,000
D) $1,600
E) $2,400
Rationale: Let total rent the motel charge for all rooms =x
If 10 rooms that were rented for 60 $ had instead been rented for 40 $,
then total difference in prices = 20 $ * 10 = 200 $
Total rent the motel charged would have been reduced by 50 %
.5x = 200
=> x= 400
Answer A
Answer: A
Question: It takes John 25 minutes to walk to the car park and 45 to drive to work. At what time should he get out of the house in order to get to work at 9:00 a.m.?
Options:
A)6:50 a.m
B)5:50 a.m
C)4:50 a.m
D)7:50 a.m
E)8:50 a.m
Rationale: The time it takes John to get to work: time to walk to car park + time to drive
25 + 45 = 70 minutes = 1 hour and 10 minutes
John needs to get out of the house 1 hour and 10 minutes before 9:00 am at
9:00 - 1:10 = 7:50 a.m
correct answer D
Answer: D
Question: A, B and C have Rs.500 between them, A and C together have Rs.200 and B and C Rs.320. How much does C have?
Options:
A)50
B)78
C)267
D)20
E)27
Rationale: A+B+C = 500
A+C = 200
B+C = 320
--------------
A+B+2C = 520
A+B+C = 500
----------------
C = 20
Answer: D
Answer: D
Question: 5n + 2 > 12 and 7n - 5 < 30; n must be between which numbers?
Options:
A)1 and 8
B)2 and 6
C)0 and 9
D)2 and 5
E)2 and 9
Rationale: 5n > 10 --> n > 2
7n < 35 --> n < 5
2 < n < 5
Answer: D
Answer: D
Question: If -1 < x < 0, which of the following must be true?
I. x^5 < x^2
II. x^6 < 1 – x
III. x^7 < x^3
Options:
A)I,II,III only
B)I,II only
C)I,III only
D)II only
E)I only
Rationale: Answer : A
Answer: A