divelab/Sys2Bench huggingface dataset:
Question: A housewife has 11 litre of solution that contains sodium carbonate solution and benzene solution in the ratio 3 : 1. She adds 250 ml of 3 : 2 solution of sodium carbonate and benzene solution to it and then uses 250 ml of the combined mixture to make strong organic solution How much of pure sodium carbonate solution is she left with?
Options:
A)1000 ml
B)912.5 ml
C)750 ml
D)720 ml
E)630 ml
Rationale: ln a mixture of 1,000 ml sodium carbonate : benzene solution = 3 : 1.
Hence, sodium carbonate: 750 ml benzene solution 250 ml
A 250 ml of 3 : 2 solution contains 150 ml sodium carbonate solution and l00ml benzene solution.
Total sodium carbonate solution = 900 ml, total benzene solution = 350 ml
After using 250 ml to make strong organic solution , sodium carbonate solution used
= 250/1250 x 900 = 180 ml
pure sodium carbonate solution left = 900 -180 =720ml
ANSWER:D
Answer: D
Question: Set X consists of the integers from 10 to 15, inclusive, while set Y consists of the integers from 5 to 10, inclusive. How many distinct integers do belong to the both sets at the same time?
Options:
A)5
B)8
C)4
D)1
E)9
Rationale: X= {10, 11, 12,13,14,15}
Y = {5,6, 7, 8, 9, 10}
Common elements = {10} = 1 element
Answer: Option D.
Answer: D
Question: Which of the following is the Highest Common Factor of 49, 63 and 77?
Options:
A)8
B)10
C)7
D)14
E)12
Rationale: THE HIGHEST COMMON FACTOR IS 7Ans is :C
Answer: C
Question: A hare and a jackal are running a race. Three leaps of the hare are equal to four leaps of the jackal. For every one leap of the hare, the jackal takes two leaps. Find the ratio of the speed of the hare to the speed of the jackal.
Options:
A)4:5
B)8:5
C)5:8
D)2:3
E)5:3
Rationale: The hare takes 1 leap and the jackal takes 2 leaps.
1 hare leap = 4/3 jackal leaps
Thus the hare's 1 leap = 4/3 jackal leaps.
The ratio of their speeds is 4/3:2 = 4:6 = 2:3.
The answer is D.
Answer: D
Question: In how many different number of ways 4 boys and 3 girls can sit on a bench such that girls always sit together?
Options:
A)720
B)740
C)760
D)780
E)790
Rationale: Option 'A'
Answer: A
Question: A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If three marbles are picked at random, what is the probability that they are all blue?
Options:
A)1/455
B)91/55
C)1/495
D)1/655
E)1/451
Rationale: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles.
Probability that all the three marbles picked at random are blue = ³C₃/¹⁵C₃ = (1 * 3 * 2 * 1)/(15 * 14 * 13) = 1/455.Answer: A
Answer: A
Question: In Goshawk-Eurasian nature reserve 30 percent of the birds are Hawks, and 40 percent of the non-Hawks are Paddyfield-Warblers. If there are 25 percent as many Kingfishers as Paddyfield-Warblers in the reserve, then what percent of the birds in the nature reserve are not Hawks, Paddyfield-Warblers, or Kingfishers?
Options:
A)25%
B)35%
C)45%
D)70%
E)80%
Rationale: Since the problem doesn't depend on the number of birds in reserve you can suppose that there are 100 birds.
From them 100*0.3=30 are Hawks.So, there are 70 non-Hawks.
There are 0.4*70=28 Paddyfield-Warblers. Therefore, there are 0.25*28=7 Kingfishers.
The total number of birds in the nature reserve that are not Hawks, Paddyfield-Warblers, or Kingfishers is 100-30-28-7=35.
The answer is B
Answer: B
Question: A trader purchased on old bicycle for 480. He spent 20% of the cost on its repair. If he wants to earn 144 as net profit on it, how much percentage should he add to the purchase price of the bicycle?
Options:
A)50%
B)48%
C)96%
D)100%
E)None of these
Rationale: Purchase price = 480
Repair cost = 20% of 480 = 96
∴ Total cost =480 + 96 = 576
Net profit = 144
∴ Selling price = Total cost + Net
profit= 576 + 144 = 720
Now, Selling price - Purchase price
= 720 – 480 = 240
∴ Reqd percentage = 240⁄280 × 100 = 50%
Answer A
Answer: A
Question: The present worth of $169 due in 2 years at 4% per annum compound interest is?
Options:
A)$145.89
B)$138.62
C)$156.25
D)$160.23
E)$158.95
Rationale: Present worth = 169/ (1 + 4/100)^2 = 169 * 25/26 * 25/26 = $156.25
Answer is C
Answer: C
Question: What least number mustbe subtracted from 427398 so that remaining no.is divisible by 15
Options:
A)3
B)5
C)7
D)8
E)9
Rationale: Explanation:
On dividing 427398 by 15 we get the remainder 3, so 3 should be subtracted
Answer: Option A
Answer: A
Question: Here is 15 dots. If you select 3 dots randomly, what is the probability that 3 dots make a triangle?
Options:
A)412/4228
B)412/455
C)412/429
D)412/418
E)412/419
Rationale: I think there seem some problem with this question. Total ways of selecting 3 dots out of 15 is 15C315C3 = 455 If 3 dots are collinear then triangle may not be formed. Now look at the above diagram. If we select any 3 dots from the red lines they may not form a triangle. They are 3 x 5C35C3 = 30. If we select the three letters from blue lines, they may not form a triangle. They are in total 5 ways. Also there are 6 others lines which don't form a triangle. Also another two orange lines. Total = 30 + 5 + 6 + 2 = 43. So we can form a triangle in 455 - 43 = 412. So answer could be 412/455.
\Answer:B
Answer: B
Question: Ten animals of a circus has to be placed inside in ten cages one in each cage. If 4 of the cage are too small for 6 of the animal then find the number of ways of caging the animal.
Options:
A)A.464
B)B.808
C)C.5024
D)D.86400
E)E.302400
Rationale: ways for cages that are too small = 5*4*3*2=120
since we have 6 cages and 6 animal left therefore ways for 6 cages =6!
total ways =120*6!=86400
Answer D
Answer: D
Question: What least number should be added to 1015, so that the sum is completely divisible by 25?
Options:
A)4
B)3
C)2
D)10
E)5
Rationale: 1015 Ã· 25 = 40 with remainder = 15
15 + 10 = 25.
Hence 10 should be added to 1015 so that the sum will be divisible by 25
Answer: Option D
Answer: D
Question: If Re.250 amounts to Rs.550 over a period of 4 years. What is the rate of simple interest?
Options:
A)31%
B)28%
C)25%
D)22%
E)30%
Rationale: 300 = (250*4*R)/100
R = 30%
Answer:E
Answer: E
Question: if x/4-x-3/6=1,then find the value of x.
Options:
A)12
B)10
C)8
D)6
E)4
Rationale: (x /4)-((x-3)/6)=1
(3x-2(x-3) )/12 = 1
3x-2x+6=12
x=6.
Option D
Answer: D
Question: 5 men are equal to as many women as are equal to 8 boys. All of them earn Rs.105 only. Menâ€™s wages are?
Options:
A)6Rs
B)7Rs
C)8Rs
D)4Rs
E)1Rs
Rationale: 5M = xW = 8B
5M + xW + 8B ----- 105 Rs.
5M + 5M + 5M ----- 105 Rs.
15M ------ 105 Rs. => 1M = 7Rs.
Answer:B
Answer: B
Question: Solve the given two equations and find the inequality of X and Y.(a) x^2-7x+12=0 and (b) y^2+y-12=0
Options:
A)If x>y
B)If x>=y
C)If x<y
D)If x<=y
E)x=y or relationship cannot be established
Rationale: Solution:-
X=4,3
Y=-4,3
So, X>=Y
B
Answer: B
Question: Laura can paint 1/x of a certain room in 20 minutes. What fraction W of the same room can Joseph paint in 20 minutes if the two of them can paint the room in an hour, working together at their respective rates?
Options:
A)1/(3x)
B)3x/(x-3)
C)(x – 3)/(3x)
D)x/(x-3)
E)(x-3)/x
Rationale: Options with variables are often done by plugging in numbers.
Both working together can paint the room in 1 hr so if their individual rates were equal, each would take 2 hours alone.
2 hours is 120 mins so in 20 mins each would complete W=120/20 = 1/6th of the room alone.
So if x = 6 (Laura completes 1/6th of the room in 20 mins), the correct option will give 1/6. (Joseph will also paint 1/6th of the room if their rates are same)
If you put x = 6 in the options, only option (C) will give 1/6
Answer (C)
Answer: C
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 Q 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 welder received an order to make a 1 million liter cube-shaped tank. If he has only 4x2 meter sheets of metal that can be cut, how many metal sheets will be required for this order P? (1 cubic meter = 1,000 liters)
Options:
A)92
B)90
C)82
D)78
E)75
Rationale: I get 75. A cube with 1 million liters cube would be a cube with the dimensions of 100*100*100. 4*2 covers 8 sq liters so 100/8 = 12.5.
P=12.5*6 = 75.E
Answer: E
Question: 12 business executives and 7 chairmen meet at a conference. If each business executive shakes the hand of every other business executive and every chairman once, and each chairman shakes the hand of each of the business executives but not the other chairmen, how many handshakes would take place?
Options:
A)150
B)131
C)115
D)90
E)45
Rationale: there are 12 business exec and in each handshake 2 business execs are involved.
hence 12C2=66
Also, each of 12 exec will shake hand with every 7 other chairmen for total of 84 handshake.
total=66+84=150
ANS: A
Answer: A
Question: If north becomes south-west ant south-west becomes east and all the directions changed in the same manner,then what will be the direction for south-east?
Options:
A)North-West
B)North-East
C)North
D)West
E)none
Rationale: North -> South-west
North-east -> West
East -> North-west
South-east -> North
South -> North-east
South-west -> east
West -> South-east
North-west -> south
ANSWER:C
Answer: C
Question: Jane makes toy bears. When she works with an assistant, she makes 80 percent more bears per week and works 10 percent fewer hours each week. Having an assistant increases Jane’s output of toy bears per hour by what percent Q?
Options:
A)20%
B)80%
C)100%
D)180%
E)200%
Rationale: C.
Let's assume just Jane 40 bears per 40/hrs a week, so that is 1 bear/hr. With an assistant she makes 72 bears per 36 hours a week or 2 bears/hr ([40 bears * 1.8] / [40 hrs * .90]).
Q=[(2 - 1)/1] * 100% = 100%
Answer: C
Question: In the xy-plane, the points (c, d), (c, -d), and (-c, -d) are three vertices of a certain square. If c < 0 and d > 0, which of the following points M is in the same quadrant as the fourth vertex of the square?
Options:
A)(-5, -3)
B)(-5, 3)
C)(5, -3)
D)(3, -5)
E)(3, 5)
Rationale: The question:In the xy-plane, the points M=(c, d), (c, -d), and (-c, -d) are three vertices of a certain square.If c < 0 and d > 0,which of the following points is in the same quadrant as the fourth vertex of the square?
I marked the tricky part in red. It seems c is anegativenumber and d is a positive number. This means
Vertex #1 = (c, d) is in QII (that is, negative x and positive y)
Vertex #2 = (c, -d) is in QIII (that is, both xy negative)
Vertex #3 = (-c, -d) is in QIV (that is y is negative, but x is positive)
That means the last vertex should be in the first quadrant --- the only first quadrant point is (5, 3), answer =E.
Answer: E
Question: Rs. 925 becomes Rs. 956 in 3 years at a certain rate of simple interest.If the rate of interest is increased by 4% ,What amount will Rs. 925 become in 3 years ?
Options:
A)Rs. 1020.80
B)Rs. 1025
C)Rs. 1067
D)Data inadequate
E)None of these
Rationale: Solution
S.I. = Rs.(956-925 )=Rs.31
Rate = (100x31/925x3) =124/111%
New rate = (124/111 +4)% = 568/111%
New S.I. = Rs.(925 x 568/111 x 3/100) Rs. 142
∴ New amount = Rs.(925+142)= Rs. 1067.
Answer C
Answer: C
Question: If x < y < z and y - x > 5, where x is an even integer and y and z are odd integers, what is the least possible value Q of z - x?
Options:
A)6
B)7
C)8
D)9
E)10
Rationale: x<y<z
To find the least possible value for z-x; we need to find the values for z and x that can be closest to each other. If x is some even number, then what could be minimum possible odd z.
If x is some even number
y-x>5; y>x+5; minimum value for y=x+5+2=x+7[Note: x+5 is as even+odd=odd and nearest odd greater than x+5 is x+5+2]
Minimum value for z=y+2=x+7+2=x+9 [Note: z=y+2 because both z and y are odd. Difference between two odd numbers is 2]
Q=z-x = x+9-x= 9
Ans:D
Answer: D
Question: Find large number from below question The difference of two numbers is 1385. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder
Options:
A)1254
B)1376
C)1659
D)1555
E)1635
Rationale: Let the smaller number be x. Then larger number = (x + 1385).
x + 1385 = 6x + 15
5x = 1370
x = 274
Large number = 274+1385 = 1659
C
Answer: C
Question: A Mersenne number is a positive integer that is one less than any power of 2. A Mersenne prime is a Mersenne number that also happens to be prime. The largest known prime number, 2^(43112609) - 1, is a Mersenne prime. If the largest known Mersenne prime were multiplied by the smallest Mersenne prime, which of the following would represent the units digit of the product?
Options:
A)2
B)3
C)4
D)6
E)8
Rationale: First of all, think which is the smallest Mersenne prime?
The smallest prime 1 less than a power of 2 is 3.
We need the last digit of 2^{43112609} - 1. What will be the last digit of 2^{43112609}?
Recall cyclicity of last digits. After every 4 powers, the last digit repeats itself. Let's look at the last digits of powers of 2.
2^1 = 2
2^2 = 4
2^3 = 8
2^4 = 6
2^5 = 2
2^6 = 4
and so on...
When 43112609 is divided by 4, you get remainder 1 (divide just the last two digits by 4. Whatever remainder you get will be the remainder when you divide the actual number by 4)
So the last digit of 2^{43112609} is 2
Last digit of 2^{43112609} - 1 is 1
Product of the last digits is 1*3 = 3
Answer (B)
Answer: B
Question: Two trains of length 200 m and 300 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 36 kmph and 72 kmph. In how much time will the trains cross each other?
Options:
A)87/7 sec
B)20 sec
C)80/9 sec
D)80/5 sec
E)20/7 sec
Rationale: Relative speed = (36 + 72)* 5/18 = 6 * 5 = 30 mps.
The time required = d/s = (100 + 200 + 300)/30
= 600/30 = 20 sec.
Answer: B
Answer: B
Question: The probability of a lottery ticket being a prized ticket is 0.2. When 4 tickets are purchased, the probability of winning a prize on atleast one ticket is?
Options:
A)0.5919
B)P(E)=0.5904
C)0.5929
D)0.5928
E)0.594
Rationale: P(winning prize atleast on one ticket)
= 1 - P("Losing on all tickets")
= 1 - (0.8)4 = (1 + (0.8)2)(1 - (0.8)2)
= (1.64)(0.36) = 0.5904
Answer: B
Answer: B
Question: There are 100 students in a college class of which 36 are boys studying Tamil & 13 girls not studying Tamil. If there are 55 girls in all, then the probability that a boy picked up at random is not studying Tamil, is
Options:
A)1/5
B)2/3
C)3/5
D)3/7
E)3/8
Rationale: There are 55 girls and 45 boys in the college. Out of 45 boys, 36 are studying Tamil and 9 are not studying Tamil. The probability that a boy picked up at random is not studying Tamil= 9/45 = 1/5
A
Answer: A
Question: If the average cost of a house was $50,000 in 1960 and was x in 2005, what was the average increase in home prices per year over this period?
Options:
A)A)(x+50,000)/40
B)E)x/40
C)C)(50,000/40)+x
D)D)(50,000-x)/40
E)B)(x-50,000)/45
Rationale: Average house price in 2005: x
Average house price in 1965: 50,000
2005-1960=45
Average increase per year: (x-50,000)/45
Answer is E
Answer: E
Question: The total of the ages of Amar, Akbar and Anthony is 50 years. What was the total of their ages three years ago ?
Options:
A)48 years
B)42 years
C)41 years
D)47 years
E)45 years
Rationale: Explanation:
Required sum = (50 - 3 x 3) years = (50 - 9) years = 41 years.
Answer: Option C
Answer: C
Question: Vijay bought 160 shirts at the rate of Rs. 200 per shirt. The transport expenditure was Rs. 1400. He paid an octroi at the rate of Rs. 1.75 per shirt and labour charges were Rs. 320. What should be the selling price of one shirt, if he wants a profit of 20%?
Options:
A)s.225
B)s.288
C)s.485
D)s.255
E)s.282
Rationale: Total CP per shirt = 200 + 1400/160 + 1.75 + 320/160 = Rs. 212.5
SP = CP[(100 + profit%)/100]
= 212.5 * [(100 + 20)/100] = Rs.255.
Answer:D
Answer: D
Question: 864.942 - ? + 45.76 = 547.905
Options:
A)A)899.015
B)B)752.804
C)C)714.642
D)D)362.797
E)of these
Rationale: Explanation:
362.797
Answer: Option D
Answer: D
Question: In an examination, 300 students appeared. Out of these students; 30 % got first division, 54 % got second division and the remaining just passed. Assuming that no student failed; find the number of students who just passed.
Options:
A)33
B)37
C)54
D)99
E)48
Rationale: The number of students with first division = 30 % of 300 = 30/100 × 300 = 9000/100 = 90
And, the number of students with second division = 54 % of 300
= 54/100 × 300
=16200/100
= 162
Therefore, the number of students who just passed = 300 – (90 + 162) = 48
Answer:E
Answer: E
Question: A rock is dropped into a well and the distance traveled is 16 t 2 feet, where t is the time. If the water splash is heard 3 seconds after the rock was dropped, and that the speed of sound is 1100 ft / sec, approximate the height of the well
Options:
A)134.8 feet
B)136.2 feet
C)132.7 feet
D)132.2 feet
E)115.3 feet
Rationale: Let T1 be the time it takes the rock to reach the bottom of the well. If H is the height of the well, we can write
H = 16 T1 2
Let T2 be the time it takes sound wave to reach the top of the well. we can write
H = 1100 T2
The relationship between T1 and T2 is
T1 + T2 = 3
Eliminate H and combine the equations H = 16 T1 2 and H = 1100 T2 to obtain
16 T1 2 = 1100 T2
We now substitute T2 by 3 - T1 in the above equation
16 T1 2 = 1100 (3 - T1)
The above is a quadratic equation that may be written as
16 T1 2 + 1100 T1 - 3300 = 0
The above equations has two solutions and only one of them is positive and is given by
T1 = 2.88 seconds (2 decimal places)
We now calculate the height H of the well
H = 16 T1 2 = 16 (2.88) 2 = 132.7 feet
Answer C
Answer: C
Question: If (10^4 * 3.456789)^10 is written as a single term, how many digits would be to the right of the decimal place?
Options:
A)12
B)16
C)20
D)32
E)48
Rationale: 3.456789^10 has 6*10 = 60 decimal places.
10^40 moves the decimal place to the right 40 places.
(10^4 * 3.456789)^10 has 60-40 = 20 digits after the decimal point.
The answer is C.
Answer: C
Question: If 1 is added to the denominator of fraction, the fraction becomes
1/2. If 1 is added to the numerator, the fraction becomes 1. The fraction is
Options:
A)4/7
B)5/9
C)2/3
D)10/11
E)None of these
Rationale: Explanation:
Let the required fraction be a/b. Then
⇒a/b+1=1/2⇒2a–b=1 ---- (1)
⇒a+1/b=1⇒a–b=–1⇒a–b=–1 ------- (2)
Solving (1) & (2) we get a = 2, b=3
Fraction = a/b=2/3
Correct Option: C
Answer: C
Question: 5 men and 12 boys finish a piece of work in 4 days, 7 men and 6 boys do it in 5 days. The ratio between the efficiencies of a man and boy is?
Options:
A)6:9
B)6:89
C)6:0
D)6:5
E)6:1
Rationale: 5M + 12B ----- 4 days
7M + 6B ------- 5 days
20M + 48B = 35M + 30B
18B = 15M => 5M = 6B
M: B = 6:5
Answer: D
Answer: D
Question: a lady's age is between 50 and 70.each of her sons has many sons as his
brothers. the sum of the sons and grandsons in the lady's age. what is her age?
Options:
A)61
B)62
C)63
D)64
E)65
Rationale: Let assume Lady has 'N' children.
Each child have (N-1) children. (Grandsons for that lady).
S0, total children = N+(N*(N-1))
By, putting N=6, we get 6+(6*(6-1)) = 36 childrens.
By, Putting N=7, we get 7+(7*(7-1)) = 49 childrens.
By, putting N=8, we get 8+(8*(8-1)) = 64 childrens.
By, putting N=9, we get 9+(9*(9-1)) = 81 childrens.
Here, Lady's age between 50 to 70.
So, answer is 64.
ANSWER:D
Answer: D
Question: If five persons sit in a row, then the probability that three particular persons are always together is?
Options:
A)3/5
B)3/4
C)1/9
D)1/6
E)3/10
Rationale: Five persons can be arranged in a row in 5! ways.
Treat the three persons to sit together as one unit then there three persons and they can be arranged in 3! ways.
Again three persons can be arranged among them selves in 3! ways.
Favourable outcomes = 3!3!
Required probability = 3!3!/5! = 3/10
Answer:E
Answer: E
Question: If a,b,c,d,e are five consecutive odd numbers, their average is :
Options:
A)22
B)77
C)288
D)22
E)20
Rationale: Correct Option: D
Explanation:
If the first number is a, then the remaining numbers a a +2, a+4, a + 6, a + 8
Average : = (a+(a+2)+(a+4)+(a+6)+(a+8)5)=(a+4)
Answer:A
Answer: A
Question: A pump can fill a tank with water in 2 hours. Because of a leak, it took 2 hours to fill the tank. The leak can drain all the water of the tank in?
Options:
A)7 hrs
B)8 hrs
C)10 hrs
D)12 hrs
E)14 hrs
Rationale: Work done by the leak in 1 hour = 1	-	3 =	1	.
2	7	14
Leak will empty the tank in 14 hrs.
E)
Answer: E
Question: A password of a computer used five digits where they are from 0 and 9. What is the probability that the first digit of the password is a 0 and the second digit is even ?
Options:
A)1/10
B)1/15
C)1/20
D)1/100
E)1/200
Rationale: There is one possibility out of ten that the first digit is zero, and five possibilities out of ten that the second digit is even. We don't care about the remaining digits, so the overall probability is 1/10 * 5/10 or 1/20 or answer C.
Answer: C
Question: Tickets to a certain concert sell for $20 each. The first 10 people to show up at the ticket booth received a 40% discount, and the next 20 received a 15% discount. If 56 people bought tickets to the concert, what was the total revenue from ticket sales?
Options:
A)$600
B)$740
C)$850
D)$980
E)$1,140
Rationale: Price of 1 ticket = 20$
Revenue generated from sales of first 10 tickets = 10 * (60/100 * 20 )
= 10 * 12 = 120
Revenue generated from sales of next 20 tickets = 20 *(85/100 * 20 )
=20*17 = 340
Revenue generated from sales of last 26 tickets = 20 * 26
= 520
Revenue generated from sales of 56 tickets = 120 + 340 + 520
= 980 $
Answer D
Answer: D
Question: There is food for 760 men for 22 days. How many more men should join after two days so that the same food may last for 5 days more?
Options:
A)2280
B)2240
C)2299
D)2288
E)2266
Rationale: 760 ---- 22
760 ---- 20
x ----- 5
x*5 = 760*20
x = 3040
760
-------
2280
Answer: A
Answer: A
Question: If xyz represents a positive three-digit number, where x, y and z are one-digit integers, which of the following CANNOT be true?
Options:
A)y – x - z = 9
B)x – y - z = 9
C)x + y + z = 9
D)xyz = 9
E)x/y/z = 9
Rationale: The (hundreds place digit, x) cannot be zero, but (tens and ones place digits; y and z) can be zero.
A is NOT possible
B is possible
C is possible
D is possible
E is possible
Answer: A
Answer: A
Question: The denominator of a fraction is 7 greater than the numerator. If the numerator and the denominator are increased by 4, the resulting fraction is equal to 5â„6. What is the value of the original fraction?
Options:
A)23/30
B)25/32
C)31/38
D)37/44
E)47/54
Rationale: Let the numerator be x.
Then the denominator is x+7.
x+4 / x+11 = 5/6.
6x+24=5x+55.
x=31.
The original fraction is 31/38.
The answer is C.
Answer: C