divelab/Sys2Bench huggingface dataset:
Question: A committee that includes 6 members is about to be divided into 2 subcommittees with 3 members each. On what percent of the possible subcommittees that Michael is a member of is David also a member?
Options:
A)10%
B).20%
C)25%
D)40%
E)50%
Rationale: there are only 2 possibility : either they both are in same team or in another team.
so probability to be in same team = 50 percernt
hence E
Answer: E
Question: A and B enter into partnership with capital as 7:9. At the end of 8 months, A withdraws. If they receive the profits in the ratio of 8:9 find how long B's capital was used?
Options:
A)months
B)months
C)months
D)months
E)months
Rationale: 7 * 8 : 9 * x = 8:9 => x= 7
ANSWER:D
Answer: D
Question: An amount of money lent against simple interest at 4 1/2 % per annum amounts to Rs.381 after 6 years. Find the sum.
Options:
A)100
B)200
C)300
D)400
E)500
Rationale: GIVEN SI+P=381
SI=381-P
SI=PTR/100
381-P=P*6*4.5/100
P=300
ANSWER:C
Answer: C
Question: The perimeter of a square is equal to the perimeter of a rectangle of length 19 cm and breadth 14 cm. Find the circumference of a semicircle whose diameter is equal to the side of the square. (Round off your answer to two decimal places)
Options:
A)22.78
B)23.54
C)23.5
D)24.55
E)25.93
Rationale: Let the side of the square be a cm.
Perimeter of the rectangle = 2(19 + 14) = 66 cm
Perimeter of the square = 66 cm
i.e. 4a =66
A = 16.5
Diameter of the semicircle = 16.5 cm
Circumference of the semicircle
= 1/2(∏)(16.5)
= 1/2(22/7)(16.5) = 25.93 cm to two decimal places
Answer: E
Answer: E
Question: Amar takes as much time in running 24 meters as a car takes in covering 60 meters. What will be the distance covered by Amar during the time the car covers 2.2 km?
Options:
A)700 m
B)500 m
C)870 m
D)880 m
E)840 m
Rationale: Distance covered by Amar
= 24/60 (2.2km)
= 2/5(2200) = 880 m
Answer: D
Answer: D
Question: A can contains a mixture of two liquids A and B in the ratio 7:5. When 9 litres of mixture are drawn off and the can is filled with B, the ratio of A and B becomes 7:9. How many litres of liquid A was contained by the can initially?
Options:
A)25
B)21
C)20
D)10
E)15
Rationale: Suppose the can initially contains 7x and 5x litres mixtures A and B
respectively
Quantity of A in mix. left =[7x –7/12 * 9 ] =[7x –21/4]
Quantity of B in mix. left =[5x –5/12 *9 ] = [ 5x - 15/4 ]
Therefore [ 7x-21/4 ] =7/9 or 28x-21 = 7/9
[5x-15/4]+9 20x+21
252x -189 =140x+147 or 112x =336 , x = 3.
Quantity of A in the can initially =7*3 =21
ANSWER:B
Answer: B
Question: A sum of Rs.4800 is invested at a compound interest for three years, the rate of interest being 10% p.a., 20% p.a. and 25% p.a. for the 1st, 2nd and the 3rd years respectively. Find the interest received at the end of the three years.
Options:
A)2987
B)3120
C)2798
D)2689
E)2761
Rationale: Let A be the amount received at the end of the three years.
A = 4800[1 + 10/100][1 + 20/100][1 + 25/100]
A = (4800 * 11 * 6 * 5)/(10 * 5 * 4)
A = Rs.7920
So the interest
=7920 - 4800
= Rs.3120
Answer:B
Answer: B
Question: In a bag, there are 2400 ball, and their colors are red, green blue.. The ratio of the balls are 15:13:17.Then how many red color balls are available in the bag?
Options:
A)900
B)1600
C)750
D)890
E)1010
Rationale: Red:green:blue = 15+13+17=45; Ratio of the red balls= 15/40 simplify =3/8*2400=900.Answer =A
Answer: A
Question: By mixing two brands of coffee and selling the mixture at the rate of Rs. 177 per kg. a shopkeeper makes a profit of 18%. If to every 2 kg of one brand costing Rs. 200 per kg, 3 kg of the other brand is added, then how much per kg does the other brand cost?
Options:
A)12.66
B)23
C)116.66
D)10.66
E)43.2
Rationale: E
C
Let the cost of the brand be Rs. X per kg.
C.P. of 5 kg = (2 * 200 + 3 * x) = Rs. (400 + 3x)
S.P of 5 kg = Rs. (5 * 177) = Rs. 885
[885 - (400 + 3x)]/(400 + 3x) * 100 = 18
24250 - 150x = 3600 + 27x
177x = 20650 => x = 116 2/3
So, cost of the other brand = Rs. 116.66.
Answer: C
Question: In how many ways can a committee consisting of 4 men and 5 women be formed from a group of 8 men and 9 women?
Options:
A)8C4 9C5
B)4C8 5C9
C)7C5 9C4
D)9C4 7C5
E)NONE
Rationale: Group consisting of 8 men and 9 women
4 men can be selected from 8 men in 8C4 ways
5 women can be selected from 9 women in 9C5 ways
Therefore, Total number of ways= 8C4 9C5
ANSWER:A
Answer: A
Question: If x < y < 0, which of the following must be true?
Options:
A)x+y is a positive integer
B)x+y is a negative integer
C)xy is a negative integer
D)x/y is a negative integer
E)2x/y is a negative integer
Rationale: Given x, y are less than 0. So both will be negative integers
negative + negative = negative
negative * negative = positive
negative / negative = positive
So, option B is true and all others are false.
Answer : B
Answer: B
Question: There is a total of 120 marbles in a box, each of which is red, green, blue, or white. If one marble is drawn from the box at random, the probability that it will be white is 1/4 and the probability that it will be green is 1/3. What is the probability that the marble will be either red or blue ?
Options:
A)1/6
B)1/4
C)2/7
D)1/3
E)5/12
Rationale: Total marbles in the box=120
white marbles=120/4=30
green marbles=120/3=40
w+g=70
red+blue=50
p(red or blue)=50/120=5/12
ANSWER:E
Answer: E
Question: Ramu bought an old car for Rs. 42000. He spent Rs. 15000 on repairs and sold it for Rs. 64900. What is his profit percent?
Options:
A)12%
B)13.85%
C)18%
D)82%
E)23%
Rationale: Total CP = Rs. 42000 + Rs. 15000 = Rs. 57000 and SP
= Rs. 64900
Profit(%) = (64900 - 57000)/57000 * 100
= 13.85%
Answer:B
Answer: B
Question: Seven cards numbered from 1 to 7 are placed in an empty bowl. First one card is drawn and then put back into the bowl, and then a second card is drawn. If the cards are drawn at random and if the sum of the numbers on the cards is 10, what is the probability that one of the two cards drawn is numbered 4?
Options:
A)2/7
B)1/10
C)1/7
D)1/5
E)2/5
Rationale: There are 5 ways to get a total sum of 10.
2 of these ways include the number 4.
The probability that one of the cards is a 4 is 2/5
The answer is E.
Answer: E
Question: How many litres of pure acid are there in 10 litres of a 25% solution
Options:
A)1.5
B)1.6
C)2.5
D)1.8
E)1.9
Rationale: Explanation:Question of this type looks a bit typical, but it is too simple, as below... It will be 10 * 25/100 = 2.5 Answer: Option C
Answer: C
Question: Last year, Bill's farm produced 768,000 oranges. If Bill distributed his apples evenly across 9 different retail shops, how many apples remained with him.
Options:
A)1 orange
B)2 oranges
C)3 oranges
D)4 oranges
E)5 oranges
Rationale: This is equivalent to finding the first number that is divisible by 9 that occurs before 768,000 oranges.
In order to divide the sum in 9 parts, the amount must be divisible by 9
Divisibility rule of 9: The sum of the digits must be divisible by 9
Sum of digits of 768,000 = 21 and 18 is divisible by 9.
Hence, we need to remove 3 to this number for it to be divisible by 9
Correct Option: C
Answer: C
Question: Sara's mother is 6 times older than Sara. Next year, however, she will be only 5 times older than her daughter. How old is Sara's mother.
Options:
A)24 years
B)25 years
C)26 years
D)27 years
E)28 years
Rationale: At the present,
Sara's age is x.
Sara's mother's age is y=6x.
Next year,
Sara's age will be x+1.
Sara's mother's age will be y+1=5(x+1).
From the two equations, we can calculate Sara's age:
y=6x
y+1=5 (x+1)
6x+1=5x+5
6x-5x=5-1
x=4
If Sara is currently 4 years old, and her mother is 6 times older, then her age is
6x=6×4=24.
ANSWER: A
Answer: A
Question: 48 persons can repair a road in 12 days, working 5 hours a day. In how many days will 30 persons, working 6 hours a day, complete the work?
Options:
A)10
B)16
C)13
D)18
E)19
Rationale: Let the required number of days be x.
Less persons, More days (Indirect Proportion)
More working hours per day, Less days (Indirect Proportion)
Persons 30 : 48 :: 12 : x
Working hours/day 6 : 5
30 x 6 x x = 48 x 5 x 12
x = (48 x 5 x 12)/(30 x 6)
x = 16
ANSWER B
Answer: B
Question: 5,7,11,19,35, (...)
Options:
A)12
B)67
C)5
D)64
E)32
Rationale: 5
5Ã— 2 - 3 = 7
7 Ã— 2 - 3 = 11
11 Ã— 2 - 3 = 19
19 Ã— 2 - 3 = 35
35 Ã— 2 - 3 = 67
Answer is B
Answer: B
Question: If 6^q is a factor of (10!)^2, What is the greatest possible value of q ?
Options:
A)2
B)4
C)6
D)8
E)10
Rationale: q 10!= 10*9*8*7*6*5*4*3*2*1 = 2*5*3*3*2*2*2*7*2*3*5*2*2*3*2 = 2^8*3^4*5^2*7
6= 2*3
Therefore only the exponents of 2 and 3 are relevant, 2^8 or 3^4 -> higher number counts = 8 -> Answer Choice D
Answer: D
Question: Find the area of the quadrilateral of one of its diagonals is 20 cm and its off sets 9 cm and 6 cm?
Options:
A)328
B)150
C)279
D)277
E)267
Rationale: 1/2 * 20(9 + 6) = 150 cm2
Answer:B
Answer: B
Question: How many 3-digit even numbers are possible such that if one of the digits is 5, the next/succeeding digit to it should be 6
Options:
A)5
B)305
C)365
D)405
E)495
Rationale: 560, 562, 564, 566, and 568, so total 5. Hence Option A.
Answer: A
Question: A certain musical scale has has 13 notes, each having a different frequency, measured in cycles per second. In the scale, the notes are ordered by increasing frequency, and the highest frequency is twice the lowest. For each of the 12 lower frequencies, the ratio of a frequency to the next higher frequency is a fixed constant. If the lowest frequency is 330 cycles per second, then the frequency of the 7th note in the scale is how many cycles per second?
Options:
A)330 * sqrt 2
B)330 * sqrt (2^7)
C)330 * sqrt (2^12)
D)330 * the twelfth root of (2^7)
E)330 * the seventh root of (2^12)
Rationale: Let the constant be k.
F1 = 330
F2 = 330k
F3 = 330 k * k = 330 * k^2
F13= 330 * k^12
we know F13 = 2 *F1 = 2 * 330 = 660
660/330 = k^12
k = twelfth root of 2
for F7...
F7 = 330 * k^6 ( as we wrote for F2 and F3)
F7 = 330 * (twelfth root of 2) ^ 6
F7 = 330 * sqrt (2)
The answer is A.
Answer: A
Question: A sells a bicycle to B at a profit of 20%. B sells it to C at a profit of 25%. If C pays Rs. 225 for it, the cost price of the bicycle for A is?
Options:
A)277
B)268
C)270
D)150
E)282
Rationale: 125% of 120% of A = 225
125/100 * 120/100 * A = 225
A = 225 * 2/3 = 150.
Answer: D
Answer: D
Question: Find the average of first 50 natural numbers.
Options:
A)A)25.5
B)B)20.5
C)C)24.5
D)D)19.9
E)E)25
Rationale: Sum of first n natural numbers = n(n+1)/2
sum of first 50 natural numbers = 50*51/2 =1275
average = 1275/50 = 25.5
Answer is A
Answer: A
Question: If x dollars is invested at 9 percent for one year and y dollars is invested at 8 percent for one year, the annual income from the 9 percent investment will exceed the annual income from the 8 percent investment by $48. If $2,000 is the total amount invested, how much is invested at 9 percent?
Options:
A)300
B)250
C)1223.53
D)1133.24
E)776.47
Rationale: 2 equations with 2 unknowns
9x / 100 - 8y / 100 = 48
and
x + y = 2000
Solving these 2 equations, x = 1223.53 and y = 776.47
Answer -C
Answer: C
Question: The parameter of a square is double the perimeter of a rectangle. The area of the rectangle is 480 sq cm. Find the area of the square?
Options:
A)288
B)270
C)289
D)480
E)211
Rationale: Let the side of the square be a cm. Let the length and the breadth of the rectangle be l cm and b cm respectively.
4a = 2(l + b)
2a = l + b
l . b = 480
We cannot find ( l + b) only with the help of l . b. Therefore a cannot be found .
Area of the square cannot be found.
Answer: D
Answer: D
Question: An urn contains 5 red, 6 blue and 8 green balls. 3 balls are randomly selected from the urn, find the probability that the drawn ball are blue?
Options:
A)20/969
B)20/875
C)21/876
D)3/512
E)2/9
Rationale: Sample space = no. of ways 3 balls were drawn from urn = 19C3 = 969
No. ways 3 blue balls were drawn from bag = 6C3 = 20
Probability = 20 / 969
Ans - A
Answer: A
Question: A dishonest shopkeeper professes to sell pulses at the cost price, but he uses a false weight of 970gm. for a kg.His gain is …%.
Options:
A)3.09%
B)5.36%
C)4.26%
D)6.26%
E)7.26%
Rationale: His percentage gain is 100*30/970 as he is gaining 30 units for his purchase of 970 units.
so 3.09%.
ANSWER:A
Answer: A
Question: Arun and Tarun can do a work in 10 days.After 4 days tarun went to his village.How many days are required to complete the remaining work by Arun alone.Arun can do the work alone in 30 days.
Options:
A)16 days.
B)17 days.
C)18 days.
D)19 days.
E)20 days.
Rationale: They together completed 4/10 work in 4 days.
balance 6/10 work will be completed by Arun alone in 30*6/10 = 18 days.
ANSWER:C
Answer: C
Question: During a sale of 20% on everything in a store, a kid is successful in convincing the store manager to give him 20 candies for the discounted price of 14 candies. The store still makes a profit of 10% on this sale. What is the mark up percentage on each candy?
Options:
A) 100%
B) 80%
C) 75%
D) 66+2/3%
E) 55%
Rationale: Hi Akhil, I can share the way I solved it..
Let's say Marked price = M
So, there's a discount of 20% on M So, new S.P. = 80% of M
Now, the child convinces the owner to sell 20 candies for the price of 14 candies .
Let's say each candy after discount is 1$. So, S.P. of 20 candies = 20$. THe child bought it for 14 $ So, he got a discount of 6/20 *100 = 30%
So, the latest S.P. = 70% of 80% of M = 0.7* 0.8 M
Now, we are given that the shopkeeper still makes a profit of 12%. So we have ,
0.7 * 0.8 * M = 1.12 C.P
So, we get, M= 2 C.P.
i.e. Marked price was kept 100% above C.P.
C
Answer: C
Question: Two pipes P and Q can fill a cistern in 12 and 15 minutes respectively. Both are opened together, but at the end of 4 minutes the first is turned off. How many more minutes will it take for the cistern to fill after the first pipe is turned off?
Options:
A)6
B)7
C)8
D)9
E)10
Rationale: Let x be the total time it takes for the cistern to fill.
4/12 + x/15 = 1
x/15 = 2/3
x = 10
After the first pipe is turned off, it takes 6 more minutes to fill the cistern.
The answer is A.
Answer: A
Question: Gaurav spends 30% of his monthly income on food articles, 40% of the remaining on conveyance and clothes and saves 50% of the remaining. If his monthly salary is Rs. 18,400, how much money does he save every month ?
Options:
A)3864
B)2338
C)3799
D)1267
E)2991
Rationale: Explanation:
Saving = 50% of (100 - 40)% of (100 - 30)% of Rs. 18,400
= Rs. (50/100 * 60/100 * 70/100 * 18400) = Rs. 3864.
Answer: A) 3864
Answer: A
Question: 4 men and 6 women finish a job in 8 days, while 3 men and 7 women finish it in 10 days. In how
many days will 10 women working together finish it ?
Options:
A)30 days
B)40 days
C)50 days
D)60 days
E)None of these
Rationale: Explanation:
Let 1 man's 1 day work = x
and 1 woman's 1 days work = y.
Then, 4x + 6y = 1/8
and 3x+7y = 1/10
solving, we get y = 1/400 [means work done by a woman in 1 day]
10 women 1 day work = 10/400 = 1/40
10 women will finish the work in 40 days
Answer: B
Answer: B
Question: In a company of 15 employees, 6 employees earn $37,000, 5 employees earn $42,000, and the 4 highest-paid employees earn the same amount. If the average annual salary for the 15 employees is $45,000, what is the annual salary for each of the highest-paid employees?
Options:
A)$56,250
B)$57,750
C)$59,250
D)$60,750
E)$62,250
Rationale: 6*37,000+5*42,000+4x=15*45,000
4x=675,000-222,000-210,000
4x=243,000
x=60,750
The answer is D.
Answer: D
Question: $500 is divided amongst A,B and C so that A may get 2/3 as much as B and C together, B may get 6/9 as much as A and C together, then the share of A is
Options:
A)$100
B)$150
C)$125
D)$200
E)$250
Rationale: A:(B+C) = 2:3
A's share = 500*2/5 = $200
Answer is D
Answer: D
Question: Eight years ago, P was half of Q in age. If the ratio of their present ages is 3:4, what will be the total of their present ages
Options:
A)A)35
B)B)28
C)C)45
D)D)25
E)E)26
Rationale: Explanation:
Let the present age of P and Q be 3x and 4x respectively.
Eight years ago, P was half of Q in age
=> 2(3x – 8) = (4x – 8)
=> 6x – 16 = 4x – 8
=> 2x = 8
=> x = 4
7x=7*4=28
Answer: Option B
Answer: B
Question: 28 is divided into two parts in such a way that seventh part of first and ninth part of second are equal. Find the smallest part?
Options:
A)13.25
B)38.25
C)33.25
D)12.25
E)31.25
Rationale: x/7 = y/9 => x:y = 7:9
7/16 * 28 = 12.25
ANSWER:D
Answer: D
Question: If the number is divided by 3, it reduced by 24. The number is
Options:
A)A)51
B)B)50
C)C)45
D)D)40
E)E)36
Rationale: Explanation:
Let the number be x. Then,
x - (x/3) = 24 => 2x/3 = 24
=> x = 36
Answer: Option E
Answer: E
Question: A grocer has a sale of Rs. 3435, Rs. 3927, Rs. 3855, Rs. 4230 and Rs. 3562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 3500?
Options:
A)s. 1991
B)s. 2991
C)s. 3991
D)s. 4991
E)s. 5991
Rationale: Explanation:
Total sale for 5 months = Rs. (3435 + 3927 + 3855 + 4230 + 3562) = Rs. 19009.
Required sale = Rs. [ (3500 x 6) â€“ 19009 ]
= Rs. (21000 â€“ 19009)
= Rs. 1991.
Answer A
Answer: A
Question: A man buys an article and sells it at a profit of 20%. If he had bought it at 20% less and sold it for Rs.74 less, he could have gained 25%. What is the cost price?
Options:
A)s.370
B)s.375
C)s.375
D)s.350
E)s.300
Rationale: CP1 = 100 SP1 = 120
CP2 = 80 SP2 = 80 * (125/100) = 100
20 ----- 100
74 ----- ? => 370
ANSWER:A
Answer: A
Question: Ian is paid an hourly wage, totaling $400 for h hours of work in a week, where h >0. If Ian's hourly wage increases by 25% and Ian decides to work 25% fewer hours each week, how much will Ian be paid in a week?
Options:
A)$200
B)$375
C)$400
D)$425
E)$600
Rationale: let No of hours ian worked = h
and wage per hour = w
therefore w*h = 400
if he decides to work 25% fewer hours = 0.75 * h
and 25% more age is paid = 1.25 * w
therefore 1.25*w*0.75*h = 1.25*0.75*400 = 375
ANSWER:B
Answer: B
Question: A and B go around a circular track of length 400 m on a cycle at speeds of 36 kmph and 36 kmph. After how much time will they meet for the first time at the starting point?
Options:
A)40 sec
B)198 sec
C)178 sec
D)665 sec
E)276 sec
Rationale: Time taken to meet for the first time at the starting point
= LCM { length of the track / speed of A , length of the track / speed of B}
= LCM { 400/ (36 * 5/18) , 400/ (36 * 5 /18) }
= LCM (40, 40) = 40 sec.
Answer:A
Answer: A
Question: If 821562 is to be divisible by 5, what is the least whole number that should be added to it?
Options:
A)6
B)4
C)5
D)2
E)3
Rationale: A number is divisible by 8 if the number formed by the last three digits is divisible by 8.
Here, 821562 =562,
the next multiple of 9 is 568.
6 must be added to 821562 to make it divisible by 8
A
Answer: A
Question: If a:b=2:3 and b:c=2:4 find a:b:c?
Options:
A)6:2:3
B)2:6:3
C)2:3:6
D)3:2:6
E)6:3:2
Rationale: a:b = 2:3, b:c = 2:4
2:3
2:4
(a = a × b, b = b × b and c = b × c)
a:b:c = 2:3:6
C
Answer: C
Question: If x = -2 and y = -4, what is the value of 5(x-y)^2 - xy ?
Options:
A)12
B)13
C)15
D)18
E)22
Rationale: x = -2 and y = -4
x-y = -2 - (-4) = -2+4 = 2
x*y = -2 * -4 = 8
Now we apply it in the equation 5(x-y)^2 - xy =5 (2)^2-8
==>5*4 -8 = 20-8 =12
Answer : A
Answer: A
Question: Country X taxes each of its citizens an amount equal to 11 percent of the first $40,000 of income, plus 20 percent of all income in excess of $40,000. If a citizen of Country X is taxed a total of $8,000, what is her income?
Options:
A)$40,000
B)$56,000
C)$64,000
D)$58,000
E)$80,000
Rationale: Equation is correct, so math must be a problem.
0.11*40,000+0.2*(x-40,000)=8,000 --> 4,400+0.2x-8,000=8,000 --> 0.2x=11,600 --> x=58,000.
Answer: D.
Answer: D
Question: A sum fetched a total simple interest of Rs. 4016.25 at the rate of 8% p.a. in 5 years. What is the sum?
Options:
A)Rs. 10060.625
B)Rs. 10040.62
C)Rs. 12040.62
D)Rs. 20040.625
E)Rs. 10030.625
Rationale: Principal = (100 * 4016.25) / (8 * 5) = Rs. 10040.625.
ANSWER:B
Answer: B
Question: If any amount is distributed among A ,B and C so that the part of A is doubled that of the part of B and part of b is 3 time the part of C .Find the ratio among their parts.
Options:
A)1:2:4
B)1:4:1
C)8:4:1
D)2:4:1
E)6:3:1
Rationale: By the assumptions as mentioned we have A=2B and B=3C. So A=2(3C) and we get A=6C. We have, therefore, A:B:C = 6C:3C:C. By cancelling the ratio with C we have 6:3:1. The answer is, therefore, E.
Answer: E
Question: An antique shop has four different vases (vase 1, vase2, vase3, vase4) which are valued at different prices. If vase2 is 30% less in value than vase1, vase3 is 10% less than vase2, and vase4 is 5% less than vase3. what percent of vase1's cost is a vase3?
Options:
A)50.85%
B)59.85%
C)60.85%
D)40.5%
E)39.85%
Rationale: Let the cost of vase1 be $100
I) vase2 is 30% less in value than vase1--100-30=70
II) vase3 is 10% less than vase2--70-7=63
III) vase4 is 5% less than vase3--63-3.15=59.85
what percent of vase1's cost is a vase3=59.85*100/100
Answer is B
Answer: B
Question: A shopkeeper buys two articles for Rs.1000 each and then sells them, making 20% profit on the first article and 20% loss on second article. Find the net profit or loss percent?
Options:
A)200
B)962
C)267
D)258
E)268
Rationale: Profit on first article
= 20% of 1000
= 200.
This is equal to the loss he makes on the second article. That, is he makes neither profit nor loss.
Answer:A
Answer: A
Question: At a loading dock, each worker on the night crew loaded 3/4 as many boxes as each worker on the day crew. If the night crew has 5/6 as many workers as the day crew, what fraction of all the boxes loaded by the two crews did the day crew load?
Options:
A)4/7
B)5/9
C)6/11
D)7/12
E)8/13
Rationale: Let x be the number of workers on the day crew.
Let y be the number of boxes loaded by each member of the day crew.
Then the number of boxes loaded by the day crew is xy.
The number of boxes loaded by the night crew is (5x/6)(3y/4) = 5xy/8
The total number of boxes is xy + 5xy/8 = 13xy/8
The fraction loaded by the day crew is xy / (13xy/8) = 8/13
The answer is E.
Answer: E
Question: A man swims downstream 72 km and upstream 45 km taking 9 hours each time; what is the speed of the current?
Options:
A)1.8
B)1.5
C)1.3
D)1.2
E)1.6
Rationale: 72 --- 9 DS = 8
? ---- 1
45 ---- 9 US = 5
? ---- 1 S = ?
S = (8 - 5)/2 = 1.5
Answer: B
Answer: B
Question: The price of a bushel of corn is currently $3.20, and the price of a peck of wheat is $5.80. The price of corn is increasing at a constant rate of 5x5x cents per day while the price of wheat is decreasing at a constant rate of 2√∗x−x2∗x−x cents per day. What is the approximate price when a bushel of corn costs the same amount as a peck of wheat?
Options:
A)$4.50
B)$5.10
C)$5.30
D)$5.50
E)$5.60
Rationale: Let yy be the # of days when these two bushels will have the same price.
First let's simplify the formula given for the rate of decrease of the price of wheat: 2√∗x−x=1.41x−x=0.41x2∗x−x=1.41x−x=0.41x, this means that the price of wheat decreases by 0.41x0.41x cents per day, in yy days it'll decrease by 0.41xy0.41xy cents;
As price of corn increases 5x5x cents per day, in yy days it'll will increase by 5xy5xy cents;
Set the equation: 320+5xy=580−0.41xy320+5xy=580−0.41xy, solve for xyxy --> xy=48xy=48;
The cost of a bushel of corn in yy days (the # of days when these two bushels will have the same price) will be 320+5xy=320+5∗48=560320+5xy=320+5∗48=560 or $5.6.
Answer: E.
Answer: E
Question: If C + D = 12 and C and D are positive integers, which of the following is a possible value for 5C + 8D?
Options:
A)111
B)121
C)150
D)171
E)180
Rationale: c + d = 11
5c + 8d = 5c + 5d + 3d = 5(c+d) + 3d = 60 + 3d=D=30
D=30
c+d=12=C+30=9=C=12-30=-18
C=-18
5C + 8D=5(-18)+8(30)=-90+240=150
Hence, C is the right answer.
Answer: C
Question: Two years ago, Ram put $1,000 into a savings account. At the end of the first year, his account had accrued $200 in interest bringing his total balance to $1,200. The next year, his account balance increased by 20%. At the end of the two years, by what percent has Ram's account balance increased from his initial deposit of $1,000 ?
Options:
A)19%
B)30%
C)42%
D)45%
E)25%
Rationale: investment 1000 dollars
1 st year total gained = 200
total amount end of first year = 1200
second year account increased by 20 % = 1200*0.2 = 240
therefore total amount by second year end = 1420
so total percentage increase in money = (1420-1000)*100/1000 = 42 %
Correct Answer C=42%
Answer: C