divelab/Sys2Bench huggingface dataset:
Question: Mary and Mike enter into a partnership by investing $600 and $400 respectively. At the end of one year, they divided their profits such that a third of the profit is divided equally for the efforts they have put into the business and the remaining amount of profit is divided in the ratio of the investments they made in the business. If Mary received $1000 more than Mike did, what was the profit made by their business in that year?
Options:
A)$8500
B)$9500
C)$7000
D)$7500
E)$6500
Rationale: Explanatory Answer
Let the profit made during the year be $3x
Therefore, $x would have been shared equally and the remaining $2x would have been shared in the ratio 6 : 4.
i.e., 60% of 2x would go to Mary and 40% of 2x would go to Mike.
Hence, Mary would get (60 - 40)% of 2x more than Mike
Or20% of 2x = $1000
i.e.,(20/100)*2x = 1000
or 2x = 5000.
Hence, the profit made by the company during the year $3x = $7500.
Answer : D
Answer: D
Question: A and B together can do a work In 8 days. A alone can do it in 12 days. What time B will take to do the work alone?
Options:
A)6 days
B)8 days
C)12 days
D)24 days
E)25 days
Rationale: Explanation:
A and B 1day's work = 1/8
A alone can do 1day's work = 1/12
what time B will take to do the work alone?
B = (A+B) - A = (1/8) - (1/12) = 24 Days
Answer: Option D
Answer: D
Question: The average age of a man and his son is 28 years. The ratio of their ages is 3 :1 respectively. What is the man's age ?
Options:
A)30 years
B)38 years
C)44 years
D)42 years
E)None of these
Rationale: Total sum of man’s age & his son’s age =28 × 2 = 56 Now, the Ratio of their ages is 3 : 1.Therefore, Man’s age = (3/4) × 56 = 42
So, the correct answer is option D.
Answer: D
Answer: D
Question: In an election between two candidates, the winner has a margin of 20% of the votes polled. If 3000 people change their mind and vote for the loser, the loser would have won by a margin of 20% of the votes polled. Find the total number of votes polled in the election?
Options:
A)15000
B)20000
C)30000
D)60000
E)45000
Rationale: Winner - Looser
60% - 40%
If 3000 people change their mind and vote for the loser:
Winner - Looser
40% - 60%
Thus 3,000 people compose 20% of all voters, which means that the total number of votes is 15,000.
Answer: A
Answer: A
Question: The price of an item is discounted 10 percent on day 1 of a sale. On day 2, the item is discounted another 10 percent, and on day 3, it is discounted an additional 15 percent. The price of the item on day 3 is what percentage of the sale price on day 1?
Options:
A)28%
B)40%
C)64.8%
D)76.5%
E)72%
Rationale: original price = 100
day 1 discount = 10%,price = 100-10 =90
day 2 discount = 10%,price = 90-9=81
day 3 discount = 15%,price = 81-12.15= 68.85
which is 68.85/90 *100 of the sale price on day 1= ~76.5%
Answer D
Answer: D
Question: A shopkeeper buys mangoes at the rate of 7 a rupee and sells them at 5 a rupee. Find his net profit or loss percent?
Options:
A)40 %
B)90 %
C)33 %
D)35 %
E)30 %
Rationale: The total number of mangoes bought by the shopkeeper be 35.
If he buys 7 a rupee, his CP = 5
He selling at 5 a rupee, his SP = 7
Profit = SP - CP = 7 - 5 = 2
Profit Percent = 2/5 * 100 = 40 %
Answer:A
Answer: A
Question: If x is odd and y is odd, then xy,
Options:
A)Odd
B)Odd whenever x-y is even
C)Even whenever x+y is odd
D)Even
E)It cannot be determined
Rationale: x is odd and y is odd, then xy is
Let's take x=7 and y=3.
x*y=7*3=21.
x*y=odd.
Option: A
Answer: A
Question: find S.P when CP=56.25,gain=20%.
Options:
A)Rs 66.50
B)Rs 65.50
C)Rs 67.50
D)Rs 69.50
E)Rs 68.50
Rationale: SP =20% of Rs 56.25 ,=Rs{(120/100)*56.25}=Rs67.50
Answer is C
Answer: C
Question: A famous film director thought of an interesting story and he made a film in Hindi, Tamil and Telugu. He release the movie at the same time in all the three languages. The movie had Dhanush, Kamalhasan, Sruthi Hasan and Akdhsay Bachchan in lead role. The collections made was interesting to study. Collections in Hindi to Tamil and Tamil to Telugu was in the ratio 5: 4. If the collection made in language Tamil alone was Rs. 19753080, what was the total collection made.
Options:
A)Rs.60246894
B)Rs.26024689
C)Rs.22602468
D)Rs.22602469
E)none of these.
Rationale: making them in equal proportion of Hindi:Tamil:Telugu=25:20:16
and given 20x=19753080 so, x=987654
so, total collection is 61*x=60246894
ANSWER:A
Answer: A
Question: A man invests some money partly in 15% stock at 105 and partly in 8% stock at 40.To obtain equal dividends from both,he must invest the money in the ratio :
Options:
A)3 : 4
B)3 : 5
C)7 : 5
D)16 : 15
E)None
Rationale: Solution
For an income of Rs. 1 in 15% stock at 105, investment = Rs. (105/15)= Rs. 7.
For an income of Rs. 1 in 8% stock at 40, investment = Rs.(40/8) = Rs. 5.
∴ Ratio of investments = 7:5 =7:5
Answer C
Answer: C
Question: John is three times as old as Sam. If John will be twice as old as Sam in six years, how old was Sam three years ago?
Options:
A)2
B)3
C)6
D)8
E)16
Rationale: j= 3s
after 6 years
j +6 = 2(s+6)
j= 2s+6
2s +6 = 3s
s= 6
three years ago
s= 6-3= 3
B is the answer
Answer: B
Question: A distributor sells a product through an on-line store, which take a commission of 20% of the price set by the distributor. The distributor obtains the product from a producer at the price of $15 per item. What is the price that the buyer observers on-line if the distributor wants to maintain a 30% profit on the cost of the item?
Options:
A)18
B)21.6
C)22
D)25.7
E)27
Rationale: Producer price = $15;
The distributor wants to maintain a 20% profit on the cost of the item, thus he must get $15*1.2 = $18 after the store takes a commission of 30% of the final price --> (final price)*0.7 = $18 --> (final price) = $25.7.
Answer: D.
Answer: D
Question: 169, 289, 361, 529, 841, ?, F ind the missing number(?).
Options:
A)930
B)789
C)961
D)920
E)788
Rationale: The series consists of squares of consecutive PRIME numbers.
Answer : C.
Answer: C
Question: The price of an item is discounted 2 percent on day 1 of a sale. On day 2, the item is discounted another 12 percent, and on day 3, it is discounted an additional 25 percent. The price of the item on day 3 is what percentage of the sale price on day 1?
Options:
A)66%
B)67.5%
C)69%
D)70%
E)72%
Rationale: Let initial price be 1000
Price in day 1 after 2% discount = 980
Price in day 2 after 12% discount = 862.4
Price in day 3 after 25% discount = 646.8
So, Price in day 3 as percentage of the sale price on day 1 will be = 646.8/980*100 => 66%
Answer will definitely be (A)
Answer: A
Question: How many 6 digit telephone numbers can be formed if each number starts with 35 and no digit appears more than once?
Options:
A)720
B)360
C)1420
D)1680
E)None of these
Rationale: Explanation :
The first two places can only be filled by 3 and 5 respectively and there is only 1 way
of doing this
Given that no digit appears more than once. Hence we have 8 digits remaining(0,1,2,4,6,7,8,9)
So, the next 4 places can be filled with the remaining 8 digits in 8P4 ways
Total number of ways = 8P4 = 8 x 7 x 6 x 5 = 1680. Answer : Option D
Answer: D
Question: A train is 300 meter long is running at a speed of 35 km/hour. In what time will it pass a bridge of 115 meter length?
Options:
A)29
B)23
C)47.119
D)44.586
E)42.686
Rationale: Speed = 35 Km/hr = 35*(5/18) m/sec = 175/18 m/sec
Total distance = 300+115 = 415 meter
Time = Distance/speed
= 415 * (18/175) = 42.686 seconds.
Answer: E
Answer: E
Question: Two employees M and N are paid a total of $572 per week by their employer. If M is paid 120 percent of the salary paid to N, how much is N paid per week?
Options:
A)$220
B)$240
C)$260
D)$300
E)$320
Rationale: 1.2N + N = 572
2.2N = 572
N = 260
The answer is C.
Answer: C
Question: If A:B = 1/2: 1/3 B:C = 1/2:1/3 then A:B:C?
Options:
A)9:6:6
B)9:7:4
C)9:6:6
D)9:6:4
E)9:3:4
Rationale: A:B = 1/2:1/3 = 3:2
B:C = 1/2:1/3 = 3:2
--------------------
A:B:C = 9:6:4
Answer: D
Answer: D
Question: Two cycles are standing side-by-side. One cycle, which is 2.5 feets tall, casts a shadow that is 5
feets long. The other cycle is 2 feets tall. Compute, in feets, the length of the shadow that
the shorter cycle casts.
Options:
A)3
B)4
C)6
D)8
E)10
Rationale: The ratio of shadow to height is constant, so if x is the length of the shadow, then
2.5/5 = 2/x and x = 4 .
correct answer B
Answer: B
Question: A train 800 m long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 min, then the length of the tunnel is?
Options:
A)677 m
B)456 m
C)500 m
D)663 m
E)757 m
Rationale: Speed = 78 * 5/18 = 65/3 m/sec.
Time = 1 min = 60 sec.
Let the length of the train be x meters.
Then, (800 + x)/60 = 65/3
x = 500 m.
Answer: C
Answer: C
Question: Working together, Wayne and his son can shovel the entire driveway in three hours. If Wayne can shovel two times as fast as his son can, how many hours would it take for his son to shovel the entire driveway on his own?
Options:
A)4
B)3
C)8
D)9
E)12
Rationale: W: the time for Wyane to do the job
S: the time for his son to do the job
We have 1/W + 1/S = 1/2 and W = 2S
Then we have 1/(2*S) + 1/S = 1/2 <=> 3/(2*S) = 1/2<=> S = 3
ANS: B
Answer: B
Question: The ‘moving walkway’ is a 300-foot long conveyor belt that moves continuously at 3 feet per second. When Bill steps on the walkway, a group of people that are also on the walkway stands 120 feet in front of him. He walks toward the group at a combined rate (including both walkway and foot speed) of 6 feet per second, reaches the group of people, and then remains stationary until the walkway ends. What is Bill’s average rate of movement S for his trip along the moving walkway?
Options:
A)2 feet per second
B)2.5 feet per second
C)3 feet per second
D)4 feet per second
E)5 feet per second
Rationale: I get E.
Their rate is 3 ft/sec and his is 6 ft/sec. Their distance is d-120 and his distance is d.
So we get two equations:
3t=d-120
6t=d
Substituting, we get 3t=6t-120, or t=40 which means that d=240 so Bill traveled 240 ft and they traveled 120 ft. (They were at 240 on the conveyor belt when they met.
So, Bill's average rate of movement S is:
He traveled 6 ft/sec for 240 ft and 40 seconds. He traveled 3 ft/sec for the remaining 60 ft for 20 seconds.
(240+60)/(20+40)= 5 ft/sec=E
Answer: E
Question: A number when divided by a certain divisor left remainder 245, when twice the number was divided by the same divisor, the remainder was 112. Find the divisor?
Options:
A)378
B)365
C)380
D)456
E)460
Rationale: Easy solution:
N= Dq1+245
2N = 2Dq1 + 490 - (1)
2N = Dq2 + 112 - (2)
As (1) = (2) = 2N
D*(q2-2q1) = 378
D * Some integer = 378
Checking all options only (A) syncs with it.
Answer A
Answer: A
Question: The cost price of 20 arƟcles is the same as the selling price of x arƟcles. If the profit is 25%, find out
the value of x
Options:
A)13
B)14
C)15
D)16
E)17
Rationale: Explanation:
Let the Cost Price of one arƟcle = Rs. 1
CP of x articles = Rs. x
CP of 20 articles = 20
Selling price of x articles = 20
Profit = 25% [Given]
⇒
(SP−CPCP)=25100=14
⇒
(20−x)x=14
⇒
80−4x=x
⇒
5x=80
⇒
x=805=16
Answer: D
Answer: D
Question: In an election, candidate A got 75% of the total valid votes. If 15% of the total votes were declared invalid and the total numbers of votes is 560000, find the number of valid vote polled in favour of candidate
Options:
A)356000
B)356500
C)357000
D)400000
E)None of these
Rationale: Total number of invalid votes = 15 % of 560000
= 15/100 × 560000
= 8400000/100
= 84000
Total number of valid votes 560000 – 84000 = 476000
Percentage of votes polled in favour of candidate A = 75 %
Therefore, the number of valid votes polled in favour of candidate A = 75 % of 476000
= 75/100 × 476000
= 35700000/100
= 357000
C)
Answer: C
Question: The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is?
Options:
A)276 m
B)167 m
C)245 m
D)167 m
E)178 m
Rationale: Speed = [45 X 5/18] m/sec
= [25/2] m/sec Time
= 30 sec Let the length of bridge be x metres. Then, (130 + x)/30
= 25/2 => 2(130 + x) = 750 => x
= 245 m.
Answer:C
Answer: C
Question: What is the area of a square field whose diagonal of length 10 m?
Options:
A)50
B)70
C)60
D)20
E)25
Rationale: d2/2 = (10 * 10)/2
= 50
Answer:A
Answer: A
Question: In a certain town, there are eight times as many people who were born in the town’s state as there are people who were born in another state or country. The ratio of those residents born in the town’s state to the town’s total population is
Options:
A)1 to 4
B)1 to 3
C)1 to 2
D)3 to 4
E)8 to 9
Rationale: Town state: 8 times the whole town or country
then ratio will be 8(times)/9 total(times)
So the answer is 8/9.
E
Answer: E
Question: Find the sum of all odd numbers up to 100.
Options:
A)2500
B)2400
C)2300
D)2200
E)2100
Rationale: The given numbers are 1, 3, 5, 7, ..., 99.
This is an A.P. with a = 1 and d = 2.
Let it contain n terms. Then,
1 + (n - 1) x 2 = 99 or n = 50.
Required sum = n/2 (first term + last term)
= 50/2 (1 + 99) = 2500.
Answer is A.
Answer: A
Question: If xy ≠ 0 and x^2y^2 − 2xy = 8, which of the following could be y in terms of x?
I. 4/x
II. -x/2
III. 3/x
Options:
A)I only
B)II only
C)I and II
D)I and III
E)II and III
Rationale: (x^2)(y^2) – 2xy - 8 = 0
(xy – 4)(xy + 2) = 0
xy – 4 = 0 or xy + 2 = 0
xy = 4 or xy = -2
Since we need y in terms of x, we can isolate y in both of our equations.
y = 4/x or y = -2/x
Answer: A
Answer: A
Question: A rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered. If the area of the field is 560 sq. feet, how many feet of fencing will be required?
Options:
A)34
B)40
C)68
D)76
E)92
Rationale: Given that length and area, so we can find the breadth.
Length x Breadth = Area
20 x Breadth = 560
Breadth = 28 feet
Area to be fenced = 2B + L = 2 (28) + 20 = 76 feet answer : D
Answer: D
Question: If 1/(n – 2) = 1/(n + 2) + 1/(n – 1), which of the following is a possible value of n?
Options:
A)-3
B)0
C)3
D)-4
E)4
Rationale: Multiply by (n-2)*(n+2)*(n-1) throughout to get:
(n+2)*(n-1) = (n-2)*(n-1) + (n+2)(n-2)
Of the given options, only n=0 satisfies this.
Answer : B
Answer: B
Question: Katie owned ten times as many cats as she did dogs. If she adopted 4 more dogs, the ratio of cats to dogs would be 1 to 1. How many dogs and cats does Katie have total after adopting the 4 more dogs.
Options:
A)There is not enough information to solve the problem.
B)10
C)33
D)99
E)None of the Above
Rationale: By checking the answer choices:
Since we have an initial ratio of 10:1, the total count should be divisible by 11.
A. There is enough information to solve this problem, therefore A is not the correct choice.
B. Out, Since not divisible by 11.
C. 33/11=3, Cats = 30, Dogs = 3, Since 30-4 is not equal to 3+4, this is not the answer.
D. 99/11=9, Cats = 90, Dogs = 9, Since 90-4 is not equal to 9+4 this as well can not be the answer.
E. Since none of the choices above are correct, E is the answer.
E is the correct answer.
Answer: E
Question: If A:B = 1/4: 1/3 B:C = 1/4:1/3 then A:B:C?
Options:
A)9:12:6
B)9:2:16
C)9:12:16
D)9:12:14
E)19:12:16
Rationale: A:B = 1/4:1/3 = 3:4
B:C = 1/4:1/3 = 3:4
--------------------
A:B:C = 9:12:16
ANSWER:C
Answer: C
Question: A and B together have $ 1210. If of A's amount is equal to of B's amount, how much amount does B have?
Options:
A)$400
B)$489
C)$484
D)$365
E)%342
Rationale: (4/15)A=(2/5)B
=>A=((2/5)*(15/4))B
=>A=(3/2)B
=>A/B=3/2
A:B=3:2
B's share=rs.(1210*(2/5))=$484
Option C
Answer: C
Question: There are two numbers. If 30% of the first number is added to the second number, then the second number increases to its five-fourth. What is the ratio of the first number to the second number?
Options:
A)3 : 25
B)25 : 8
C)8 : 5
D)5 : 6
E)7 : 2
Rationale: Let the two numbers be x and y.
(3/10) * x + y = (5/4) * y
(3/10) * x = (1/4) * y
x/y = 10/12 = 5/6
The answer is D.
Answer: D
Question: The area of a rectangle is 24 cm2. The width is two less than the length. What is the length and width of the rectangle?
Options:
A)3
B)4
C)5
D)6
E)7
Rationale: Solution
Let x be the length and let x - 2 be the width
Area = lenth × width = x × ( x - 2) = 24
x × ( x - 2) = 24
x2 + -2x = 24
x2 + -2x - 24 = 0
Since -24 = 4 × -6 and 4 + -6 = -2, we get:
(x + 4) × ( x + -6) = 0
This leads to two equations to solve:
x + 4 = 0 and x + -6 = 0
x + 4 = 0 gives x = -4. Reject this value since a dimension cannot be negative
x + -6 = 0 gives x = 6
Therefore, length = 6 and width = x - 2 = 6 - 2 = 4
Answer B
Answer: B
Question: The area of a rectangular field is 144 m2. If the length had been 6 metres more, the area would have been 54 m2 more. The original length of the field is
Options:
A)22 metres
B)18 metres
C)16 metres
D)24 metres
E)None of these
Rationale: Let the length and breadth of the original rectangular field be x m and y m respectively.
Area of the original field = x × y = 144 m2
∴ x = 144⁄y .....(i)
If the length had been 6 m more, then area will be
(x + 6) y = 144 + 54
⇒ (x + 6)y = 198… (ii)
Putting the value of x from eq (i) in eq (ii), we get
(144⁄y + 6)y = 198
⇒ 144 + 6y = 198
⇒ 6y = 54 ⇒ y = 9m
Putting the value of y in eq (i) we get x = 16 m
Answer C
Answer: C
Question: If Rs.440 amount to Rs.540 in 4 years, what will it amount to in 6 years at the same rate % per annum?
Options:
A)s.575
B)s.595
C)s.590
D)s.580
E)s.585
Rationale: 80 = (440*4*R)/100
R = 5.68%
I = (440*6*5.68)/100 = 150
440 + 150 = 590
ANSWER:C
Answer: C
Question: The average salary of all the workers in a workshop is Rs.8000. The average salary of 7 technicians is Rs.8000 and the average salary of the rest is Rs.6000. The total number of workers in the workshop is
Options:
A)20
B)21
C)22
D)7
E)24
Rationale: Solution
Let the toatl number of workers be x.
Then 8000x=(8000 x 7) + 6000 (x -7)
x= 7.
Answer D
Answer: D
Question: If both 5^2 and 3^3 are factors of n x (2^5) x (6) x (7^3), what is the smallest possible positive value of n?
Options:
A)75
B)125
C)145
D)175
E)225
Rationale: (2^5) x (6) x (7^3) has one appearance of 3 (in the 6) and no appearances of 5.
Thus n must include at least 3^2 * 5^2 = 9 * 25 = 225
The answer is E.
Answer: E
Question: The average age 9 members of a committee are the same as it was 2 years ago, because an old number has been replaced by a younger number. Find how much younger is the new member than the old number?
Options:
A)7 yrs
B)10 yrs
C)18 yrs
D)20 yrs
E)25 yrs
Rationale: Explanation:
9 * 2 = 18 years
ANSWER C
Answer: C
Question: There are three foam generators in the factory, each of the first two can generate 10 liters of foam in one hour and the third can generate 16 liters in an hour. The three generators start working together at the same time and after one hour and a half one of the first generators stops working and two hours after that the third generator stops working and only one generator is left. If 5 hours after they all started to work the last generator stops working, how many liters of foam were generated?
Options:
A)120.
B)121
C)146.
D)154.
E)166.
Rationale: Let the foam generators capacity be -
A = 10 lit/hr
B = 10 lit/hr
C = 16 lit/hr
Total foam generation in 1 hour will be 36 lit ( 10 + 10 + 16 ) ; since in 1 and 1/2 hr they will generate 36 + 18 => 54 litres...
Now one of the first generators stops working ( Say A stops working ) , so we have -
B = 10 lit/hr
C = 16 lit/hr
Total foam generation in 2 hour will be 52 litres {2 (10+16)}
The third generator stops working and now only B works for the remaining time 1 and 1/2 ( 5 - 1 and 1/2 - 2 )...
Foam generated by B will be 3/2 * 10 => 15 litres
So, total foam generated will be 121 Litres ( 54 + 52 + 15 ) ; hence answer will be (B)
Answer: B
Question: If the length of an edge of cube M is five times the length of an edge of cube N, what is the ratio of the volume of cube N to the volume of cube M?
Options:
A)1/125
B)1/25
C)1/5
D)1/16
E)1/32
Rationale: The length of cube N = 1;
The length of cube M = 5;
The ratio of the volume of cube N to the volume of cube M = 1^3/5^3 = 1/125
Answer : A
Answer: A
Question: Two trains of equal lengths take 10 seconds and 15 seconds respectively to cross a telegraph post. If the length of each train be 120 metres, in what time (in seconds) will they cross each other travelling in opposite direction?
Options:
A)10
B)12
C)15
D)20
E)25
Rationale: Explanation:
Speed of the first train =120/10 m/sec = 12 m/sec.
Speed of the second train =120/15 m/sec = 8 m/sec.
Relative speed = (12 + 8) = 20 m/sec.
Therefore Required time =(120+120)/20 sec = 12 sec.
ANSWER IS B
Answer: B
Question: Of 30 applicants for a job, 12 had at least 4 years' experience, 19 had degrees, and 6 had less than 4 years' experience and did not have a degree. How many of the applicants had at least 4 years' experience and a degree?
Options:
A) 14
B) 13
C) 9
D) 7
E) 5
Rationale: set A : people with more than 4 years exp
set B : people with degree
AUB = total - (less than 4 exp and no degree)
AUB = 30-6=24
AUB = A + B - AiB
AiB = 19+12-24
=7
Answer D
Answer: D
Question: A man is 24 years older than his son. In two years, his age will be twice the age of his son. The present age of the son is?
Options:
A)16
B)19
C)15
D)22
E)10
Rationale: Let the son's present age be x years.
Then, man's present age = (x + 24) years.
(x + 24) + 2 = 2(x + 2) x + 26 = 2x + 4
=> x = .
Answer: D
Answer: D
Question: The average amount with a group of seven numbers is Rs. 20. If the newly joined member has Rs. 38 with him, what was the average amount with the group before his joining the group?
Options:
A)s.17
B)s.12
C)s.15
D)s.22
E)s.12
Rationale: Total members in the group = 7
Average amount = Rs. 20
Total amount with them = 7 * 20 = Rs. 140
One number has Rs. 38. So, the amount with remaining 6 people = 140 - 38 = Rs. 102
The average amount with them = 102/6 = Rs.17.
Answer:A
Answer: A
Question: If 1*548 is divisible by 3, which of the following digits can replace *?
Options:
A)0
B)1
C)2
D)3
E)4
Rationale: Solution
1 + x + 5 + 4 + 8 = (18 + x).
Clearly, when x=0, then sum of digits divisible by 3.
Answer D
Answer: D
Question: A = {2, 3, 4, 5}
B = {4, 5, 6, 7, 8}
Two integers will be randomly selected from the sets above, one integer from set A and one integer from set B. What is the probability T that the sum of the two integers will equal 9 ?
Options:
A) 0.15
B) 0.20
C) 0.25
D) 0.30
E) 0.33
Rationale: Rearrange the first set:
A = {5,4,3,2}
B = {4,5,6,7, 8}
As you can see numbers in each column (the numbers of the same color) give the sum of 9. So there are 4 such pares possible, total # of pairs is 4*5=20. T=favorable/total=4/20=0.2.
Answer: B.
Or: we can select ANY number from set A (4/4=1) but in this case we must select its matching pair from set B (the number of the same color) and since there are only one matching pair of this particular number in B then the probability of this is 1/5. So, overall: T=1*1/5.
Answer: B.
Answer: B
Question: 3*15 + 3*16 + 3*19 + 11 = ?
Options:
A)125
B)126
C)130
D)148
E)161
Rationale: 3*15 + 3*16 + 3*19 + 11 = 45 + 48 + 57 + 11 = 161
The answer is E.
Answer: E
Question: A fashion designer sold a pair of jeans to a retail store for 40 percent more than it cost to manufacture the pair of jeans. A customer bought the pair of jeans for 10 percent more than the retailer paid for them. The price the customer paid was what percent greater than the cost of manufacturing the jeans?
Options:
A)54%
B)70%
C)75%
D)85%
E)95%
Rationale: find the product of the two increases: (1.4) * (1.1), which is 1.54 and a 54% increase.
A
Answer: A
Question: The perimeter of a rhombus is 68 cm and one of its diagonals is 16 cm. Find its area?
Options:
A)288
B)240
C)267
D)299
E)162
Rationale: 4a = 68 => a = 17
172 – 82 = 152
1/2 * 16 * 30 = 240
Answer:B
Answer: B
Question: In what time will a train 100 meters long cross an electric pole, if its speed is 180 km/hr
Options:
A)5 seconds
B)4.5 seconds
C)3 seconds
D)2 seconds
E)None of these
Rationale: Explanation:
First convert speed into m/sec
Speed = 180*(5/18) = 50 m/sec
Time = Distance/speed
= 100/50 = 2 seconds
Answer: D
Answer: D