divelab/Sys2Bench huggingface dataset:
Question: In the county of Veenapaniville, there are a total of 50 high schools, of three kinds: 25 public schools, 16 parochial schools, and 9 private independent schools. These 50 schools are divided between three districts: A, B, and C. District A has 18 high schools total. District B has 17 high schools total, and only two of those are private independent schools. If District C has an equal number of each of the three kinds of schools, how many private independent schools are there in District A?
Options:
A)2
B)3
C)4
D)5
E)6
Rationale: “In the county of Veenapaniville, there are a total of 50 high schools, of three kinds: 25 public schools, 16 parochial schools, and 9 private independent schools.”
“District A has 18 high schools total.”
“District B has 17 high schools total, and only two of those are private independent schools.”
“District C has an equal number of each of the three kinds of schools.” Hmm. That’s not a simple number. Let’s put that on hold for a moment. So far, from the matrix it looks like we could figure out the missing number in the “totals” row. That number must be 15, because 18 + 17 + 15 = 50.
Now, go back to that last fact: “District C has an equal number of each of the three kinds of schools.” Now that makes sense. District C has 15 schools, so it must have 5 of each kind:
The question is asking: “how many private independent schools are there in District A?” Well, now that’s just a matter of adding across the “private independent” row. We know 2 + 2 + 5 = 9, so the missing number must be 2.
There’s still a good deal of information we can’t figure out from the information given in the question, but we are able to answer the specific question asked here. There are 2 private independent schools in District A, so the answer = (A).
Answer: A
Question: A sum was put at simple interest at certain rate for 3 years. Had it been put at 1% higher rate it would have fetched Rs. 75 more. The sum is: A. Rs. 2,400 B. Rs. 2,100 C. Rs. 2,200 D.Rs. 2,480
Options:
A)2500
B)2100
C)2200
D)2300
E)2400
Rationale: 1 percent for 3 years= 75
1 percent for 1 year = 25
=> 100 percent = 2500
ANSWER:A
Answer: A
Question: The unit digit in the product (611 * 704 * 912 * 261) is:
Options:
A)2
B)5
C)6
D)8
E)10
Rationale: Explanation:
Unit digit in the given product = Unit Digit in (1*4*2*1) = 2
ANSWER: A
Answer: A
Question: The perimeter of one square is 48 cm and that of another is 20 cm. Find the perimeter and the diagonal of a square which is equal in area to these two combined?
Options:
A)13√7
B)13√2
C)13√8
D)13√9
E)12√2
Rationale: 4a = 48 4a = 20
a = 12 a = 5
a2 = 144 a2 = 25
Combined area = a2 = 169 => a = 13
d = 13√2
Answer:B
Answer: B
Question: Ratio of ages of three persons is 4:7:9, Eight years ago, the sum of their ages was 56. Find their present ages.
Options:
A)16,35,36
B)12,28,36
C)16,28,27
D)16,28,36
E)None of these
Rationale: Explanation:
Let the present ages are 4x, 7x, 9x.
=> (4x-8) + (7x-8) + (9x-8) = 56
=> 20x = 80
=> x = 4
So their present ages are: 16,28,36
Option D
Answer: D
Question: An error 2% in excess is made while measuring the sideofa square. The % of error in the calculated area of the square is?
Options:
A)4%
B)4.04%
C)4.15%
D)5%
E)5.24%
Rationale: 100 cm is read as 102 cm.
A1 = (100 x 100) cm2 and A2 (102 x 102) cm2.
(A2 - A1) = [(102)2 - (100)2]
= (102 + 100) x (102 - 100)
= 404 cm2.
Percentage error = 404	x 100	%	= 4.04%
100 x 100
B
Answer: B
Question: Which of the following describes all the values of x for which 8−4x < 18x−18?
Options:
A)x > 5/7
B)x < 5/11
C)5/11 < x
D)x > 13/11
E)13/11 > x
Rationale: 8−4x < 18x−18
i.e. 8+18 < 18x+4x
i.e. 26 < 22x
i.e. x>26/22
i.e. x>13/11
Answer: Option D
Answer: D
Question: How much does a watch lose per day, if its hands coincide ever 64 minutes?
Options:
A)32 8/11
B)32 8/12
C)32 8/18
D)32 8/17
E)32 8/14
Rationale: 55min spaces are covered in 60min
60 min. spaces are covered in (60/55 x 60) min= 65+5/11 min.
loss in 64min=(65+5/11)- 64 =16/11
Loss in 24 hrs (16/11 x 1/64 x 24 x 60) min= 32 8/11.
Answer: A
Answer: A
Question: An athlete runs 200 metres race in 24 seconds. What is his speed?
Options:
A)23
B)38
C)37
D)30
E)28
Rationale: Speed=DistanceTime=20024 m/s=20024×185 km/hr=40×34 km/hr=10×3 km/hr=30 km/hr
Answer :D
Answer: D
Question: A dishonest dealer professes to sell goods at the cost price but uses a weight of 800 grams per kg, what is his percent?
Options:
A)65%
B)67%
C)45%
D)78%
E)25%
Rationale: E
800 --- 200
100 --- ? => 25%
Answer: E
Question: What is the diffference between the place value and face value of 7 in the numeral 9751?
Options:
A)691
B)692
C)693
D)694
E)695
Rationale: place value of 7 = 7 * 100 = 700
face value of 7 = 7
700 - 7 = 693
C
Answer: C
Question: A rectangular-shaped carpet that measures x feet by y feet is priced at $40. What is the cost of the carpet, in dollars per square yard? (1 square yard = 9 square feet)
Options:
A)xy/360
B)9xy/40
C)40xy/9
D)360xy
E)360/(xy)
Rationale: The area of the carpet in feet is xy.
The area in square yards is xy / 9.
The price per square yard is 40 / (xy/9) = 360/(xy).
The answer is E.
Answer: E
Question: A sum of money is to be distributed among A, B, C, D in the proportion of 5:2:4:3. If C gets Rs. 1000 more than D, what is B's share?
Options:
A)Rs.2029
B)Rs.2028
C)Rs.2000
D)Rs.2022
E)Rs.2021
Rationale: Let the shares of A, B, C and D be 5x, 2x, 4x and 3x Rs. respectively.
Then, 4x - 3x = 1000 => x = 1000.
B's share = Rs. 2x = 2 * 1000
= Rs.2000.
Answer: C
Answer: C
Question: A woman swims downstream 45 km and upstream 15 km taking 3 hours each time, what is the speed of the woman in still water?
Options:
A)10
B)12
C)14
D)16
E)18
Rationale: 45 --- 3 DS = 15
? ---- 1
15 ---- 3 US = 5
? ---- 1 M = ?
M = (15 + 5)/2 = 10
Answer:A
Answer: A
Question: If 2 cards are selected at random from the deck of 52 cards then What is the probability of one of the selected cards will be King and other will be Jack?
A deck of cards has a total of 52 cards, consisting of 4 suits; (spades(Black), hearts(Red), diamond(Red)s, and clubs(Black)); and 13 cards including 1 king, 1 queen and 1 jack in each suit
Options:
A)8/2652
B)1/2652
C)18/2652
D)12/2652
E)6/2652
Rationale: 2 possible cases:
King - Jack or Jack -King (4 kings and 4 Jacks).
Either way,
the total probability = 2( King -Jack) = 2 (4/52 * 4/51) = 18/2652. C is the correct answer.
Answer: C
Question: 1,3,5,7,9,..50 find term of sequnce for this.
Options:
A)1200
B)1345
C)1456
D)1478
E)2500
Rationale: This is an arithmetic progression, and we can write down
a=1a=1 ,d=2d=2 , n=50n=50 .
We now use the formula, so that
Sn=12n(2a+(n−1)l)Sn=12n(2a+(n−1)l)
S50=12×50×(2×1+(50−1)×2)S50=12×50×(2×1+(50−1)×2)
=25×(2+49×2)=25×(2+49×2)
=25×(2+98)=25×(2+98)
=2500=2500 .
E
Answer: E
Question: Compute the probability that two random integers, independently chosen and both taking on
an integer value between 1 and 10 with equal probability, have a prime product.
Options:
A)1/25
B)2/25
C)3/25
D)4/25
E)5/25
Rationale: There are 4 primes between 1 and 10. In order for the product of the integers to be
prime, one of them must be one of these primes (2, 3, 5, or 7) and the other must be the number
There are therefore 8 possible pairs of generated integers that will yield a prime product.
Since there are 100 possible pairs overall, the desired probability is
2/25
correct answer B
Answer: B
Question: Audrey 4 hours to complete a certain job. Ferris can do the same job in 3hours. Audrey and Ferris decided to collaborate on the job, working at their respective rates. While Audrey worked continuously, Ferris took 1 breaks of equal length. If the two completed the job together in 2 hours, how many minutes long was each of Ferris’ breaks ?
Options:
A)5
B)30
C)15
D)20
E)25
Rationale: Audery and Ferris collective Work rate:
1/4 + 1/3 = 7/12
Collective work Time = 12/7 = 1.7 Hrs
Job Was actually done in = 2 (Includes breaks)
Breaks = Actual time taken - Collective work time
= 2 - 1.7
= .3 Hrs = 1/2
so ferrais took 1 breaks
=.3/1=.3 hrs = 30 m
so Answer is B) 30 mins
Answer: B
Question: If r is even and t is odd, which of the following is odd?
Options:
A)rt
B)5rt
C)6(r^2)t
D)5r + 6t
E)6r + 5t
Rationale: R is even, A B and C are out a even number multiplied by any number is even.
D is out because 5r = even, 6t =even so even + even = even
E is correct because: 6r = even, 5t = odd as any number of the form odd x integer... the integer value determines the even/odd nature.
so, even + odd = odd ;Answer: E
Answer: E
Question: If x and y are prime numbers such that x > y > 3, then x^2 − y^2 must be divisible by which one of the following numbers?
Options:
A) 3
B) 7
C) 5
D) 9
E) 12
Rationale: If x=6 and y=4, then x^2-y^2=20and 20 is divisible only by 5 from the options, thus it must be correct.
Answer: C.
Answer: C
Question: If M = N/O, -1 < O < 0 and 4 < N, which of the following is correct?
Options:
A)M > 4.
B)0 < M <4.
C)-4 < M < 0.
D)M < -4.
E)M < -20.
Rationale: N is +veO is -ve
Eliminate AB
For min. value max. numerator and minimize dinominator
take N=4.1M=-0.9
M=4.1/-0.9
M<-4
Ans D
Answer: D
Question: there are 4 consonants 3 vowels how many 6 letter strings can u form with atleast one vowels in each?
Options:
A)5
B)6
C)7
D)8
E)9
Rationale: 6 letter strings with atleast one vowel means possibilities are
1) 4 Constants and 2 Vowels = 4c4*3c2 = 3
2) 3 Constants and 3 Vowels = 4c3*3c3 = 4
So the answer is 3+4 = 7
ANSWER:C
Answer: C
Question: The radius of a cylindrical water tank is reduced by 50%. However, the speed by which water is filled into the tank is also decreased by 50%. How much more or less time B will it take to fill the tank now?
Options:
A) 50% less time
B) 50% more time
C) 75% less time
D) 75% more time
E) 100% more time
Rationale: (VC)Volume of the cylinderical vessal is directly proportional to R^2.
So if radius is 50% less volume will be 1/4th of the original volume.(VC/4)
Now if with velocity V tank can be filled in T1 time of volume VC
So now Velocity is 50% less i..e V/2
So time taken to fill the capacity VC/4 by V/2 velocity is T2.
VT1 = VC
V/2*T2 = VC/4
So T1/T2 = 1/2
So Tank will be filled in less time. that is B=50 % less.A
Answer: A
Question: A cat chases a rat 6 hours after the rat runs. cat takes 4 hours to reach the rat. If the average speed of the cat is 90 kmph, what s the average speed of the rat?
Options:
A)32kmph
B)26kmph
C)35kmph
D)36kmph
E)32kmph
Rationale: cat take 10 hours and rat take 4 hours...then Distance chased by them is 90*4.so speed of rat is (90*4)/10=36kmph.
ANSWER IS D
Answer: D
Question: How many seconds will a 500 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
Options:
A)26 sec
B)30 sec
C)13 sec
D)19 sec
E)12 sec
Rationale: Speed of train relative to man = 63 - 3 = 60 km/hr.
= 60 * 5/18 = 50/3 m/sec.
Time taken to pass the man = 500 * 3/50
= 30 sec.
Answer:B
Answer: B
Question: In a stack of cards, 11 cards are blue and the rest are red. If 2 cards are to be chosen at random from the stack without replacement, the probability that the cards chosen will both be blue is 5/6 . What is the number of cards in the stack?
Options:
A)10
B)11
C)12
D)15
E)18
Rationale: This question can be solved by TESTing THE ANSWERS.
Answer C: 12 total cards
With 12 total cards, and 11 blue cards, the probability of pulling two blue cards is...
(11/12)(10/11) = 110/132 ~= 5/6
This is an exact MATCH for what we were told, so this MUST be the answer.
Final Answer:
C
Answer: C
Question: A woman has three blouses of different colors, three skirts of different colors, and thee different pairs of shoes. She refuses to wear her pink blouse with her green skirt. How many different blouseskirt-shoe combinations could she wear?
Options:
A)8
B)12
C)25
D)17
E)18
Rationale: total ways = 3*3*3=27..
now its better to find the ways in which the pink blouse and green skirt are together and subtract from total to get the answer..
the ways in which the pink blouse and green skirt are together=1*1*2=2..
total ways =27-2=25..
ANSWER:C
Answer: C
Question: If the sum of five consecutive positive integers is A, then the sum of the next three consecutive integers in terms of A is:
Options:
A)3A/5
B)3A/5 +12
C)A
D)5A/3
E)5A/3 +12
Rationale: In Case of Consecutive Integers or Integers in Arithmetic Progression Mean = Median
I.e. Median = A/5 = Mean = Third Integer
First Integer = A/5 - 2
Second Integer = A/5 - 1
Third Integer = A/5
Fourth Integer = A/5 + 2
Fifth Integer = A/5 + 2
i.e.
Sixth Integer = A/5 + 3
Seventh Integer = A/5 + 4
Eighth Integer = A/5 + 5
Now Mean of next 3 Integers = Median = A/5 + 4
i.e. Sum of Next 3 integers = (A/5 + 4)*3 = 3A/5 +12
Answer: option B
Answer: B
Question: Find value of x: 121 × 54 = x
Options:
A)34545
B)46576
C)67887
D)57687
E)75625
Rationale: 121×54=121×(102)4=121×1000016=7.5625×10000=75625
E
Answer: E
Question: What is the smallest no. that should be added to 45454 to make it exactly divisible by 9?
Options:
A)1
B)3
C)5
D)6
E)9
Rationale: If a number is divisible by 9, the sum of its digits must be a multiple of 9.
Here, 4+5+4+5+4=22, the next multiple of 9 is 27.
5 must be added to 45454 to make it divisible by 9
C
Answer: C
Question: The true discount on a bill of Rs. 2360 is Rs. 360. What is the banker's discount?
Options:
A)Rs. 432
B)Rs. 425
C)Rs. 412
D)Rs. 442
E)None of these
Rationale: Explanation :
F = Rs. 2360
TD = Rs. 360
PW = F - TD = 2360 - 360 = Rs. 2000
True Discount is the Simple Interest on the present value for unexpired time
=>Simple Interest on Rs. 2000 for unexpired time = Rs. 360
Banker's Discount is the Simple Interest on the face value of the bill for unexpired time
= Simple Interest on Rs. 2360 for unexpired time
=360/2000 × 2360 = 0.18 × 2160 = Rs. 425 Answer : Option B
Answer: B
Question: How many cubes of 25 cm edge can be put in a cubical box of 1 m edge.
Options:
A)177 cm
B)100 cm
C)86 cm
D)64 cm
E)87 cm
Rationale: Number of cubes =100âˆ—100âˆ—100/25âˆ—25âˆ—25=64
Note: 1 m = 100 cm
Answer:D
Answer: D
Question: A person crosses a 600 m long street in 5 minutes. What is his speed in km per hour?
Options:
A)2 km/hr
B)5 km/hr
C)7.2 km/hr
D)9 km/hr
E)11 km/hr
Rationale: Explanation:
Speed =(600/5*60)m/sec
= 2 m/sec.
Converting m/sec to km/hr
=(2*18/5)km/hr=7.2 km/hr
ANSWER:C
Answer: C
Question: If the cost price of 17 articles is equal to the selling price of 16 articles, What is the percentage of profit or loss that the merchant makes?
Options:
A)20% loss
B)6.25% profit
C)33.33 % loss
D)30.33% loss
E)None of these
Rationale: Explanation :
Let Cost price of 1 article be Re.1.
Therefore, Cost price of 17 articles = Rs. 17.
Selling price of 16 articles = Rs. 17
Therefore, Selling price of 17 articles is :-
=>17/16Ã—17
=>18.06
Therefore, Profit = Selling price - Cost price.
=>18.06âˆ’17=1.06
Hence, the percentage of profit = profit x 100/C.P.
=>1.06/17Ã—100.
=>6.25% Profit.
Answer : B
Answer: B
Question: If a man can cover 12 metres in one second, how many kilometres can he cover in 3 hours 45 minutes?
Options:
A)228
B)162
C)5528
D)256
E)191
Rationale: 12 m/s = 12 * 18/5 kmph
3 hours 45 minutes = 3 3/4 hours = 15/4 hours
Distance = speed * time = 12 * 18/5 * 15/4 km = 162 km.
Answer: B
Answer: B
Question: A man buys Rs. 20 shares paying 9% dividend. The man wants to have an interest of 12% on his money. The market value of each share is:
Options:
A)Rs. 12
B)Rs. 15
C)Rs. 18
D)Rs. 21
E)Rs. 24
Rationale: Dividend on Rs. 20 = Rs.	9/100	x 20 =Rs.	9/5	.
Rs. 12 is an income on Rs. 100.
Rs.	9/5	is an income on Rs.100/12 x 9/5	= Rs. 15.
Answer: Option B
Answer: B
Question: The area of a parallelogram is 128sq m and its altitude is twice the corresponding base. Then the length of the base is?
Options:
A)121
B)10
C)16
D)12
E)71
Rationale: Due to stoppages, it covers 9 km less.
Time taken to cover 9 km = 9/54 * 60
= 10 min.
Answer: B
Answer: B
Question: Complete the sequence:
B E J Q ?
Options:
A)M
B)D
C)S
D)D
E)Z
Rationale: E
B+3=E
E+5=J
J+7=Q
Q+9=Z
Answer: E
Question: In the coordinate plane, points (x, 1) and (10, y) are on line k. If line k passes through the origin and has slope 1/3, then x + y =
Options:
A) 4.5
B) 7
C) 8
D) 19/3
E) 12
Rationale: Line k passes through the origin and has slope 1/3 means that its equation is y=1/3*x.
Thus: (x, 1)=(3, 1) and (10, y) = (10,10/3) --> x+y=3+10/3=19/3.
Answer:D.
Answer: D
Question: 7.51 8.22 7.86 8.36
8.09 7.83 8.30 8.01
7.73 8.25 7.96 8.53
A vending machine is designed to dispense 8 ounces of coffee into a cup. After a test that recorded the number of ounces of coffee in each of 1000 cups dispensed by the vending machine, the 12 listed amounts, in ounces, were selected from the data above. If the 1000 recorded amounts have a mean of 7.2 ounces and a standard deviation of 0.3 ounces, how many of the 12 listed amounts are within 1.5 standard deviation of the mean?
Options:
A)One
B)Six
C)Nine
D)Ten
E)Eleven
Rationale: Mean = 7.2
Standard Deviation = 0.3
within 1.5 standard deviation of the mean
i.e. 1.5 standard deviation ABOVE the mean = 7.2+1.5*0.3 = 7.65
and 1.5 standard deviation BELOW the mean = 7.2-1.5*0.3 = 6.75
hence, 1 value fall within 1.5 SD from Mean
Answer: Option A
Answer: A
Question: What will be the cost of building a fence around a square plot with area equal to 289 sq ft, if the price per foot of building the fence is Rs. 58?
Options:
A)Rs. 3944
B)Rs. 3828
C)Rs. 4176
D)Cannot be determined
E)None of these
Rationale: Let the side of the square plot be a ft.
a2 = 289 => a = 17
Length of the fence = Perimeter of the plot = 4a = 68 ft.
Cost of building the fence = 68 * 58 = Rs. 3944.
ANSWER:A
Answer: A
Question: If the 5th date of a month is Tuesday, what date will be 3 days after the 3rd Friday in the month?
Options:
A)17
B)18
C)20
D)22
E)33
Rationale: B
18
5th date of a month is Tuesday
Friday will be on = 5 + 3
= 8th of a month
1st Friday is on 1 st of a month
2nd Friday is on 8th of a month
3rd Friday will be on 15th of a month
3 days after 15th = 15 + 3 = 18
Answer: B
Question: A and B put in Rs.300 and Rs.400 respectively into a business. A reinvests into the business his share of the first year's profit of Rs.210 where as B does not. In what ratio should they divide the second year's profit?
Options:
A)39:40
B)39:48
C)39:49
D)39:46
E)39:41
Rationale: 3: 4
A = 3/7*210 = 90
390: 400
39:40
Answer:A
Answer: A
Question: There are 2 available positions and 50 candidates, one half of whom are democrats and another half are republicans. If it was decided that the positions would be filled at random, then what is the probability E that the both positions will be taken by members of just one party?
Options:
A)1/25
B)12/49
C)1/4
D)24/49
E)1/2
Rationale: E probability of one party having both spots:
(1/2) * (24/49) = 12/49
(1/2) or (25/50) because it does not matter which party or which person gets the first spot. (24/49) because after one person from a particular party is chosen, there are 24 members of the same party left out of 49 total candidates.
Since this result can happen for both parties, (12/49) + (12/49) = (24/49)
Answer: D
Answer: D
Question: An order was placed for the supply of a carper whose length and breadth were in the ratio of 3 : 2. Subsequently, the dimensions of the carpet were altered such that its length and breadth were in the ratio 7 : 3 but were was no change in its parameter. Find the ratio of the areas of the carpets in both the cases.
Options:
A)8:9
B)8:7
C)8:1
D)8:2
E)8:8
Rationale: Let the length and breadth of the carpet in the first case be 3x units and 2x units respectively.
Let the dimensions of the carpet in the second case be 7y, 3y units respectively.
From the data,.
2(3x + 2x) = 2(7y + 3y)
=> 5x = 10y
=> x = 2y
Required ratio of the areas of the carpet in both the cases
= 3x * 2x : 7y : 3y
= 6x2 : 21y2
= 6 * (2y)2 : 21y2
= 6 * 4y2 : 21y2
= 8 : 7
Answer:B
Answer: B
Question: A man arranges to pay off a debt of Rs 3600 by 40 annual installments which are in A.P. When 30 of the installments are paid he dies leaving one-third of the debt unpaid.
The value of the 8th installment is:
Options:
A)Rs 35
B)Rs 50
C)Rs 65
D)Rs 70
E)Rs 80
Rationale: Explanation :
Let the first installment be 'a' and the common difference between any two consecutive installments be 'd'
Using the formula for the sum of an A.P :-
S=n/2[2a+(n−1)d].
We have,
3600=40/2[2a+(40-1)d].
3600=20[2a+39d].
180 =2a+39d. ----(i)
Similarly,
2400=30/2[2a+(30-1)d].
160=2a+29d. ----(ii)
On solving both the equations we get:
d=2 and a=51
Hence, the Value of 8th installment is :-
=51+(8−1)2.
=65.
Answer : C
Answer: C
Question: Use distributive property to solve the problem below:
Maria bought 12 notebooks and 6 pens costing 2 dollars each.How much did Maria pay?
Options:
A)30 dollars
B)36 dollars
C)50 dollars
D)60 dollars
E)70 dollars
Rationale: Solution
2 × (12 + 6) = 2 × 12 + 2 × 6 = 24 + 12 = 36 dollars
Answer B
Answer: B
Question: The average age of a husband, wife and their child 3 years ago was 27 years and that of wife and the child 5 years ago was 20 years. The present age of the husband is?
Options:
A)19 years
B)18 years
C)61 years
D)14 years
E)13 years
Rationale: Sum of the present ages of husband, wife and child
= (23 * 2 + 5 * 2) = 57 years.
Required average
= 57/3
= 19 years.
Answer:A
Answer: A
Question: Together, 15 type A machines and 7 type B machines can complete a certain job in 4 hours. Together 8 type B machines and 15 type C machines can complete the same job in 11 hours. How many hours R would it take one type A machine, one type B machine, and one type C machine working together to complete the job (assuming constant rates for each machine)?
Options:
A) 22 hours
B) 30 hours
C) 44 hours
D) 60 hours
E) It cannot be determined from the information above.
Rationale: Say the rates of machines A, B and C are a, b, and c, respectively.
Together 15 type A machines and 7 type B machines can complete a certain job in 4 hours --> 15a + 7b = 1/4;
Together 8 type B machines and 15 type C machines can complete the same job in 11 hours --> 8b + 15c = 1/11.
Sum the above: 15a + 15b + 15c = 1/4 + 1/11 = 15/44 --> reduce by 15: a + b + c = 1/44 --> so, the combined rate of the three machines is 1/44 job/hour --> time is reciprocal of the rate, thus machines A, B and C can do the job R in 44 hours.
Answer: C.
Answer: C
Question: A can do a piece of work in 8 hours; B and C together can do it in 12 hours, while A and C together can do it in 16 hours. How long will B alone take to do it?
Options:
A)7 8/5 hours
B)5 9/8 hours
C)5 6/8 hours
D)6 6/7 hours
E)none of the above
Rationale: A's 1 hour's work = 1/8 ;
(B + C)'s 1 hour's work = 1/12 ;
(B + C)'s 1 hour's work = 1/16
(A + B + C)'s 1 hour's work = (1/8 + 1/12) = 5/24
B's 1 hour's work = (5/24 - 1/16) = 7/48
B alone will take 48/7 hours to do the work.
=6 6/7
Answer = D
Answer: D
Question: An electric pump can fill a tank in 7 hours. Because of a leak in the tank, it took 14hours to fill the tank. If the tank is full, how much time will the leak take to empty it?
Options:
A)10hours
B)12hours
C)8hours
D)5hours
E)14hours
Rationale: Work done by the leak in 1 hour = 1/7 - 1/14 = 1/14
The leak will empty the tank in 14hours
Answer is E
Answer: E
Question: In the storage room of a certain bakery, the ratio of sugar to flour is 5 to 5, and the ratio of flour to baking soda is 10 to 1. If there were 60 more pounds of baking soda in the room, the ratio of flour to baking soda would be 8 to 1. How many pounds of sugar are stored in the room?
Options:
A)600
B)1200
C)1500
D)1600
E)2400
Rationale: Sugar:Flour = 5:5 = 10:10;
Flour:Soda = 10:1 = 10:1;
Thus we have that Sugar:Flour:Soda = 10x:10x:1x.
Also given that 10x/(1x+60) = 8/1 --> x=240 --> Sugar = 10x = 2400
Answer: E.
Answer: E
Question: After a storm deposits 115 billion gallons of water into the city reservoir, the reservoir is 80% full. If the original contents of the reservoir totaled 245 billion gallons, the reservoir was approximately what percentage full before the storm?
Options:
A)45%
B)48%
C)54%
D)58%
E)65%
Rationale: When the storm deposited 115 billion gallons, volume of water in the reservoir = 245 + 115 = 360 billion gallons
If this is only 80% of the capacity of the reservoir, the total capacity of the reservoir = 360/0.8 = 450 billion gallons
Therefore percentage of reservoir that was full before the storm = (245/450)*100 = 54.4%
Option C
Answer: C