divelab/Sys2Bench huggingface dataset:
Question: Anthony and Michael sit on the six member board of directors for company X. If the board is to be split up into 2 three-person subcommittees, what percent Q of all the possible subcommittees that include Michael also include Anthony?
Options:
A) 20%
B) 30%
C) 40%
D) 50%
E) 60%
Rationale: The answer is C. Let's look at a committee where Mike belongs (he's person # 1) on that committee. When we choose person #2, there is a 1/5 probability that it's going to be Anthony (then it doesn't matter who the third person is), and 4/5 probability that it's going to be someone else (then person #3 is going to be Anthony with probability 1/4). Total probability Q= 1/5+4/5*1/4 = 2/5.C
Answer: C
Question: 78 laboratories raise the bacterium, the laboratory have 48 culture dishes on average, which has about 25,075 bacteria each. How many bacteria are there approximately?
Options:
A)10^7
B)10^8
C)10^9
D)10^10
E)10^11
Rationale: 78 laboratories raise the bacterium, the laboratory have 48 culture dishes on average, which has about 25,075 bacteria each. How many bacteria are there approximately?
A. 10^7
B. 10^8
C. 10^9
D. 10^10
E. 10^11
-> Due to approximately, 78=80, 48=50, 25,075=25,000 are derived, which makes (78)(48)(25,075)=(80)(50)(25,000)=10^8. The answer is B.
Answer: B
Question: A, B and C enter into partnership. A invests some money at the beginning, B invests double the amount after 6 months, and C invests thrice the amount after 8 months. If the annual gain be Rs.18900. A's share is?
Options:
A)6300
B)2765
C)6000
D)1298
E)1261
Rationale: x* 12 : 2x* 6: 3x* 4
1:1:1
1/3 * 18900 = 6300
Answer:A
Answer: A
Question: What is the 4 digit no. in which the 1st digit is 1/3 of the second, the 3rd is the sum of the 1st and 2nd, and the last is 3 times the second?
Options:
A)1123
B)1234
C)1349
D)1455
E)1567
Rationale: First digit is 1/3 second digit => The numbers can be 1 & 3, 2& 6, 3 & 9.
First + second = third => we can eliminate 3 & 9 since 3 + 9 = 12.
Last is 3 times the second => we can eliminate option 2 & 6 since 3 * 6 = 18.
Hence the number is 1349
C
Answer: C
Question: $2,000 is deposited in a savings account that pays 4% annual interest compounded semiannually. To the nearest dollar, how much is in the account at the end of the year?
Options:
A)$2125.15
B)$2083.12
C)$2184.22
D)$2150.84
E)$2080.80
Rationale: this is the case of semi-annual compoundingso, multiply time period by 2 and divide rate by 2
So,
new time=2periods and new rate=4/2=2%
Now,
CA=2000(1+2/100)^2=$2080.80
Hence answer is E
Answer: E
Question: Sides of a rectangular park are in the ratio 3: 2 and its area is 3750 sq m, the cost of fencing it at 50 ps per meter is?
Options:
A)287
B)369
C)125
D)279
E)361
Rationale: 3x * 2x = 3750 => x = 25
2(75 + 50) = 250 m
250 * 1/2
= Rs.125
Answer:C
Answer: C
Question: In what time will a train 100 m long cross an electric pole, it its speed be 144 km/hr?
Options:
A)2.5 sec
B)2.6 sec
C)2.7 sec
D)2.8 sec
E)2.9 sec
Rationale: Speed = 144 * 5/18 = 40 m/sec
Time taken = 100/40 = 2.5 sec.
Answer: Option A
Answer: A
Question: What is the probability of flipping a fair coin four times and the coin landing on heads on exactly two flips?
Options:
A)1/6
B)3/4
C)1/3
D)2/5
E)3/8
Rationale: Probability = (Favorable combination)/(Total combination)
Favorable combination = (HHTT, HTHT, HTTH,THHT,THTH,TTHH) ==> 6
Total combination = 16 (2^4)
Probability = (6)/(16) = 3/8
(E)
Answer: E
Question: A bus trip of 360 miles would have taken 1 hour less if the average speed V for the trip had been greater by 5 miles per hour. What was the average speed V, in miles per hour, for the trip?
Options:
A)35
B)40
C)45
D)50
E)55
Rationale: The time is the distance/speed. The time difference is 1 hour.
360/V - 360/(V+5) = 1
360(V+5) - 360V = (V)(V+5)
1800 = (V)(V+5)
40*45 = (V)(V+5)
V = 40 mph
The answer is B.
Answer: B
Question: By selling 10 pencils for a rupee a man loses 15%. How many for a rupee should he sell in order to gain 15%?
Options:
A)8.39
B)6.39
C)7.39
D)9.39
E)2.39
Rationale: 85% --- 10115% --- ?85/115 * 10 = 7.39Answer: C
Answer: C
Question: 4,6,8,10,12,....
Options:
A)58
B)14
C)61
D)62
E)63
Rationale: 2*2=4
3*2=6
4*2=8
5*2=10
6*2=12
7*2=14
ANSWER:B
Answer: B
Question: Johnson has a corporate proposal. The probability that vice-president Adams will approve the proposal is 0.6. If VP Adams approves the proposal, then the probability that vice-president Baker will approve the proposal is 0.2. If VP Adams doesn’t approve the proposal, then the probability that vice-president Baker will approve the proposal is 0.3. What is the probability that at least one of the two VPs, approves Johnson’s proposal?
Options:
A)0.36
B)0.24
C)0.28
D)0.48
E)0.72
Rationale: (1at approves * second rejects ) + (1st rejects * 2nd approves ) + (both approves )
=0.6*0.2+0.4*0.3+0.6*0.2
= 0.12+0.12+0.12
=0.36
A
Answer: A
Question: JOHN and Antony can finish the work 36 days if they work together. They worked together for 24 days and then Antony left. JOHN finished the remaining work in another 24 days. In how many days JOHN alone can finish the work?
Options:
A)30 days
B)72 days
C)70 days
D)80 days
E)90 days
Rationale: Amount of work done by JOHN and Antony in 1 day = 1/36
Amount of work done by JOHN and Antony in 24 days = 24 Ã— (1/36) = 2/3
Remaining work â€“ 1 â€“ 2/3 = 1/3
JOHN completes 1/3 work in 24 days
Amount of work JOHN can do in 1 day = (1/3)/24 = 1/72
=> JOHN can complete the work in 72 days
Answer : B
Answer: B
Question: A cycle is bought for Rs.750 and sold for Rs.1080, find the gain percent?
Options:
A)22
B)44
C)99
D)88
E)11
Rationale: 750 ---- 180
100 ---- ? => 44%
Answer:B
Answer: B
Question: The sum of first four prime numbers is?
Options:
A)17
B)23
C)24
D)28
E)30
Rationale: Required sum = (2 + 3 + 5 + 7) = 17.
Note: 1 is not a prime number.
Definition: A prime number (or a prime) is a natural number that has exactly two distinct natural number divisors: 1 and itself.
A
Answer: A
Question: If x is equal to the sum of the integers from 50 to 60, inclusive, and y is the number of EVEN integers from 50 to 60, inclusive, what is the value of x+y ?
Options:
A)171
B)281
C)391
D)491
E)611
Rationale: sum s= n/2{2a+(n-1)d} = 11/2{2*50+ (11-1)*1} =11*55=605 =X
number of even number =( 60-50)/2 +1 = 6= Y
X+Y = 605+6 =611
E
Answer: E
Question: 3 men and 8 women complete a task in same time as 6 men and 2 women do. How much fraction of work will be finished in same time if 5 men and 2 women will do that task.
Options:
A)6/7
B)3/10
C)3/18
D)3/16
E)3/11
Rationale: 3 m + 8 w = 6 m + 2 w
3 m = 6 w
1 m = 2 w
Therefore 3 m + 8 w = 14 w
5 m +2 w =12 w
Answer is 12/14 =6/7
Answer: A
Answer: A
Question: Micheal and Adam can do together a piece of work in 20 days. After they have worked together for 14 days Micheal stops and Adam completes the remaining work in 10 days. In how many days Micheal complete the work separately.
Options:
A)50 days
B)100 days
C)120 days
D)110 days
E)90 days
Rationale: Rate of both = 1/20
Together they do = 1/20*14 = 7/10
Left work = 1 - 7/10 = 3/10
Adam completes 3/10 work in 10 day
so he took 10*10/3 = 100/3 days to complete the left work alone.
Thus the rate of adam is 3/100
Rate of Micheal = 1/20 - 3/100 = 1/50
Thus micheal takes 50 days to complete the whole work.
ans. A
Answer: A
Question: There were two candidates in an election. Winner candidate received 62% of votes and won the election by 360 votes. Find the number of votes casted to the winning candidate?
Options:
A)456
B)744
C)930
D)1200
E)1400
Rationale: W = 62% L = 38%
62% - 38% = 24%
24% -------- 360
62% -------- ? => 930
ANSWER:C
Answer: C
Question: Alfred buys an old bike for Rs. 4700 and spends Rs. 800 on its repairs. If he sells the bike for Rs. 5800, his gain percent is?
Options:
A)5 5/11%
B)5%
C)5/7%
D)6%
E)6/11%
Rationale: Cost Price (C.P.) = Rs. (4700 + 800) = Rs. 5500.
Selling Price (S.P.) = Rs. 5800.
Gain = (S.P.) - (C.P.) = Rs.(5800 - 5500) = Rs. 300.
Gain % = 300	x 100	%	= 5	5	%
5500	11
A)
Answer: A
Question: Diane find 2 and a half cans of paint are just enough to paint one third of her room. How many more cans of paint will she need to finish her room and paint a second room of the same size?
Options:
A)5
B)7 and a half
C)10
D)12 and a half
E)15
Rationale: We know that 2.5 cans = 25/10 is used to paint 1/3 of a room. We need to find how much paint we'll need in order to paint the rest of the room (1-1/3=2/3) and 1 room more, hence 2/3+1=5/3
25/10 : 1/3 = x : 5/3
(25/10)*(5/3) = (1/3)*x
25/6=x/3
6*x=25*3
x=75/6
x=12.5
ANSWER:D
Answer: D
Question: Two cars, Car1 and Car2 move towards each other from Q and Y respectively with respective speeds of 20 m/s and 15 m/s. After meeting each other Car1 reaches Y in 10 seconds. In how many seconds does Car 2 reach Q starting from Y?
Options:
A)15.5 sec
B)8.4 sec
C)33.6 sec
D)31.11 sec
E)16.8 sec
Rationale: Q--------------------------------------|----------------------------Y
Car A(20mps)------------------------->P<---------------Car B(15mps)
Let 2 cars meet each other at point P in t seconds.
Car1 covers distance= 20t. Car2 covers distance=15t. So, total distance QY= 35t.
From P, Car 1 reaches onto Y in 10 secs. So it covers 15t further.
so, 15t/20 = 10
So t=40/3 sec and total distance = (35*40)/3
Hence Car2 will cover total distance in (35*40)/(3*15) = 31.11 sec approx.
Answer D
Answer: D
Question: If, in a baseball game, a single picher can decide to throw either a 100mph fastball or 60 mph knuckleball on any pitch, how much less time, in seconds, does the batter have from when the ball is released as a fastball than when the ball is released as a knuckle ball? (Assume where the batter's point of contact is exactly 60ft away from the pitcher's release point. 5280 ft = 1 mile.)
Options:
A)6/22s
B)7/22s
C)8/22s
D)9/22s
E)15/22s
Rationale: One conversion to know is = 1 mile = 5280 ft
Time taken for fastball = (60 / (100 * 5280)) * 60 * 60 = 9/22
Time taken for knuckle ball = (60 / (60 * 5280)) * 60 * 60 = 15/22
Qn is the difference between the time taken by the two balls => 15/22 - 9/22 = 6/22
Option A
Answer: A
Question: It takes 8 high school students, working at identical constant individual rates, 10 hours to paint a certain house. At what time will the house be fully painted if 8 students start painting at 9:00 am and one student, working at the same rate, is added per hour starting at 5:00 pm?
Options:
A)6:06 pm
B)6:12 pm
C)6:24 pm
D)6:42 pm
E)6:56 pm
Rationale: Each student paints at a rate of 1/80 of the house per hour.
In 8 hours, the 8 students can paint 64/80 of the house.
From 5 pm to 6 pm, 9 students paint another 9/80 for a total of 73/80.
10 students can paint the remaining 7/80 of the house in 7/10 of an hour = 42 minutes.
The house is completed at 6:42 pm.
The answer is D.
Answer: D
Question: A cylindrical can has a radius of 3 centimeters and a height of 12 centimeters. What is the area, in square centimeters, of a rectangular label that completely covers the curved surface of the can without over-lapping?
Options:
A)16 pi
B)72 pi
C)96 pi
D)192 pi
E)576 pi
Rationale: They are asking the lateral surface area of the cylinder.
the Lateral surface area = 2* pi * r *h
= 2*pi*3*12=72 pi
Answer is B.
Answer: B
Question: What profit percent is made by selling an article at a certain price, if by selling at 1/3rd of that price, there would be a loss of 20%?
Options:
A)140%
B)29%
C)70%
D)27%
E)28%
Rationale: SP2 = 1/3 SP1
CP = 100
SP2 = 80
1/3 SP1 = 80
SP1 = 240
100 --- 240 => 140%
Answer: A
Answer: A
Question: Firm A's revenues are described by the equation Ra = 15.12x and its costs by Ca = 12.87x + 2400.
Firm B's revenues are described by the equation Rb = 13.27x and its costs by Cb = 8.77x + 1500.
(x denotes the quantity of sales).
If A's volume of sales increases from 1000 to 2000 over the same period that B's volume increases from 2000 to 3000, the percent increase in profits for the firm with the biggest dollar increase in profits is
Options:
A)20%
B)30%
C)60%
D)50%
E)33%
Rationale: Ok, I do not know whether it is exactly what you want to hear but I did it that way: first look at difference between revenue and variable cost => take the bigger one (b) which gives you: 4.5x-1500 just plug in 2000 and 3000. you get 7500 and 12000 (difference 4500). 4500> 0.5*7500 so 50%
D
Answer: D
Question: In a graduating class, the difference between the highest and lowest salaries is $100,000. The median salary is $50,000 higher than the lowest salary and the average salary is $20,000 higher than the median. What is the minimum number of students E in the class?
Options:
A)A)10
B)B)12
C)C)15
D)D)20
E)E)25
Rationale: the difference between the highest and lowest salaries is $100,000.
So there are at least 2 people - say one with salary 0 and the other with 100k. No salary will be outside this range.
Median = 50k more than lowest. So median is right in the center of lowest and highest since lowest and highest differ by 100k. In our example, median = 50k. Since there are more than 2 people, there would probably be a person at 50k.
Mean = 20k more than median so in our example, mean salary = 70k
On the number line,
0........50k (median)........100k
Mean = 70k
So there must be people more toward 100k to bring the mean up to 70k. Since we want to add minimum people, we will add people at 100k to quickly make up the right side deficit. 0 and 50k are (70k + 20k) = 90k away from 70k. 100k is 30k away from 70k. To bring the mean to 70k, we will add two people at 100k each to get:
0....50k.....100k, 100k, 100k
But when we add more people to the right of 70k, the median will shift to the right. We need to keep the median at 50k. So every time we add people to the right of 70k, we need to add people at 50k too to balance the median. 50k is 20k less than 70k while 100k is 30k more than 70k. To keep the mean same, we need to add 2 people at 100k for every 3 people we add at 50k. So if we add 3 people at 50k and 2 people at 100k, we get:
0, ... 50k, 50k, 50k, 50k, ... 100k, 100k, 100k, 100k, 100k
the median is not at 50k yet.
Add another 3 people at 50k and another 2 at 100k to get
0, 50k, 50k, 50k, 50k, 50k, 50k, 50k, 100k, 100k, 100k, 100k, 100k, 100k, 100k
Now the median is 50k and mean is 70k.
Total number of people is 15.
Answer (C)
Answer: C
Question: A man can row 8.4 kmph in still water and he finds that it takes him twice as long to row up as to row down the river. Find the rate of stream.
Options:
A)2.8 km/hr
B)12.5 km/hr
C)1 2.6 km/hr
D)22.5 km/hr
E)22.6 km/hr
Rationale: Given that, time taken to travel upstream = 2 × time taken to travel downstream
When distance is constant, speed is inversely proportional to the time
Hence, 2 × speed upstream = speed downstream
Let speed upstream = x
Then speed downstream = 2x
we have, 1/2(x+2x) = speed in still water
⇒1/2(3x)=8.4
3x = 16.8
x = 5.6
i.e., speed upstream = 5.6 km/hr
Rate of stream = 1/2(2x−x)=x/2=5.6/2=2.8 km/hr
Answer is A
Answer: A
Question: A train passes a station platform in 36 sec and a man standing on the platform in 23 sec. If the speed of the train is 54 km/hr. What is the length of the platform?
Options:
A)288
B)195
C)881
D)1277
E)121
Rationale: Speed = 54 * 5/18 = 15 m/sec.
Length of the train = 15 * 23 = 345 m.
Let the length of the platform be x m . Then,
(x + 345)/36 = 15 => x = 195 m.
Answer: B
Answer: B
Question: In a km race, A beats Bby 28 metres or 7 seconds. Find A's timeoverthe course
Options:
A)4 min
B)3 min 3 sec
C)4 min 4 sec
D)5 min 3 sec
E)4 min 3 sec
Rationale: Clearly, B covers 28 m in 7 seconds.
:. B's time over the course = (278 x 1000) sec = 250 seconds.
:. A's time over the course = (250 - 7-) sec = 243 sec
= 4 min. 3 sec.
ANSWER E 4 min 3 sec
Answer: E
Question: What is the units digit of the product of the first 3 primes?
Options:
A)1
B)3
C)6
D)0
E)2
Rationale: 1*2*3 =6
Answer : C
Answer: C
Question: If 5 < x < 9 and y = x + 7, what is the greatest possible integer value of x + y?
Options:
A)21
B)22
C)23
D)24
E)25
Rationale: x+y = x+x+7 = 2x+7
We need to maximize this value and it needs to be an integer.
2x is an integer when the decimal of x is .0 or .5
The largest such value is 8.5
Then x+y = 8.5 + 15.5 = 24.
The answer is D.
Answer: D
Question: The price of lunch for 12 people was $207 including a 15% gratuity for service. What was the average price per person, EXCLUDING the gratuity?
Options:
A)11.73
B)12
C)13.8
D)14
E)15
Rationale: Clearly E is the answer
I used POE here
Lets consider option (E)
12*15= 180 now 180(115/100)=207
=> possible ANSWER IMO E
Answer: E
Question: Three persons invested Rs.9000 in a joint business. The second person invested Rs.1000 more than the first and the third Rs.1000 more than second. After two years, they gained Rs.4500. How much third person will get?
Options:
A)2400
B)2429
C)2980
D)2000
E)2872
Rationale: First persons investment = x
Second persons investment = x + 1000
Third persons investments = x + 2000
x + x + 1000 + x + 2000 = 9000
3x = 6000
x = 2000
Ratio = 2000 : 3000 : 4000
2:3:4
4/9 * 4500 = 2000
Answer:D
Answer: D
Question: A river 3m deep and 32 m wide is flowing at the rate of 2 kmph the amount of water that runs into the sea per minute is?
Options:
A)4500
B)3200
C)3400
D)2761
E)2882
Rationale: (2000 * 3 * 32)/60
= 3200 M3
Answer:B
Answer: B
Question: A batsman scored 140 runs which included 3 boundaries and 8 sixes. What percent of his total score did he make by running between the wickets?
Options:
A)50%
B)40%
C)60%
D)57%
E)80%
Rationale: Number of runs made by running = 140 - (3 x 4 + 8 x 6)
= 140 - (60)
= 80
Now, we need to calculate 80 is what percent of 140.
=> 80/140 x 100 = 57 %
ANSWER:D
Answer: D
Question: In the first 10 overs of a cricket game, the run rate was only 3.2. What should be the rate in the remaining 40 overs to reach the target of 282 runs?
Options:
A)6.25
B)6.28
C)6.11
D)6.19
E)6.21
Rationale: Required run rate
= [282 - (3.2 * 10)]/40
= 250/40
= 6.25
Answer:A
Answer: A
Question: Find the odd man out
1,25, 31,37, 127, 503,
Options:
A)503
B)37
C)31
D)1
E)25
Rationale: 25 is square of 5 which is a square number where as all others are prime numbers.
ANSWER:E
Correct Option:	C) E . Answer : E
Answer: E
Question: A train 600 m long can cross an electric pole in 20 sec and then find the speed of the train?
Options:
A)115 Kmph
B)100 Kmph
C)102 Kmph
D)105 Kmph
E)108 Kmph
Rationale: Length = Speed * time
Speed = L/T
S = 600/20
S = 30 M/Sec
Speed= 30*18/5 (To convert M/Sec in to Kmph multiply by 18/5)
Speed = 108 Kmph
ANSWER:E
Answer: E
Question: A train running at the speed of 60 km/hr crosses a pole in 15 sec. What is the length of the train?
Options:
A)535 m
B)178 m
C)250 m
D)168 m
E)150 m
Rationale: Speed = 60 * 5/18
= 50/3 m/sec
Length of the train
= speed * time
= 50/3 * 15
= 250 m
Answer:C
Answer: C
Question: What will come in place of the x in the following Number series? 46080, 3840, 384, 48, 8, 2, x
Options:
A)1
B)9
C)12
D)14
E)15
Rationale: 46080 /12 = 3840
3840 /10 = 384
384 /8 = 48
48 /6 = 8
8/4 = 2
2 /2 = 1
A
Answer: A
Question: Reena took a loan of $. 1200 with simple interest for as many years as the rate of interest. If she paid $ 432 as interest at the end of the loan period, what was the rate of interest?
Options:
A)3.6
B)6
C)18
D)Cannot be determined
E)None of these
Rationale: Let rate = R% and time = R years.
Then,1200 x R x R/100= 432
12R2 = 432
R2 = 36
R = 6.
Answer:B
Answer: B
Question: What will be the compound interest on Rs. 40000 after 3 years at the rate of 12 % per annum
Options:
A)Rs 16123.20
B)Rs 16123.30
C)Rs 16197.12
D)Rs 16123.50
E)None of these
Rationale: Explanation:
(40000×(1+12/100)3)
=>40000×28/25×28/25×28/25
=>56197.12
So Compound interest will be 56197.12 - 40000
= Rs 16197.12
Option C
Answer: C
Question: Every disk in a bag is either blue, yellow or green. The ratio of blue disks to yellow disks to green disks in this bag is 3 : 7 : 8. If the total number of disks in the bag is 72, how many more green disks than blue disks are in the bag?
Options:
A)20
B)28
C)30
D)35
E)40
Rationale: Let B:Y:G = 3x:7x:8x.
3x + 7x + 8x = 18x = 72 --> x= 4.
G - B = 8x - 3x = 5x = 20.
The answer is A.
Answer: A
Question: How much is 90% of 40 is greater than 4/5 of 25?
Options:
A)22
B)16
C)88
D)12
E)66
Rationale: (90/100) * 40 – (4/5) * 25
= 16
Answer: B
Answer: B
Question: If a two-digit positive integer has its digits reversed, the resulting integer differs from the original by 45. By how much do the two digits differ?
Options:
A) 3
B) 4
C) 5
D) 6
E) 7
Rationale: Given that (10a + b) - (10b + a) = 45 --> 9a - 9b =45 --> a - b = 5.
Answer: C.
Answer: C
Question: On Monday, Lou drives his vehicle with 27-inch tires, averaging x miles per hour. On Tuesday, Lou switches the tires on his vehicle to 32-inch tires yet drives to work at the same average speed as on Monday. What is the percent change from Monday to Tuesday in the average number of revolutions that Lou's tires make per second?
Options:
A)Decrease by 14.3%
B)Decrease by 16%
C)Increase by 14.3%
D)Increase by 12.5%
E)Cannot be determined with the given information.
Rationale: 864 is the LCM
On Tuesday 864/32 =27
On Monday 864/27 = 32
Therefore, 27-32/32 = -1/6=-16% decrease
Answer is B
Answer: B
Question: The ratio of boys to girls in a class is 2:3. the career preference of the students in the class are to be represented in a circle graph. If the area of the graph allocated to each career preference is to be proportional to the number of students who have that career preference, how many degrees of the circle should be used to represent a career that is preferred by one third of the boys and two-third of the girls in the class?
Options:
A)a)160 degree
B)b) 168 degree
C)c)191 degree
D)d)272 degree
E)e)192 degree
Rationale: let the common ratio be x.. so B=2x and G=3x and Total=5x
1/3 of M= 2x/3 and 2/3 of F= 2x..
Total preferring that carrer = 2x/3+2x=8x/3..
Now 5x= 360, so x=360/5=72..
so x*8/3= 72*8/3=192
ans 192
E
Answer: E
Question: Working together, printer A and printer B would finish the task in 10 minutes. Printer A alone would finish the task in 30 minutes. How many pages does the task contain if printer B prints 5 pages a minute more than printer A ?
Options:
A)125
B)150
C)175
D)200
E)225
Rationale: 10*A + 10*B = x pages
in 10 mins printer A will print = 10/30 * x pages = 1/3*x pages
thus in 10 mins printer printer B will print x - 1/3*x = 2/3*x pages
Also it is given that printer B prints 5 more pages per min that printer A. In 10 mins printer B will print 50 more pages than printer A
thus 2/3*x - 1/3*x = 50 => x = 150 pages
Answer : B
Answer: B
Question: If d= (b-1)(b+2), then what is the least possible value of d?
Options:
A)1
B)2
C)3
D)4
E)-9/4
Rationale: Answer : E
Answer: E
Question: Papaya, a popular soft drink, contains only four ingredients. Soda water comprise 4/7 of Papaya and natural lemon juice makes 1/3 of Papaya. The amounts of sugar and papaya puree in Papaya are equal. Due to a malfunction, the mixing machine mixes double the regular amount of lemon juice and three times the regular amount of papaya puree. If no other changes were made to the relative quantities of the ingredients, what is the fractional portion of soda water in the drink that comes out of the malfunctioning machine?
Options:
A)7/30
B)7/21
C)2/5
D)12/29
E)4/7
Rationale: Soda water = 12/21
Natural lemon juice = 7/21
The quantities of sugar and papaya puree are equal. Total units are 21 of which 12 + 7 = 19 are used up by above two. Remaining is 2 which is equally divided between sugar and papaya puree:
Sugar = 1/21
Papaya puree = 1/21
Thus ratio of soda:lemon:sugar:puree = 12:7:1:1
Now, lemon is doubled, puree is three times and remaining are the same.
Resultant ratio is = 12:14:1:3
Ratio of soda water in the resultant mixture = 12/(12+14+1+3) = 12/30 = 2/5
ANSWER:C
Answer: C
Question: Each shelf of a bookcase contained 11 books. If the librarian took out 15 books and rearranged the remaining books so that all shelves but the last one contained 7 books and that last shelf contained 12 books, how many shelves does the bookcase have?
Options:
A)5
B)6
C)7
D)8
E)9
Rationale: Let x be the number of shelves.
11x - 15 = 7(x-1) + 12
4x = 20
x= 5
The answer is A.
Answer: A