divelab/Sys2Bench huggingface dataset:
Question: A clock loses a minute every three hours for 4 days and gains 1% in the subsequent 6 days. If it was set right on Friday at 09 AM, what will be the time at the end of 10 days?
Options:
A)09:54:40 AM
B)09:56:24 AM
C)10:16:40 AM
D)10:06:36 AM
E)09:54:24 AM
Rationale: Loses 8 minutes each day.
so total loss = 4×8 = 32min
subsequent 6 days = 6×24×60 minutes
1% gain = ( 6×24×60)/100 = 86.4 minutes
so, total gain = 86.4 - 32 = 54.4 min = 54 + 0.4 min = 54 minutes + 0.4 × 60 seconds = 54min + 24seconds
10 days later the clock should be 54 min and 24seconds fast.
so time , 09:54:24 am (Answer E)
Answer: E
Question: If the average of 9 digits is 18 and the average of 4 of them is 8, calculate the average of the remaining 5 numbers?
Options:
A)21
B)26
C)27
D)22
E)29
Rationale: Explanation:
Total of the 9 digits - 9*18 = 162
Total of the 4 digits - 4*8 = 32
Total of the remaining 5 digits - 162-32 = 130
average of the remaining 3 numbers = 130/5 = 26
ANSWER: B
Answer: B
Question: 4 weavers can weave 4 mats in 4 days. At the same rate, how many mats would be woven by 6 weavers in 6 days?
Options:
A)6
B)9
C)12
D)15
E)18
Rationale: 1 weaver can weave 1 mat in 4 days.
6 weavers can weave 6 mats in 4 days.
6 weavers can weave 9 mats in 6 days.
The answer is B.
Answer: B
Question: If y is 40 percent greater than x, then x is what percent less than y?
Options:
A)18%
B)21%
C)25%
D)29%
E)35%
Rationale: y = 1.4x
x = y/1.4 = 10y/14 = y - (2/7)*y
2/7 is about 29%.
The answer is D.
Answer: D
Question: If an object travels at sixty feet per minute, how many feet does it travel in one hour?
Options:
A)60
B)3000
C)2400
D)1800
E)3600
Rationale: If an object travels at 60 feet per minute it covers covers 60x60 feet in in one hour.
Answer = 3600 Answer:E
Answer: E
Question: Siddharth wants to borrow Rs.8000 at rate of interest 6% p.a. at S.I and lend the same amount at C.I at same rate of interest for two years. What would be his income in the above transaction?
Options:
A)s.28.80
B)s.21.68
C)s.21.18
D)s.21.98
E)s.21.29
Rationale: Amount of money Siddharth borrowed at S.I at 6% p.a. for two years = Rs.8,000
He lend the same amount for C.I at 6% p.a. for two years.
=> Siddharth's income = C.I - S.I
= p[1 + r/ 100]n - p - pnr/100
= p{ [1 + r/ 100]2 - 1 - nr/100
= 8,000{ [1 + 6/100]2 - 1 - 12/100}
= 8,000 {(1.06)2- 1 - 0.12} = 8,000(1.1236 - 1 - 0.12)
= 8,000 (0.0036) = 8 * 3.6
= Rs.28.80
Answer: A
Answer: A
Question: A company’s four cars running 10 hrs a day consume 1500 lts of fuel in 10 days. In the next 6 days, the company will need to run 9 cars for 12 hrs each so it rents 5 more cars which consume 20% less fuel than the company’s four cars. How many lts of fuel will be consumed in the next 6 days?
Options:
A)1200 lt
B)1555 lt
C)1664 lt
D)1728 lt
E)2160 lt
Rationale: Given that
4 cars running 10 hrs a day consume 1200 lts. of fuel in 10 days.
1 car consumption per hour per day = 1500 /4 *10 *10 = 3.75 litre
Now question say new car consume 20% less fuel than the company’s four cars = 80/100 of 3.75 = 3 ( 20 percent less than 3.75)
Hence we calculate total consumption for next 6 days, the company will need to run 5 new cars for 12 hrs = 3 *12 *6*5 =1080
similarly = old 4 car consumption for next 6 days for 12 hrs = 3.75*6*12*4 = 1080
hence total is = 1080+1080= 2160 lt
Ans is E .
Answer: E
Question: In a sample of college students, 50 percent are third year students and 70 percent are not second-year students. What fraction of those students who are not third-year students are second-year students?
Options:
A)2/3
B)1/4
C)2/5
D)3/7
E)2/9
Rationale: required answer= 40/60. = 2/3
Answer is A
Answer: A
Question: A firm has 5 senior partners and 6 junior partners. How many different groups of 3 partners can be formed in which at least one member of the group is a senior partner? (Note that two groups are considered different if at least one group member is different.)
Options:
A)130
B)135
C)140
D)145
E)150
Rationale: The number of ways to form a group of 3 is 11C3 = 165
The number of groups with no senior partner is 6C3 = 20
The number of groups with at least one senior partner is 165-20 = 145
The answer is D.
Answer: D
Question: What profit percent is made by selling an article at a certain price, if by selling at 2/3rd of that price, there would be a loss of 20%?
Options:
A)20%
B)33.0%
C)22%
D)77%
E)54%
Rationale: Explanation:
SP2 = 2/3 SP1
CP = 100
SP2 = 80
2/3 SP1 = 80
SP1 = 120
100 --- 20 => 20%
Answer: Option A
Answer: A
Question: The price of a car is Rs. 3,25,000. It was insured to 85% of its price. The car was damaged completely in an accident and the insurance company paid 90% of the insurance. What was the difference between the price of the car and the amount received?
Options:
A)Rs.32.500
B)Rs.48,750
C)Rs.76,375
D)Rs.81,250
E)None
Rationale: Solution
Amount paid to car owner	= 90% of 85% of Rs. 3,25,000.
= Rs. (90/100 ×85/100 ×325000)
= Rs. 2,48,625.
Required differene	= Rs. (325000 - 248625)
= Rs. 76,375.
Answer C
Answer: C
Question: 90, 180, 12, 50, 100, 160, ?, 3, 40, 4, 25, 2, 6, 30, 3
Options:
A)100
B)150
C)180
D)120
E)220
Rationale: 30*3=90
6*30=180
6*2=12
25*2=50
4*25=100
40*4=160
3*40=120 ans is 120
ANSWER:D
Answer: D
Question: Pipe A can fill a tank in 6 hours. Due to a leak at the bottom, it takes 10 hours for the pipe A to fill the tank. In what time can the leak alone empty the full tank?
Options:
A)13
B)17
C)15
D)19
E)12
Rationale: Let the leak can empty the full tank in x hours 1/6 - 1/x = 1/10
=> 1/x = 1/6 - 1/10 = (5 - 3)/30 = 2/30 = 1/15
=> x = 15.
Answer: C
Answer: C
Question: What is the place value of 7 in the numeral 2734?
Options:
A)70
B)7
C)700
D)7.0
E)800
Rationale: Explanation:
7 × 100 = 700
Answer: Option C
Answer: C
Question: WINK, Inc. follows a certain procedure that requires two tasks to be finished independently in order for a job to be done. On any given day, there is a 7/8 probability that task 1 will be completed on time, and a 1/5 probability that task 2 will be completed on time. On a certain day, what is the probability that task 1 will be completed on time, but task 2 will not?
Options:
A)1/20
B)3/40
C)13/40
D)7/10
E)13/22
Rationale: P(1 and not 2)=7/8*(1-1/5)=7/10.
Answer: D.
Answer: D
Question: When Greenville State University decided to move its fine arts collection to a new library, it had to package the collection in 20-inch by 20-inch by 12-inch boxes. If the university pays $0.50 for every box, and if the university needs 2.16 million cubic inches to package the collection, what is the minimum amount the university must spend on boxes?
Options:
A)$155
B)$225
C)$510
D)$850
E)$1250
Rationale: The volume of each box is 20*20*12 = 4800 cubic inches.
Number of boxes = 2,160,000/4800 = 450 boxes
Total cost = 450×$0.5=$225
The answer is B.
Answer: B
Question: Evaluate (12 + 22 + 32 + ... + 102)
Options:
A)430
B)720
C)385
D)265
E)295
Rationale: We know that (12 + 22 + 32 + ... + n2) =	1/6	n(n + 1)(2n + 1)
Putting n = 10, required sum =1/6 x 10 x 11 x 21 =385
Option C
Answer: C
Question: A train met with an accident 70km away from station A. It completed the remaining journey at 5/6th of the original speed and reached station B 1hr 12mins late. Had the accident taken place 60km further, it would have been only 1hr late. what was the original speed of the train?
Options:
A)60 km/hr
B)55 km/hr
C)65 km/hr
D)70 km/hr
E)48 km/hr
Rationale: let the original speed be 6x. A/q, traveling 70 km at 5/6th of original speed costs him 12 minutes etc
70/5x =70/6x +12/70 -> x =10 , 7x= 70.
Ans D
Answer: D
Question: If R, x, y, and z are positive integers and (x)×(y)×(z)=R^2, which of the following could be the values of x, y, and z?
Options:
A)3, 16, 25
B)9, 25, 24
C)2, 9, 32
D)2, 9, 16
E)8, 16, 36
Rationale: This is one of those questions where using the given options is fastest way to get the solution. We need to find a set where 3 numbers can be paired into 2 pairs of some numbers because we need a product which is a square number.
C fits the bill. 2*9*32 = 2*3*3*8*4 = 3*3*8*8
ans C
Answer: C
Question: The average of 5 quantities is 8. The average of 3 of them is 4. What is the average of remaining 2 numbers?
Options:
A)14
B)10
C)8
D)9.5
E)None of these
Rationale: ANSWER: A
(5x8-3x4)/2=14
Answer: A
Question: In the first 10 overs of a cricket game, the run rate was only 2.1. What should be the rate in the remaining 30 overs to reach the target of 282 runs?
Options:
A)6.25
B)8.28
C)6.11
D)8.7
E)8.11
Rationale: Required run rate
= [282 - (2.1 * 10)]/30
= 261/30
= 8.70
Answer:D
Answer: D
Question: The area of a square is equal to five times the area of a rectangle of dimensions 125 cm * 64 cm. What is the perimeter of the square?
Options:
A)388
B)800
C)277
D)126
E)191
Rationale: Area of the square = s * s = 5(125 * 64)
=> s = 25 * 8 = 200 cm
Perimeter of the square = 4 * 200 = 800 cm.
Answer: B
Answer: B
Question: A is twice as good a work man as B and together they finish the work in 14 days. In how many days A alone can finish the work?
Options:
A)23
B)21
C)77
D)92
E)61
Rationale: WC = 2:1
2x + x = 1/14 => x = 1/42
2x = 1/21
A can do the work in 21 days.
Answer: B
Answer: B
Question: A bag contains 18 purple jellybeans, 12 green jellybeans, and 16 yellow jellybeans; these jellybeans are the only items in the bag. If a person picks a jellybean at random out of the bag, what is the probability that the jellybean will be green?
Options:
A)15%
B)20%
C)26%
D)30%
E)35%
Rationale: Probability of green beans = 12 / (18 + 12 + 16) = 12/46 = 26%
Answer is C
Answer: C
Question: 24 men can complete a work in 16 days.32 women can complete the same work in 24 days.16 men and 16 women started working and worked for 12 days. How many more men are to be added to complete the remaining work in 2 days?
Options:
A)16
B)24
C)36
D)48
E)49
Rationale: Explanation:
1man’s 1 day work = 1/384
1 woman’s 1 day work = 1/768
work done in 12 days =12(16/384+16/768) =12*3/48 = 3/4
remaining work =1/4
(16 men + 16 women)’s 2 day work =2(16/384+16/768) = 1/8
remaining work = 1/4 - 1/8 =1/8
1/384 work is done in 1 day by 1man 1/8 work will be done in 2 days by 384 x 1/8 x 1/2 = 24 men
Answer: Option B
Answer: B
Question: Raju age after 15 years will be 5 times his age 5 years back, What is the present age of Raju
Options:
A)28
B)17
C)10
D)77
E)66
Rationale: Clearly,
x+15 = 5(x-5)
<=> 4x = 40 => x = 10
Answer:C
Answer: C
Question: Arun purchased 35 kg of rice at the rate of Rs 9.50 per kg and 30 kg at the rate of Rs 10.50 per kg. He mixed the two. Approximately, at what price per kg should he sell the mixture to make 35 % profit in the transaction?.
Options:
A)12 Rs
B)13 Rs
C)13.5 Rs
D)14 Rs
E)None of these
Rationale: Explanation :
Cost Price of 65 kg rice = Rs. (35 x 9.50 + 30 x 10.50)
= 647.50 Rs
Sell Price of 65 kg rice = 135 % of 647.50 = Rs (135/100) x 647.50
Sell Price per kg = (135/100) x 647.50 x (1/65) = 13.44=Rs. 13.50 (Appx.)
Answer : C
Answer: C
Question: In what time will a train 150 m long cross an electric pole, it its speed be 144 km/hr?
Options:
A)2.5 sec
B)3.75 sec
C)3.5 sec
D)7.5 sec
E)2.4 sec
Rationale: Speed = 144 * 5/18 = 40 m/sec
Time taken = 150/40
= 3.75 sec.
Answer: B
Answer: B
Question: How long does a train 110 m long traveling at 60 kmph takes to cross a bridge of 170 m in length?
Options:
A)16.7
B)16.8
C)16.5
D)16.1
E)16.2
Rationale: D = 110 + 170 = 280 m
S = 60 * 5/18 = 50/3
T = 280 * 3/50 = 16.8 sec
Answer:B
Answer: B
Question: A women travels from X to Y distance of 1000 miles in 10 hours. she returns to X in 4 hours. Find her average speed
Options:
A)300mph
B)150.2mph
C)142.8mph
D)200mph
E)111.01mph
Rationale: Speed from X to Y = 1000/10 = 100 mph
Speed from Y to X = 1000/4 = 250 mph
Average speed = 2*100*250 / 350 = 142.8mph
Answer is C
Answer: C
Question: In her backyard, Florry grows only yellow roses and white roses. Some of the rose bushes have flowers of both colors, and some have flowers of one color only. The number of rose bushes that have only yellow roses is 50% greater than the number of rose bushes that have only white roses. If there are yellow roses on 80% of Florry's rose bushes, then what percent H of her bushes have only yellow roses?
Options:
A)20
B)30
C)50
D)70
E)80
Rationale: let, the number of bushes with only yellow flowers be x
so, number of bushes with only yellow flowers will be 1.5x
if total number of bushes of flowers= T
then total number of bushes with yellow flowers= 0.8T
we can say that total number of bushes with yellow flowers+ bushes with only white flowers= total number of bushes with flowers
so,H= 0.8T+x=T
x=0.2T
so, 1.5x=0.3T
30% flowers are yellow flowers
OA B
Answer: B
Question: If the diagonals of a rhombus are 24 cm and 10 cm, what will be its perimeter
Options:
A)42 cm
B)64 cm
C)56 cm
D)52 cm
E)None of these
Rationale: Explanation : Let the diagonals be PR and SQ such that PR = 24 cm and SQ = 10 cm PO = OR = 24/2=12 cm
SO = OQ = 10/2=5 cm
PQ = QR = RS = SP = √(122 + 52) = √(144+25) = √169 = √13 cm
perimeter = 4 × 13 = 52 cm Answer : Option D
Answer: D
Question: If a bike moving at the speed of x km/hr travels a distance of y km, which of the following cannot be equal to the distance traveled?
Options:
A)x-y km
B)x/2 km
C)y-x km
D)y/x km
E)(x-y)/2 km
Rationale: This question can be solved by TESTing VALUES, but there's a particular pattern that you have to recognize to make the workeasy.
We're not really limited by anything in this question, so X and Y can be anything. Under normal circumstances, I won't TEST the number 1 in PS questions (as it often leads to duplicate answers), but here it's a great option (since we're looking to eliminate 4 answers, multiple TESTs are going to be likely anyway).
We're given information on speed (X km/hour) and distance (Y km). We're asked which of the 5 answer choices CANNOT be the distance traveled.
IF....
X = 2 and Y = 1
Answers A (2-1 = 1) and B (2/2 = 1) are POSSIBLE. Eliminate A and B.
IF....
X = 3 and Y = 1
Answer E ([3-1]/2 = 1) is POSSIBLE. Eliminate E.
IF....
X = 1 and Y = 1
Answer D (1/1 = 1) is POSSIBLE. Eliminate D.
Final Answer:
C
Answer: C
Question: A tank is filled in eight hours by three pipes A, B and C. Pipe A is twice as fast as pipe B, and B is twice as fast as C. How much time will pipe B alone take to fill the tank?
Options:
A)24 hours
B)28 hours
C)32 hours
D)36 hours
E)None of these
Rationale: Explanation:
1/A + 1/B + 1/C = 1/8 (Given)
Also given that A = 2B and B = 2C
=> 1/2B + 1/B + 2/B = 1/8
=> (1 + 2 + 4)/2B = 1/8
=> 2B/7 = 8
=> B = 28 hours.
ANSWER IS B
Answer: B
Question: The price of a jacket is reduced by 25%. During a special sale the price of the jacket is reduced another 30%. By approximately what percent must the price of the jacket now be increased in order to restore it to its original amount?
Options:
A)105
B)45
C)85
D)95
E)90.5
Rationale: 1) Let the price of jacket initially be $100.
2) Then it is decreased by 25% , therefore bringing down the price to $75.
3) Again it is further discounted by 30%, therefore bringing down the price to $52.5.
4) Now 52.5 has to be added byX %in order to equal the original price.
52.5 + ( X% )52.5 = 100.
Solving this eq for X, we get X = 90.5
Ans is E
Answer: E
Question: A trader marks his articles 20% more than the cost price. If he allows 20% discount, then find his gain or loss percent?
Options:
A)1
B)2
C)3
D)7
E)4
Rationale: Let CP of an article = RS. 100
MP= Rs. 120
Discount = 20%
SP = M[(100 - d%)/100] = 120(80/100) = Rs. 96
Clearly, the trader gets 4% loss.
Answer: E
Answer: E
Question: A survey was sent to 80 customers, 7 of whom responded. Then the survey was redesigned and sent to another 63 customers, 9 of whom responded. By approximately what percent did the response rate increase from the original survey to the redesigned survey?
Options:
A)2%
B)5%
C)14%
D)28%
E)63%
Rationale: case 1: (7/80)=x/100
x=9%
case 2: (9/63)=y/100
y=14%
So percent increase is =(y-x)=(14-9)%=5%
Answer is B
Answer: B
Question: How many multiples of 5 are there between 5 to 85?
Options:
A)15
B)18
C)17
D)none of these
E)Cannot be determined
Rationale: Explanation :
As you know, multiples of 5 are integers having 0 or 5 in the digit to the extreme right (i.e. the units place).
So the numbers are 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80.
Answer : A
Answer: A
Question: Divide 71 into 2 parts such that 1 part exceeds the other by 8. What are the 2 no.'s in that part?
Options:
A)26
B)30
C)31
D)34
E)35
Rationale: Let $let n$ be the smaller and 71 - n be the larger number. Now, since the larger number exceeds the smaller number by 7, we can form the equation
larger number – smaller number = 7
which is equivalent to
Simplifying, we have 71 - 2n = 7. This gives us 2n = 78 which implies that the larger number is . The smaller is 71-39=31.
C
Answer: C
Question: A can do a work in 15 days and B in 20 days. If they work on it together for 5 days, then the fraction of the work that is left is
Options:
A)8/17
B)7/15
C)3/15
D)5/12
E)1/4
Rationale: Person ( A ) ( B ) ( A+B )
Time - ( 15 ) ( 20 ) (-)
Rate - ( 20 ) ( 15 ) ( 35 )
Work -(300) (300) (300)
therefore A+B requires (300/35) days to complete entire work
For 1st 5 days they work 35 * 5 = 175
Remaining work is 300 - 175 = 125
Remaining fraction of work is = 125/300 = 5/12
Answer D
Answer: D
Question: What is the value of 3x^2 − 1.8x + 0.8 for x = 0.6?
Options:
A)−0.3
B)0.8
C)0.3
D)1.08
E)2.46
Rationale: 3x^2-1.8x+0.8 for x=0.6
=3(0.6*0.6)-3*0.6*(0.6)+0.8
=0+0.8
=0.8
ANSWER:B
Answer: B
Question: John purchased some shirts and trousers for $700. He paid $400 less for the shirts than he did for the trousers. If he bought 5 shirts and the cost of a shirt is $20 less than that of a trouser, how many trousers did he buy?
Options:
A)4
B)5
C)6
D)7
E)11
Rationale: Given that the total purchase of two items cost 700.
So the average purchase of one item will cost 700/2 = 350.
Its given as total shirt cost 400$ less. Hence Total Shirt cost = 350 - 50 and Total trouser cost = 350 + 50
5 shirts = 150$ ==> One shirt = 30$
One trouser = 30 + 20 = 50$
Total trousers = 550 / 50 = 11.
E
Answer: E
Question: The current of a stream at 1 kmph. A motor boat goes 35 km upstream and back to the starting point in 12 hours. The speed of the motor boat in still water is ?
Options:
A)7 kmph
B)6 kmph
C)4 kmph
D)3 kmph
E)2 kmph
Rationale: Explanation:
Speed of the stream = 1
Motor boat speed in still water be = x kmph
Down Stream = x + 1 kmph
Up Stream = x - 1 kmph
[35/(x + 1)] + [35/(x - 1)] = 12
x = 6 kmph
Answer: B
Answer: B
Question: In how many ways can 5 letters be posted in 3 post boxes, if any number of letters can be posted in all of the three post boxes?
Options:
A)5 C 3
B)5 P 3
C)5(3)
D)3(5)
E)2(5)
Rationale: Explanatory Answer
Sampling with replacement
The first letter can be posted in any of the 3 post boxes. Therefore, we have 3 possibilities.
Similarly, the second, the third, the fourth and the fifth letter can each be posted in any of the 3 post boxes.
Each of the 5 letters has 3 possibilities because we can post any number of letters in all of the boxes.
Therefore, the total number of ways the 5 letters can be posted in 3 boxes is 3 * 3 * 3 * 3 * 3 = 3(5)
Choice D
Answer: D
Question: -84x29+365=?
Options:
A)2436
B)2801
C)-2801
D)-2071
E)None of them
Rationale: Given exp.=-84x(30-1)+365
=-(84x30)+84+365
=-2520+449
=-2071
Answer is D
Answer: D
Question: In a certain mathematical activity, we start with seven cards, each with a different prime number written on it. These seven cards are randomly put into three boxes in the following way: one box must get four cards, one must get two, and one gets only one. Then, for each box, we find the product of all the cards in the box, and that’s the “number” of the box. Then, we put those three numbers in order, from lowest to highest, and that is our set. How many different sets R can be created from this process?
Options:
A) 35
B) 105
C) 210
D) 420
E) 630
Rationale: R=7C4 * 3C2 = 105 Answer B.
7C4 ways to choose 4 numbers for Box 1
3C2 ways to choose 2 numbers for Box2
1 way for Box 3 .
every combination will give a different product and can be arranged least to highest only in one way .B
Answer: B
Question: 48 gallon solution of salt and water is 10% salt. How many gallons of water must be added to the solution in order to decrease the salt to 8% of the volume?
Options:
A)8
B)12
C)13
D)14
E)16
Rationale: Amount of salt = 4.8
Assume x gallons of water are added.
4.8 / 48 + x = 8/100
480 = 8x + 384
8x = 96
x = 12
Correct Option: B
Answer: B
Question: Gauri went to the stationers and bought things worth Rs. 25, out of which 30 paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?
Options:
A)15
B)15.7
C)19.7
D)19.2
E)18
Rationale: Let the amount taxable purchases be Rs. x.
Then, 6% of x =30/100
x =(	(30/100)x(100/6) )= 5.
Cost of tax free items = Rs. [25 - (5 + 0.30)] = Rs. 19.70
ANSWER C
Answer: C
Question: The triplicate ratio of 1:9 is?
Options:
A)1:0
B)1:8
C)1:7
D)1:2
E)1:729
Rationale: 13: 93 = 1:729
Answer: E
Answer: E
Question: If a and b are positive real numbers, and a^3 + b^3 = 20, then the greatest possible value of a is between:
Options:
A)0 and 3
B)3 and 4
C)4 and 5
D)5 and 7
E)7 and 9
Rationale: If a > 3, then a^3 + b^3 > 20.
The answer is A.
Answer: A
Question: In how many ways can 5 letters be posted in 3 post boxes, if any number of letters can be posted in all of the three post boxes?
Options:
A)3
B)9
C)35
D)25
E)215
Rationale: The first letter can be posted in any of the 3 post boxes. Therefore, we have 3 possibilities.
Similarly, the second, the third, the fourth and the fifth letter can each be posted in any of the 3 post boxes.
Each of the 5 letters has 3 possibilities because we can post any number of letters in all of the boxes.
Therefore, the total number of ways the 5 letters can be posted in 3 boxes is
3 * 3 * 3 * 3 * 3 = 35
Option C
Answer: C
Question: In a class, there are 21 boys who are over 160 cm tall. If these constitute three-fourths of the boys and the total number of boys is two-thirds of the total number of students in the class, what is the number of girls in the class ?
Options:
A)8
B)14
C)18
D)24
E)26
Rationale: Explanation:
Let the number of boys be x. Then, (3/4)x = 21 or x = 21 x(4/3) = 28.
If total number of students is y, then (2/3) y = 28 or y = 28 x (3/2) = 42.
Therefore Number of girls in the class = (42 - 28) = 14.
Answer: B
Answer: B
Question: How many 3 digit positive integers E exist that when divided by 7 leave a remainder of 5?
Options:
A)128
B)142
C)143
D)141
E)129
Rationale: Minimum three digit number is 100 and maximum three digit number is 999.
The first three digit number that leaves remainder 5 when divided by 7 is 103.
14 * 7 = 98 +5 = 103
The second three digit number that leaves remainder 5 when divided by 7 is 110.
15 * 7 = 105 +5 =110
The third three digit number that leaves remainder 5 when divided by 7 is 117
and so on
The last three digit number that leaves remainder 5 when divided by 7 is 999
142 * 7 = 994 + 5 = 999
Therefore, we identify the sequence
103,110,117.....999
use the formula of last term
Last term = first term + (n - 1) * common difference
you will get the answer 129 that is definitely E.
Answer: E
Question: On a wedding catering service, An experienced chef can prepare a service for a wedding in 6 hours while an novice chef would finish the preparations in 7 hours.
If the catering service employs the same number of novice and experienced chefs, then how many chefs would it take to prepare a wedding service in 1 hour and 36 minutes?
Options:
A)2
B)3
C)4
D)6
E)8
Rationale: Experienced chefs work = 1 wedding/6 hours
Novice chefs work = 1 wedding/7 hours
Since we don't know the number of experienced or novice chefs but know that there is an equal number each, let the number of chefs for each group equalx
1hr and 36mins = 8/5 an hour
x/6 + x/7 = 1 wedding / (8/5)
x/6 + x/7 = 5/8
x=2
So there are 2 novice chefs and 2 experienced chefs. In total there are 4. The answer is C.
Answer: C
Question: If (x+3)^2/(2x+15)=3, then the difference between the two possible values of x is:
Options:
A)8
B)10
C)12
D)14
E)16
Rationale: (x+3)^2/(2x+15)=3
(x+3)^2=3(2x+15)
x^2+6x+9=6x+45
x^2-36=0
(x-6)(x+6)=0
x=6 or x=-6
The answer is C.
Answer: C