divelab/Sys2Bench huggingface dataset:
Question: In a kilometer race, A beats B by 50 meters or 10 seconds. What time does A take to complete the race?
Options:
A)190 sec
B)120 sec
C)130 sec
D)210 sec
E)220 sec
Rationale: A
190 sec
Time taken by B run 1000 meters = (1000 * 10)/50 = 200 sec.
Time taken by A = 200 - 10 = 190 sec.
Answer: A
Question: A cycle is bought for Rs.900 and sold for Rs.1080, find the gain percent?
Options:
A)28%
B)20%
C)29%
D)27%
E)10%
Rationale: 900 ---- 180
100 ---- ? => 20%
Answer:B
Answer: B
Question: A certain university will select 1 of 4 candidates eligible to fill a position in the mathematics department and 2 of 7 candidates eligible to fill 2 identical positions in the computer science department. If none of the candidates is eligible for a position in both departments, how many different sets of 3 candidates are there to fill the 3 positions?
Options:
A)81
B)82
C)84
D)86
E)88
Rationale: 1C4*2C7 = 4*21 = 84
the answer is (C)
Answer: C
Question: Two pipes A and B can fill a cistern in 37 minutes and 45 minutes respectively. Both pipes are opened. The cistern will be filled in just half an hour, if the B is turned off after:
Options:
A)9
B)7
C)6
D)5
E)4
Rationale: Let B be turned off after x minutes. Then, Part filled by (A + B) in x min. + Part filled by A in (30 -x) min. = 1. x(2/75 + 1/45) + (30 - x). 2/75 = 1 11x/225 + (60 - 2x)/75 = 1 11x + 180 - 6x = 225. x = 9.
Answer:A
Answer: A
Question: If e is an even integer and q is an odd integer, which of the following must be an odd integer?
Options:
A)e/q
B)eq
C)2e+q
D)2(e+q)
E)3e/q
Rationale: this is a must question:
A. e/q
can be a non-integer
B. eq
always even
C. 2e+q
e = even -> even+odd = odd
D. 2(e+q)
always even - e+q = odd *2 -> even
E. e/q
might be a non integer.
C
Answer: C
Question: Of the 90 people in a room, 2/5 are women. If 2/3 of the people are married, what is the maximum number of women in the room who could be unmarried?
Options:
A)26
B)30
C)32
D)34
E)36
Rationale: women = 2/5 * 90 = 36
married = 2/3 * 90 = 60
unmarried = 30
max(un-married women) = 30
B
Answer: B
Question: Matt buys a roses for his wife for rs.64.99 and then they get into a fight, so he decides to sell them for rs.74.99. Find his gain %.
Options:
A)17.92%
B)12.46%
C)2%
D)15.39%
E)16.88%
Rationale: sol. cp=rs64.99, sp=rs 74.99
gain=rs(74.99 –64.99)=rs10.00
so gain%={(10.00/64.99)*100}=15.39%
Answer is D.
Answer: D
Question: How many five-digit numbers are there, if the two leftmost digits are even, the other digits are odd and the digit 8 cannot appear more than once in the number.
Options:
A)2200
B)2290
C)2280
D)2300
E)2375
Rationale: N=(4*5-1)*5*5*5=2375
where
4 cases of first digit {2,4,6,8}
5 cases of second digit {0,2,4,6,8}
1 case of 88 for two leftmost digit
5 cases of third digit {1,3,5,7,9}
5 cases of fourth digit {1,3,5,7,9}
5 cases of fifth digit {1,3,5,7,9}
E
Answer: E
Question: In a graduating class of 232 students, 144 took geometry and 119 took biology. What is the difference between the greatest possible number I and the smallest possible number of students that could have taken both geometry and biology?
Options:
A)144
B)119
C)113
D)88
E)31
Rationale: OFFICIAL SOLUTION:
First of all, notice that since 144 took geometry and 119 took biology, then the number of students who took both geometry and biology cannot be greater than 119.
{Total} = {geometry} + {biology} - {both} + {neither};
232 = 144 + 119 - {both} + {neither};
{both} = 31 + {neither}.
{both} is minimized when {neither} is 0. In this case {both} = 31.
The greatest possible number I of students that could have taken both geometry and biology, is 119.
Thus, the answer is 119 - 31 = 88.
Answer: D.
Answer: D
Question: Dhoni is 25 years older than his daughter Mary. In 10 years Ross will be twice as old as Mary. What is Mary current age.
Options:
A)14
B)16
C)17
D)18
E)15
Rationale: Now: Mary = x, Dhoni =x+25
In 10 years Mary = x+10, Dhoni= x+25+10 or 2(x+10)
x+25+10 = 2(x+10)
x+35=2x+20
35-20=2x-x
15=x
Mary is 15 years old
Answer : E
Answer: E
Question: The mean of 50 observations was 36. It was found later that an observation 90 was wrongly taken as 23. The corrected new mean is?
Options:
A)37.3
B)36.1
C)36.5
D)36.9
E)36.3
Rationale: Correct sum
= (36 * 50 + 90 - 23)
= 1867.
Correct mean = 1825/50
= 37.3
Answer:A
Answer: A
Question: 80 white and black tiles will be used to form a 10x10 square pattern. If there must be at least one black tile in every row and at least one white tile in every column, what is the maximum difference between the number of black and white tiles that can be used?
Options:
A)75
B)80
C)85
D)90
E)60
Rationale: Answer = E
Please refer diagram below
70 - 10 = 60
Answer: E
Question: An object thrown directly upward is at a height of h feet after t seconds, where h = -14 (t-3)^2 + 140. At what height, in feet, is the object 2 seconds after it reaches its maximum height?
Options:
A)62
B)68
C)76
D)84
E)96
Rationale: We see that h will be a maximum h=140 when t-3=0, that is when t=3.
At t=5, h = -14(5-3)^2 + 140 = -14(4) + 140 = 84
The answer is D.
Answer: D
Question: A policeman noticed a criminal from a distance of 180 km. The criminal starts running and the policeman chases him. The criminal and the policeman run at the rate of 8 km and 10 km per hour respectively. What is the distance between them after 3 minutes ?
Options:
A)100 m
B)80 m
C)130 m
D)150 m
E)None of these
Rationale: Explanation :
Solution: Relative speed = (10 - 8) = 2 km/hr.
Distance covered in 3 minutes = (2 * 3/60) km = 1/10 km = 100 m.
.'. Distance between the criminal and policeman = (180 - 100) m = 80 m.
Answer : B
Answer: B
Question: A transport company’s 120 buses running 20 hrs a day consume 360 of fuel in a day. In the next 3 days, the company will invest in 30 more green buses that use 30% less fuel. How many lts of fuel will be consumed in a five day week after the new buses are added to the fleet?
Options:
A)3,060
B)1, 512
C)1,800
D)1,260
E)3,312
Rationale: old buses use 360* 5 days = 1,800 lts
New buses use (0.70* 360)/120* 5 days * 30 buses = 1,512 lts
Total fuel is 3,312 lts
Answer is E
Answer: E
Question: The cross-section of a cannel is a trapezium in shape. If the cannel is 10 m wide at the top and 6 m wide at the bottom and the area of cross-section is 640 sq m, the depth of cannel is?
Options:
A)22
B)28
C)27
D)80
E)21
Rationale: 1/2 * d (10 + 6) = 640
d = 80
Answer:D
Answer: D
Question: Evaluate 28% of 450 + 45% of 280
Options:
A)232
B)242
C)252
D)262
E)272
Rationale: Explanation:
= (28/100) * 450 + (45/100) * 280
= 126 + 126 = 252
Option C
Answer: C
Question: If the mean of a, b, c is M and ab + bc + ca = 0, then the mean of a2, b2, c2 is:
Options:
A)M2
B)3M2
C)6M2
D)9M2
E)None of these
Rationale: Explanation :
We have : (a + b + c)/3 = M or (a + b + c) = 3M.
Now, (a + b + c)*(a + b + c) = (3M)^2 = 9M^2
a2 + b2 + c2 + 2 (ab + bc + ca) = 9M^2
a2 + b2 + c2 = 9M^2
Required mean = (a2 + b2 + c2)/3 = 9M^2/3 = 3M2
Answer : B
Answer: B
Question: Two boats are heading towards each other at constant speeds of 5 miles/hr and 25 miles/hr respectively. They begin at a distance 20 miles from each other. How far are they (in miles) one minute before they collide ?
Options:
A)1/12
B)5/12
C)1/6
D)1/2
E)1/5
Rationale: The question asks: how far apart will they be 1 minute=1/60 hours before they collide?
Since the combined rate of the boats is 5+25=30 mph then 1/60 hours before they collide they'll be rate*time=distance --> 30*1/60=1/2 miles apart.
Answer: D.
Answer: D
Question: The average weight of 8 person's increases by 2.5 kg when a new person comes in place of one of them weighing 35 kg. What is the weight of the new person?
Options:
A)75
B)65
C)55
D)95
E)80
Rationale: Total increase in weight = 8 × 2.5 = 20
If x is the weight of the new person, total increase in weight = x−35
=> 20 = x - 35
=> x = 20 + 35= 55
Answer is C.
Answer: C
Question: The number of arrangements that can be made with the letters of the word MAETHS so that the word starts with M and ends with S
Options:
A)A)2!
B)B)3!
C)C)4!
D)D)6!
E)E)7!
Rationale: M _ _ _ _ S
the remaining 4 places can be filled by 4!
C
Answer: C
Question: Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?
Options:
A)210
B)1050
C)25200
D)21400
E)None
Rationale: Solution
Number of ways of selecting (3 consonants out of 7) and (2 vowels out of 4)
7C3x 4C2 = ( 7x 6x5/3x2x1x 4x 3/2x1 ) = 210
Number of group,each having 3 consonants and 2 vowels = 201 .
Each group contains 5 letter.
Number of ways of arranging 5 letters among themselves
= 5 ! = (5 × 4 × 3 × 2 × 1) = 120 .
So, Required number of words = (210 × 120) = 25200 .
Answer C
Answer: C
Question: In how many ways can a cricket eleven be chosen out of a batch of 15 players.
Options:
A)1523
B)1365
C)1234
D)4512
E)1234
Rationale: Required number of ways
= 15C 11 = 15C (15-11)
= 15 C 4
15C4 = 15 * 14 * 13 * 12 / 4 * 3 * 2 *1
= 1365
Ans: B
Answer: B
Question: At what price must an article costing Rs.47.50 be marked in order that after deducting 5% from the list price. It may be sold at a profit of 25% on the cost price?
Options:
A)62.5
B)62.9
C)62.6
D)62.1
E)22.4
Rationale: CP = 47.50
SP = 47.50*(125/100) = 59.375
MP*(95/100) = 59.375
MP = 62.5
Answer: A
Answer: A
Question: The greatest number of four digits which is divisible by 18,27,54 and 72 is:
Options:
A)9300
B)9480
C)9600
D)9860
E)9936
Rationale: Greatest number of 4-digits is 9999.
L.C.M. of 18, 27, 54 and 72 is 216.
On dividing 9999 by 216, the remainder is 63.
Required number (9999 - 63) = 9936.
Answer: Option E
Answer: E
Question: Jill is dividing her six-person class into two teams of equal size for a basketball game. If no one will sit out, how many different match-ups between the two teams are possible?
Options:
A)10
B)25
C)126
D)252
E)630
Rationale: With 6 players, the process of figuring out how many groups of 3 can be formed is pretty straight-forward....
6C3 = 6!/(3!3!) = 20 possible groups of 3
Once forming that first group of 3, the remaining 3 players would all be placed on the second team by default.
The 'twist' is that the two teams of 3 canshow upin either order:
A
Answer: A
Question: The compound interest on a sum of money for 2 years is rs.832 and the simple interest on the same sum for the same period is rs.800 .the difference between the compound interest and simple interest for 3 years
Options:
A)98.5
B)08.56
C)98.56
D)98.86
E)98.46
Rationale: Explanation:
difference in C.I and S.I in 2years =Rs.32
S.I for 1year =Rs.400
S.I for Rs.400 for one year =Rs.32
rate=[100*32)/(400*1)%=8%
difference between in C.I and S.I for 3rd year
=S.I on Rs.832= Rs.(832*8*1)/100=Rs.66.56
Answer: C) Rs.98.56
Answer: C
Question: If 5% more is gained by selling an article for Rs. 220 than by selling it for Rs. 160, the cost of the article is?
Options:
A)127
B)1200
C)1600
D)1400
E)1202
Rationale: Let C.P. be Rs. x.
Then, 5% of x = 220 - 160= 60
x/20 = 60 => x = 1200
Answer: B
Answer: B
Question: A train running at the speed of 72 km/hr crosses a pole in 9 sec. What is the length of the train?
Options:
A)288
B)279
C)277
D)272
E)180
Rationale: Speed = 72 * 5/18 = 20 m/sec
Length of the train = speed * time = 20 * 9
= 180 m
Answer: E
Answer: E
Question: Ram paid a sum of money for purchasing 25 pens, which he recovered in full when he sold 10 of them. What was his percentage of profit or loss per pen?
Options:
A)80%
B)125%
C)100%
D)70%
E)90%
Rationale: B
125%
If the sum he paid whilst purchasing 25 pens = A,
Then the Cost Price of each pen = A/25.
Since the amount he got whilst selling 10 pens is also = A
Then the Selling Price of each pen = A/10.
Since Selling Price > Cost Price, he made a profit.
Profit per pen = Selling Price - Cost Price = A/10 - A/25 = 3A/50.
Profit percentage per pen = Profit per pen / Cost per pen x 100 = (3A/60) / (A/25) x 100 = 125%. Answer :B
Answer: B
Question: In a group of hats consisting of only blue hats, green hats, and purple hats, the ratio of blue hats to green hats to purple hats is 7:4:12. If there are a total of 46 hats in this group, how many of these hats are not blue?
Options:
A)28
B)42
C)48
D)32
E)76
Rationale: Since the hats Blue, Green and Purple are in ratio of 7:4:12...The total no. of balls will be
7x+4x+12x=46 or 23x=46...here 7x,4x and 12x represent hats of each type
23x=46 so x=2...Blue hats =7*2=14...Not blue will be 46-14=32.
Ans D
Answer: D
Question: The 8 spokes of a custom circular bicycle wheel radiate from the central axle of the wheel and are arranged such that the sectors formed by adjacent spokes all have different central angles, which constitute an arithmetic series of numbers (that is, the difference between any angle and the next largest angle is constant). If the largest sector so formed has a central angle of 80°, what fraction of the wheel’s area is represented by the second smallest sector?
Options:
A)1/72
B)1/36
C)1/18
D)1/12
E)1/9
Rationale: Its an AP question .... it is given clearly in the question .
Let the smallest angle be a
and the circle has 8 sectors and hence 8 angle with a common difference d
hence all the angles can be written in AP form with Cd as d ,
a, a+d, a+2d, a+3d ,a+4d, a+5d, a+6d ,a+7d,
given that a+7d = 80 --------1
also
a + a+d + a+2d + a+3d +
a+4d + a+5d + a+6d + a+7d = 360 ( as sum of all the angle is 360)
which is 8a + 28d = 360 --------2
solving 1 and 2
we get a=10
We are almost done ,
now the question ask what fraction of the wheel’s area is represented by the smallest sector ?
(20/360)( pie r*r)/ (pie r*r) = 20/360= 1/18
C ans ....
Answer: C
Question: A student worked for 20 days. For each of the amounts shown in the first row of the table, the second row gives the number of days that the student earned that amount. What is the total amount of money that the students earned for the 16 days?
Amounts earned per day : $96 $84 $80 $70 $48
Number of days : 4 7 4 3 2
Options:
A)(1) $320
B)(2) $210
C)(3) $284
D)(4) $282
E)(5) $196
Rationale: 4+7+4+3+2 = 20
The series is as follows. Arrange the terms in increasing order of amounts earned and cumulatively add up the number of days of each amount.
1st to 2nd term = 48 (2 days)
3rd to 5th term = 70 (3 days)
6th to 9th term = 80 (4 days)
10th to 16th term = 84 (7 days)
total amount earned = 48+70+80+84
= 282
Pick D
Answer: D
Question: Of the female students at Barkely University, 5/6 are on the honor roll. Of the male students, 2/3 are on the honor roll. If 2/5 of the students are female, what fraction of all the students are on the honor roll?
Options:
A)5/9
B)3/15
C)23/30
D)22/30
E)53/90
Rationale: let the total students be 30
given 2/5 of the students are females = 12
then males = 3/5 = 18
5/6 of the females are on honor roll = 10
males on the honor roll = 2/3= 12
total students on honor roll = 12+10 =22
fraction = 22/30
D
Answer: D
Question: A man in a train notices that he can count 51 telephone posts in one minute. If they are known to be 100 metres apart, then at what speed is the train travelling?
Options:
A)250km/hr
B)150km/hr
C)225km/hr
D)300km/hr
E)315km/hr
Rationale: Number of gaps between 51 telephone posts = 50
distance travelled in 1 minute = 100*50 = 5000m = 5km
speed = 300km/hr
Answer is D
Answer: D
Question: The average of 13 numbers is 60. Average of the first 7 of them is 57 and that of the last 7 is 61. Find the 8th number?
Options:
A)46
B)77
C)88
D)544
E)33
Rationale: Sum of all the 13 numbers = 13 * 60 = 780
Sum of the first 7 of them = 7 * 57 = 399
Sum of the last 7 of them = 7 * 61 = 427
So, the 8th number = 427 + 399 - 780 = 46.
Answer: A
Answer: A
Question: Linda and Angela contract to paint a neighbor's house. Even though Linda
spends 25% more time painting the house than Angela, each receives a payment
of m dollars when the work is completed. If Angela decides to pay Linda n
dollars so that they would have received the same compensation per hour
worked, what is n in terms of m?
Options:
A)A)(1/2)m
B)B)(1/9)m
C)C)(1/4)m
D)D)(1/5)m
E)E)(1/6)m
Rationale: let angela work for 8hrs and get 900 rs. (m =900)
According to question, linda works 25% more time and gets the same amount. so let linda work 10 hrs and get 900 rs.
so they do a total of 10 +8 =18 hrs of work and get 1800 rs together . The question basically asks to equalise their payment. so a total of 1800 rs is received by them and they do 18 hrs work together. average rate will be 1800/18 = 100 rs per hr. so linda should get 10*100 =1000 rs. But she got only 900. so angela should give 100 rs to linda. answer = 100/900 =1/9
answer B
Answer: B
Question: A tank has 5 inlet pipes. Three pipes are narrow and two are wide. Each of the three narrow pipes works at 1/2 the rate of each of the wide pipes. All the pipes working together will take what fraction Q of time taken by the two wide pipes working together to fill the tank?
Options:
A) 1/2
B) 2/3
C) 3/4
D) 3/7
E) 4/7
Rationale: I always plug in for these questions.. I find them easier
Let 2 large pipes each work fill 10lts/hr
small ones = 1/2*10 = 5
total 5 = 10+10+5+5+5 = 35 lts/hrs
now assume the total capacity = 140 lts ( LCM of 20,35)
Qn :All the pipes working together will take what fraction of time taken by the two wide pipes working together to fill the tank
all working together will take 140/35 = 4 hrs
two large pipes working will take 140/20 = 7 hrs
hence ratio Q= 4/7 = E
Answer: E
Question: A certain company that sells only cars and trucks reported that revenues from car sales in 1997 were down 11 percent from 1996 and revenues from truck sales were up 7 percent from 1996. If total revenues from car sales and truck sales in 1997 were up 1 percent from 1996, what is the ratio W of revenue from car sales in 1996 to revenue from truck sales in 1996?
Options:
A) 1:2
B) 4:5
C) 1:1
D) 3:2
E) 5:3
Rationale: A.. I have probably solved this question 3-4 times by now.. Remember the answer.. 1:2
Answer: A
Question: On Thursday Mabel handled 90 transactions. Anthony handled 10% more transactions than Mabel, Cal handled 2/3rds of the transactions that Anthony handled, and Jade handled 16 more transactions than Cal. How much transactions did Jade handled?
Options:
A)56
B)35
C)82
D)89
E)90
Rationale: C
82
Mabel handled 90 transactions
Anthony handled 10% more transactions than Mabel
Anthony = 90 + 90 × 10%
= 90 + 90 × 0.10
= 90 + 9
= 99
Cal handled 2/3rds of the transactions than Anthony handled
Cal = 2/3 × 99
= 66
Jade handled 16 more transactions than Cal.
Jade = 66 + 16
= 82
Jade handled = 82 transactions.
Answer: C
Question: Three number are in the ratio of 3 : 4 : 5 and their L.C.M. is 1500. What is their H.C.F.?
Options:
A)5
B)15
C)25
D)35
E)45
Rationale: Let the numbers be 3x, 4x and 5x.
Then, their L.C.M. = 60x
60x = 1500
x = 25
The numbers are (3 x 25), (4 x 25) and (5 x 25).
The H.C.F. is 25.
The answer is C.
Answer: C
Question: (1000)7÷(10)15=?
Options:
A)10
B)100
C)1000000
D)10000
E)None of these
Rationale: Explanation:
=(103)7/(10)15
=(10)21/(10)15=10(6)=1000000
Option C
Answer: C
Question: If e > a and L < a, which of the following cannot be true?
Options:
A) d + L = 14
B) d - L = 7
C) d - L = 1
D) a - e = 9
E) a + d = 9
Rationale: Is the answer D?
If e>a, then e-a>0 (always positive). The converse would be a-e<0 (always negative). Option D states that a-e=9, which can never be true.
Answer: D
Question: A bag contains a certain number of 50 paise coins, 20 paise coins and 10 paise coins inthe ratio 2:3:4. If the total value of all the coins in the bag is Rs.400, find the number of coins of each kind?
Options:
A)50p coins = 400 20p coins = 600 10p coins = 800
B)50p coins = 300 20p coins = 700 10p coins = 200
C)50p coins = 800 20p coins = 400 10p coins = 200
D)50p coins = 400 20p coins = 500 10p coins = 300
E)60p coins = 500 20p coins = 400 10p coins = 300
Rationale: 50*2k + 20*3k + 10*4k = 40000
200k = 40000 => k = 200
50p coins = 2k = 2*200 = 400
20p coins = 3k = 3*200 = 600
10p coins = 4k = 4*200 = 800
Answer:A
Answer: A
Question: The difference between a number and its two-fifth is 510. What is 10% of that number?
Options:
A)12.75
B)85
C)204
D)250
E)None of these
Rationale: Explanation:
Let the number be x. Then,
x - 2/5 x = 510
x = (510 * 5)/3 = 850
10% of 850 = 85.
Answer IS B
Answer: B
Question: If e + xy = e and x is not equal to 0, which of the following must be true?
Options:
A)x<y
B)x+y=0
C)x=e
D)x=0
E)y=0
Rationale: e + xy = e --> xy=0. Since x is not equal to 0, thus y = 0.
Answer: E.
Answer: E
Question: The probability that event A occurs is 0.4, and the probability that events A and B both occur is 0.25. If the probability that either event A or event B occurs is 0.8, what is the probability that event B will occur?
Options:
A)0.05
B)0.15
C)0.45
D)0.5
E)0.65
Rationale: P(A or B) = P (A) + P(B) - p(a n b)
0.8= 0.4 + P(B) - 0.25
P(B) = 0.65
Ans : E
Answer: E
Question: Tanks A and B are each in the shape of a right circular cylinder. The interior of tank A has a height of 8 meters and a circumference of 8 meters, and the interior of tank B has a height of 8 meters and a circumference of 10 meters. The capacity of tank A is what percent of the capacity of tank B?
Options:
A)64%
B)80%
C)100%
D)120%
E)125%
Rationale: For A, r=8/2pi. Its capacity = (4pi)^2 * 8= 128pi
For B, r=10/pi. Its capacity = (5pi)^2 *8 = 200pi
A/B = 128pi/200pi = 0.64
A
Answer: A
Question: The difference between a 6 digit number and the number formed by reversing its digit is not a multiple of
Options:
A)3
B)92439
C)30813
D)10271
E)10272
Rationale: Another approach is to TEST a number.
Let's say the original number is 123004
So, the REVERSED number is 400321
The DIFFERENCE = 400321-123004
No check the answer choices
277317 is a multiple of 3,92439,30813,10271
10272 is NOT a multiple of 277317
Answer:E
Answer: E
Question: In a recent election, James received 0.5 percent of the 2,000 votes cast. To win the election, a candidate needed to receive more than 45 percent of the vote. How many additional votes would James have needed to win the election?
Options:
A)901
B)989
C)990
D)891
E)1,001
Rationale: James = (0.5/100)*2000 = 10
Votes to win = (45/100)*Total Votes +1 = (45/100)*2000 +1 = 901
Remaining Voted needed to win election = 901 - 10 = 891
Answer: option D
Answer: D
Question: A freight elevator can carry a maximum load of 1300 pounds. Sean, who weighs 200 pounds, is in the elevator with two packages weighing 150 pounds and 280 pounds. If he needs to fit three more packages in the elevator that weigh as much as possible without exceeding the elevator limit, what is the difference between their average and the average of the two packages already in the elevator?
Options:
A)8
B)85
C)190
D)215
E)210
Rationale: The average of existing 2 package is150 + 280/2 = 430/2 = 215
Remaining allowed weight = 1300 - 200 - 430 = 670.
allowed per package = 670 / 3 =223
So difference in average of existing and allowable = 223-215 = 8
Hence A
Answer: A
Question: Two teams are distributing information booklets. Team A distributes 60% more boxes of booklets than Team W, but each box of Team A’s has 60% fewer booklets than each box of Team W’s. Which of the following could be the total number of booklets distributed by the two groups?
Options:
A)2,000
B)3,200
C)4,100
D)4,800
E)4,900
Rationale: Let x be the no of booklets in each box that team W distributes. So, Team A has 60% fewer - 0.4x.
Let y be the no. of boxes distributed by team W. So, Team A distributes 60% more - 1.6y
Total booklets distributed by team A = xy
Total booklets distributed by teamW=0.64xy
Total booklets distributed = xy+0.64xy=1.64xy
As no. of booklets can only be integer, plugging the answer choice equal to 1.64xy should give an integer.
Choice A - 1.64xy=2000; xy=2000/1.64 = doesn't provide an integer value.
Similarly all answer choices, except choice C, fail to provide an integer value.
Choice C = 4100/1.64= 2500 and is the correct answer.
Answer: C
Question: Wn = 2Wn-1 + 4 and Qn = 4Qn-1 + 8 for all n > 1. If W5 = Q4 and W7 = 316, what is the first value of n for which Qn is an integer?
Options:
A) 1
B) 2
C) 3
D) 4
E) 5
Rationale: Assuming I have understood the symbols used correctly answer is C- 3
W7 = 2S6 +4 = 316
W6 = 312/2 = 156 = 2W5 + 4
W5 = 152/2 = 76 = Q4
Q4 = 4Q3 + 8 = 76
Q3 = 68/4 = 17
Q3 = 4Q2 + 8 = 17
Q2 = 9/4 = 2.25
Q2 = 4Q1 + 8
Q1 will not be integer
Answer: C