divelab/Sys2Bench huggingface dataset:
Question: What is the sum of all possible solutions to the equation √2x^2−x−9 = x+1 ?
Options:
A)-2
B)2
C)3
D)5
E)6
Rationale: First of all notice that since LHS is the square root of a number, it must be non-negative (the square root function cannot give negative result), then the RHS must also be non-negative: x+1≥0 --> x≥−1
Square the equation: 2x^2−x−9=x^2+2x+1 --> x^2−3x−10=0 --> x=-2 or x=5. Discard x=-2 because it's not >=-1. We are left with only one root: 5.
Answer: D
Answer: D
Question: Jayes can eat 25 marshmallows is 20 minutes. Dylan can eat 25 in one hour. In how much time will the two eat 150 marshmallows?
Options:
A)40 minutes.
B)1 hour and 30 minutes.
C)1 hour.
D)1 hour and 40 minutes.
E)2 hours and 15 minutes.
Rationale: Rate =Output/Time
Jayes Rate=25/20=5/4
Dylan Rate=25/60=5/12
Combined rate = 5/4+5/12= 20/12
CombinedRate*CombinedTime= CombinedOutput
20/12*t=150
t=90 mins => 1 hr 30 min
Answer: C
Question: What positive number, when squared, is equal to the cube of the positive square root of 14?
Options:
A)64
B)32
C)8
D)4
E)2
Rationale: Let the positive number be x
x^2 = ((16)^(1/2))^3
=>x^2 = 4^3 = 4
=> x =4
Answer D
Answer: D
Question: A money lender lends Rs.1500 for six months at 20% p.a. rate. It the interest is reckoned quarterly than find the amount given after time limit?
Options:
A)2205
B)1978
C)1653.75
D)2827
E)2781
Rationale: A = 1500(21/20)2
= 1653.75
Answer: C
Answer: C
Question: A welder received an order to make a 1 million liter cube-shaped tank. If he has only 2x5 meter sheets of metal that can be cut, how many metal sheets will be required for this order? (1 cubic meter = 1,000 liters)
Options:
A)92
B)90
C)60
D)78
E)75
Rationale: The question say:A welder received an order to make a 1 million liter cube-shaped tank. (1 cubic meter = 1,000 liters)
In other words, the tank is going to have a volume of 1000 cubic meters. That would equal 1 million liters.
A cube with a volume of 1000 cubic meters must be (10 meters) x (10 meters) x (10 meters).
The question doesn't specify whether this tank should have a closed top or an open top. (The real GMAT is good about specifying things like that.) Here, we are going to assume a closed top, only because if the top is open, we don't use enough metal --- we get an answer smaller than any of the answer choices. A closed-top cube, a full cube, has 6 sides, each of which is (10 meters) x (10 meters). That's a total surface area of 600 sq m.
The question tells us:he has only 2x5 meter sheets of metal that can be cut.
Each sheet has an area of 10 sq m. How many of these need to fill up 600 sq m? 600/10 = 60. He needs 60 sheets.
Answer =C
Answer: C
Question: If a man crosses a 600 m long street in 5 minutes. What is his speed?
Options:
A)6.9 km/hr
B)7 km/hr
C)7.2 km/hr
D)8.9 km/hr
E)9 km/hr
Rationale: distance = 600 meter
time = 5 minutes = 5 x 60 seconds = 300 seconds
Speed = distancetime=600300=2m/s=2×185 km/hr=365 km/hr=7.2 km/hr
C
Answer: C
Question: Find the area of trapezium whose parallel sides are 12 cm and 16 cm long, and the distance between them is 14 cm?
Options:
A)288 cm2
B)277 cm2
C)285 cm2
D)196 cm2
E)287 cm2
Rationale: Area of a trapezium = 1/2 (sum of parallel sides) * (perpendicular distance between them)
= 1/2 (12 + 16) * (14)
= 196 cm2
Answer: D
Answer: D
Question: 10, 15, 22.5, 33.75, 50.62, (...)
Options:
A)60
B)60.75
C)75.93
D)76.33
E)70.1
Rationale: 10
(10Ã—3)Ã· 2 = 15
(15Ã—3)Ã· 2 = 22.5
(22.5Ã—3)Ã· 2 = 33.75
(33.75Ã—3)Ã· 2 = 50.62
(50.62Ã—3)Ã· 2 = 75.93
Answer is C
Answer: C
Question: A can complete a project in 20 days while B can complete same project in 30 days. If A and B start working together and A leaves the work 15 days before completion of project, then in how many days the project will be completed?
Options:
A)18
B)19
C)20
D)21
E)22
Rationale: A's 1day work=1/20;
B's 1day work=1/30;
(A+B) 1day work=(1/20+1/30)=1/12;
It is given that A leaves the work 15 days before completion of the project..
Thus,B alone does the remaining job in 15 days.
So,In 15 days ,B can do 1/2 w ..
Thus,(A+B) have worked (1-1/2)=1/2 w..
(A+B)can do 1/12 work in 1 day...
They did 1/2 w in 6 days.
Total days=(6+15) = 21
ANSWER:D
Answer: D
Question: A dishonest dealer professes to sell goods at the cost price but uses a weight of 920 grams per kg, what is his percent?
Options:
A)22%
B)25%
C)77%
D)99%
E)8.7%
Rationale: 920 --- 80
100 --- ? => 8.7%
Answer: E
Answer: E
Question: Find the next number in the series
3,3,5,4,4,3,5,5,4,3,...
Options:
A)3
B)4
C)5
D)6
E)7
Rationale: (3, 3, 5), (4 ,4 ,3), (5, 5, 4), (3, x, y)
In first group , middle digit = 3
In 2nd group , middle digit = 4
In 3rd group , middle digit = 5
In 4th group , middle digit should be 6
ANSWER:D
Answer: D
Question: On a certain farm the ratio of horses to cows is 4:1. If the farm were to sell 15 horses and buy 15 cows, the ratio of horses to cows would then be 7:3. After the transaction, how many more horses than cows would the farm own?
Options:
A)20
B)40
C)50
D)60
E)80
Rationale: Originally, there were 4k horses and k cows.
3(4k-15) = 7(k+15)
12k-7k = 105+45
5k = 150
k = 30
The difference between horses and cows is (4k-15)-(k+15) = 3k-30 = 60
The answer is D.
Answer: D
Question: Two people stand back to back next to the rails in a small railway station. As the head of the express train that passes the station reaches them, they start to walk parallel to the rails. As the tail of the train reaches each of them, they stop, having walked 30m and 40m respectively.
If they both walked with identical, constant speed and the train kept its speed as well, can you tell how long the train was?
Options:
A)140m
B)240m
C)340m
D)440m
E)540m
Rationale: Let d be the length of the train, and
let t1 be the time it took for the tail of the train to reach
the first person, and
let t2 be the time it took for the tail of the train to reach
the second person.
By time t1, the head of the train is d-30 meters beyond the point where it passed the two people.
By time t2, the head was d+40 meters beyond where it passed the two people. The ratio of these distances,
d-30 : d+40
is equal to the ratio of t1:t2, because the train is moving at a constant speed.
Since both people walk at the same constant rate, this ratio is 3:4.
d-30 : d+40 = 3:4
The product of the means equals the product of the extremes, so
3(d+40) = 4(d-30)
3d + 120 = 4d - 120
240 = d
Answer B
Answer: B
Question: Murali travelled from city A to city B at a speed of 40 kmph and from city B to city C at 60 kmph. What is the average speed of Murali from A to C given that the ratio of distances between A to B and B to C is 3 : 3?
Options:
A)16
B)48
C)277
D)92
E)11
Rationale: Let the distances between city A to B and B to C be 3x km and 3x km respectively.
Total time taken to cover from A to C
= (3x)/40 + (3x)/60 = (9x + 6x)/120 = 15x/120 = x/8 Average speed = (3x + 3x)/(x/8) = 48 kmph.
Answer:B
Answer: B
Question: What will be the difference between simple and compound interest at 12% per annum on a sum of Rs. 1000 after 4 years?
Options:
A)94.19
B)94.12
C)93.5
D)64.1
E)64.11
Rationale: S.I. = (1000 * 12 * 4)/100 = Rs. 480
C.I. = [1000 * (1 + 12/100)4 - 1000] = Rs. 573.5 Difference = (573.5 - 480) = Rs. 93.5
Answer: C
Answer: C
Question: There are three departments having students 66,58,24 .In an exam they have to be seated in rooms such that each room has equal number of students and each room has students of one type only (No mixing of departments). Find the minimum number of rooms required?
Options:
A)73
B)74
C)75
D)76
E)77
Rationale: WE NEED TO TAKE GCD WHICH IS 2
THUS ALL THE ROOMS WILL HAVE 2 STUDENTS OF THE SAME DEPT
1) 66/2 = 33
2) 58/2 = 29
3) 24/2 = 12
TOTAL NO. OF MIN ROOMS REQD = 33+12+29 = 74
ANSWER:B
Answer: B
Question: Every student in a certain classroom was given a lollypop. 1/3 of the students were given a green lollypop, 1/4 of the students were given a yellow lollypop, and all of the other students were given a red lollypop. After lunch, 1/4 of the students who had green lollypops and 2/3 of the students who had yellow lollypops left the classroom; the other students did not leave. What fraction of all students have either a green or yellow lollypop?
Options:
A)5/9
B)4/9
C)2/3
D)4/7
E)3/5
Rationale: Lets pick smart numbers. Total number of students in the classroom: 12
Green lollypop (1/3): 4
Yellow lollypop (1/4): 3
Red lollypop (5/12): 5
After lunch
Green lollypop: 3
Yellow lollypop: 1
Red lollypop: 5
New Total number of students in the classroom: 9
Green and yellow lollypops: 4
Answer 4/9 or B
Answer: B
Question: What is the sum of all the composite numbers up to 12?
Options:
A)228
B)28
C)60
D)49
E)50
Rationale: Explanation:
4 + 6 + 8 + 9 + 10 + 12 = 49
Answer: D
Answer: D
Question: If 10^(v-1)< 0.000125 <10^v, what is the value of an integer v?
Options:
A)-4
B)-3
C)-2
D)3
E)4
Rationale: -> Multiply 10^6- > (10^6){10^(v-1)}<125<(10^6)(10^v) -> 125 is bigger than 100
-> (10^6)(10^(v-1))=100 -> 10^(6+v-1)=10^2, v+5=2 -> v=-3
Thus, the answer is B
Answer: B
Question: Total ages of p,q,r be 27.P is two years elder than Q. Who is twice as old as R. Then how old is Q?
Options:
A)10
B)12
C)14
D)16
E)18
Rationale: p+q+r=27.........(1)
p= q+2
q= 2r
so,r=q/2
(1)........ is
q+2+q+q/2= 27
or,2q+q/2=25
5q=50
so,q =10
ANSWER:A
Answer: A
Question: A person crosses a 1080 m long street in 14 minutes. What is his speed in km per hour?
Options:
A)4.1
B)4.5
C)4.6
D)5.4
E)5.5
Rationale: Speed = 1080/(12x60) m/sec
= 1.3 m/sec.
Converting m/sec to km/hr =1.3 x(18/5) km/hr
= 4.6 km/hr.
ANSWER :C
Answer: C
Question: A bag contains 6 black and 8 white balls. One ball is drawn at random. What is the probability that the ball drawn is white?
Options:
A)4/7
B)3/7
C)2/7
D)11/7
E)8/7
Rationale: Let number of balls = (6 + 8) = 14.
Number of white balls = 8.
P (drawing a white ball) = 8/14
= 4/7
Answer should be A
Answer: A
Question: The music class consists of 4 girls and 7 boys. How many ways can a group of 3 be formed if it has to include at least one boy?
Options:
A)155
B)158
C)161
D)165
E)172
Rationale: Classic combination problem
At least 1 boy = Total - all girls
All girls = C(4,3) = 4
Total combination = C(11,3) = 165
Ans = 165-4 = 161
ANS:C
Answer: C
Question: If Rs. 782 be divided into three parts, proportional to 1/2:1/3:3/4, then the first part is?
Options:
A)A)426
B)B)526
C)C)247
D)D)204
E)E)297
Rationale: Given ratio
= 1/2:2/3:3/4 = 6:4:9
1st part = 782 * 6/19
= Rs. 247
Answer:C
Answer: C
Question: The total age of A and B is 15 years more than the total age of B and C. C is how many year younger than A
Options:
A)11
B)12
C)13
D)14
E)15
Rationale: Explanation:
Given that A+B = 15 + B + C
=> A ? C = 15+ B ? B = 15
=> C is younger than A by 15 years
Answer: Option E
Answer: E
Question: In a sequence of 12 numbers, each term, except for the first one, is 12^14 less than the previous term. If the greatest term in the sequence is 12^15, what is the smallest term in the sequence?
Thus, A12 = A1+12-1d
Where d is the difference between each pairs of consecutive terms. Since each term is 1211 less than the previous term, d=-1211Click individual answer choices for specific explanations.
From what I undersltand the formula for an arithmetic sequence represents
some-number-in-the-sequence= first-number-in-sequence +the-place-of-that-number - 1x the-difference-of-each-#-in-the-sequence
Options:
A)12^14
B)0
C)12^11
D)11·12^11
E)12^12
Rationale: there are total 12 terms. andgreatestterm is 12^15. Each term is 12^14 less than previous one. What does this signify? This shows it is an AP - a decreasing one. (NoticeEach term is 12^14 less than previous one')
Therefore, 12^15 is the first term of the AP and -12^14 is the difference between successive terms, the smallest term should be the last one.
Last term = First term + (n-1)*d
therefore, Last term = 12^15 + 11*(-12^14)
=> Last term = 12^15 - 11*12^14
=> Last term = 12^14 (12-11) = 12^14
Which is the smallest term.
Hence Ans A it is.
Answer: A
Question: The sequence a1, a2, a3, a4. a5 is such that an = a n-1 +5 for 2≤ n ≤ 5. If a5 = 35 what is the value of a1 ?
Options:
A)1
B)6
C)15
D)16
E)21
Rationale: Here, each value of an is the previous value plus 5
Since the numbers are less, the fastest way to solve this problem is to successively subtract 5 from a5 till you reach a1
a5 = 35
a4 = 30
a3 = 25
a2 = 20
a1 = 15 <<<< Ans C
Answer: C
Question: A milk vendor has 2 cans of milk. The first contains 25% water and the rest milk. The second contains 50% water. How much milk should he mix from each of the containers so as to get 12 litres of milk such that the ratio of water to milk is 3 : 5?
Options:
A)6 litres, 6 litres
B)6 litres, 7 litres
C)7 litres, 5 litres
D)5 litres, 5 litres
E)None
Rationale: Let the cost of 1 litre milk be Re. 1
Milk in 1 litre mix. in 1st can =	3	litre, C.P. of 1 litre mix. in 1st can Re.	3
4	4
Milk in 1 litre mix. in 2nd can =	1	litre, C.P. of 1 litre mix. in 2nd can Re.	1
2	2
Milk in 1 litre of final mix. =	5	litre, Mean price = Re.	5
8	8
By the rule of alligation, we have:
C.P. of 1 litre mixture in 1st can C.P. of 1 litre mixture in 2nd can
3
4
Mean Price
5
8
1
2
1
8
1
8
Ratio of two mixtures =	1	:	1	= 1 : 1.
8	8
So, quantity of mixture taken from each can = 1/2	x 12 = 6 litres
Option A
Answer: A
Question: Ram professes to sell his goods at the cost price but he made use of 900 grms instead of a kg, what is the gain percent?
A. 11%
Options:
A)11 1/9%
B)11 1/8%
C)11 9/9%
D)11 5/9%
E)11 1/5%
Rationale: 900 --- 100
100 --- ? => 11 1/9%
Answer:A
Answer: A
Question: The average age of a class of 32 students is 16 yrs. if the teacher's age is also included, the average increases by one year. Find the age of the teacher
Options:
A)28 Years
B)30 Years
C)32 Years
D)37 Years
E)49 Years
Rationale: Total age of students is 32X16 = 512 Years
Total age inclusive of teacher = 33X (16+1) = 561
So, Teacher's age is 561-512 = 49 Yrs
There is a shortcut for these type of problems
Teacher's age is 16+(33X1) = 49 Years
E
Answer: E
Question: Three pipes of same capacity A,B,C can fill a tank in 24 hours. If there are only two pipes A and B of same capacity, the tank can be filled in?
Options:
A)12
B)24
C)6
D)36
E)8
Rationale: The part of the tank filled by three pipes in one hour
= 1/24
=> The part of the tank filled by two pipes in 1 hour
= 2/3 * 1/24 = 1/36.
The tank can be filled in 36 hours.
Answer:D
Answer: D
Question: The difference of two numbers is 1565. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder. What is the smaller number ?
Options:
A)A)270
B)B)280
C)C)290
D)D)300
E)E)310
Rationale: Let the smaller number be x. Then larger number = (x + 1565).
x + 1565 = 6x + 15
5x = 1550
x = 310
Smaller number = 310.
E)
Answer: E
Question: Twenty percent of Country Y's yearly exports come from fruit exports. One-sixth of all fruit exports from Country Y are orange exports. If country Y generates $3 million from its orange exports, how much money does it generate from its yearly total of exports?
Options:
A)$21.25m
B)$25.5m
C)$90m
D)$127.5m
E)$153m
Rationale: 2/10*1/6*(total) = 3
1/30*(total) = 3
(total) = 3*30 = 90
Answer: C.
Answer: C
Question: Among 500 people, 56% like strawberry jam, 44% like apple jam, and 40% like raspberry jam. If 30% of the people like both strawberry and apple jam, what is the largest possible number of people who like raspberry jam but do not like either strawberry or apple jam?
Options:
A)20
B)60
C)80
D)86
E)150
Rationale: 56%+44%-30%=70% who like either Strawberry, Apple, or both.
That means 100%-70% = 30% do not like either Apple of Strawberry jam.
30% is the most possible that like raspberry jam but do not like either strawberry or apple (assuming nobody in the group does not like any)
E
Answer: E
Question: Becky, Merry and John want to share a chocolate bar evenly.
What part of the bar will each of them take?
What part of the bar will Becky and Merry have together?
Options:
A)1/3
B)2/3
C)2/4
D)None of these
E)Cannot be determined
Rationale: Solution
The children need to divide the bar into three pieces. So everyone will take 1/3 of the chocolate bar.
Two girls together will have two pieces, hence, mathematically speaking, they will have 2/3 of the bar
Answer B
Answer: B
Question: Two employees A and B are paid a total of Rs. 450 per week by their employer. If A is paid 150 percent of the sum paid to B, how much is B paid per week?
Options:
A)130
B)140
C)150
D)170
E)180
Rationale: Let the amount paid to A per week = x
and the amount paid to B per week = y
Then x + y = 450
But x = 150% of y = 150y/100 = 15y/10
∴15y/10 + y = 450
⇒ y[15/10 + 1] = 450
⇒ 25y/10 = 450
⇒ 25y =4500
⇒ y = 4500/25 =Rs.180
E
Answer: E
Question: A man jogging inside a railway tunnel at a constant speed hears a train approaching the tunnel from behind at a speed of 30 km/h, when he is one third of the way inside the tunnel. Whether he keeps running forward or turns back, he will reach the end of the tunnel at the same time the train reaches that end. The speed at which the man is running is:
Options:
A)6 km/hr
B)8 km/hr
C)10 km/hr
D)12 km/hr
E)None of these
Rationale: Explanation :
Let the train is at distance y km from the tunnel and the length of the tunnel is x km. Man is at point C which is x/3 km away from B.
A ----------- B -------------- C ----------------D
<---- y------><------x/3-------><------2x/3------->
AB=y, BC =x/3 and CD =2x/3.
Let, M km/h be the speed of man.
Now, train is at A and man is at C and both will take same time for reaching from B.
=>y/30=x/3M.
=>M=10x/y . ----------------------(i)
Also, train and man will take some time for reaching at D.
=>(x+y)/30=2x/M.
=>M=20x/(x+y). ---------------------(ii)
From both the equations we get: x=y
And on putting value in any equation we get: M = 10 km/hr.
Answer : C
Answer: C
Question: If 45-[28-{37-(15-*)}]= 58, then * is equal to:
Options:
A)-29
B)-19
C)19
D)29
E)39
Rationale: 45-[28-{37-(15-*)}]= 58 => 45-[28-{37-15+*}]=58
45-[28-37+15-*]=58 => 45[43-37-*]=58
45-[6-*]=58 => 45-6+*=58
39+*=58 => *=58-39
= 19
ANSWER:C
Answer: C
Question: X and Y invest Rs.21000 and Rs.17500 respectively in a business. At the end of the year, they make a profit of Rs.26400. What is the share of X in the profit?
Options:
A)Rs.14400
B)Rs.26400
C)Rs.12000
D)Rs.12500
E)None of these
Rationale: Explanation :
Ratio of the investment = 21000 : 17500 = 210 : 175 = 42 : 35 = 6 : 5
Share of X in the profit = 26400 * (6/11) = 2400 * 6 = 14400 .. Answer : Option A
Answer: A
Question: If 0.75: x :: 5:8, then x is equal to:
Options:
A)1.29
B)1.28
C)1.20
D)1.21
E)1.22
Rationale: Explanation:
(x * 5) = (0.75 *8)
X=6/5 = 1.20
Answer: C) 1.20
Answer: C
Question: A train running at the speed of 60 km/hr crosses a pole in 5 seconds. Find the length of the train.
Options:
A)83.33
B)882
C)772
D)252
E)121
Rationale: Speed = 60*(5/18) m/sec = 50/3 m/sec
Length of Train (Distance) = Speed * Time
(50/3) * 5 = 83.33 meter.Answer: A
Answer: A
Question: Difference of two numbers is 1660. If 7.5% of the number is 12.5% of the other number , find the number ?
Options:
A)2490 and 4150
B)249 and 415
C)2400 and 4100
D)2290 and 4350
E)229 and 435
Rationale: Let the numbers be x and y. Then , 7.5 % of x =12.5% of y
X = 125*y/75 = 5*y/3.
Now, x-y =1660
5*y/3 –y =1660
2*y/3= 1660
y =[ (1660*3)/2] =2490.
One number = 2490, Second number =5*y/3 =4150
Answer is A.
Answer: A
Question: Helen went to the stationers and bought things worth Euro 26, out of which 30 paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?
Options:
A)uro 16.70
B)uro 15.70
C)uro 13.70
D)uro 18.70
E)uro 20.70
Rationale: E
Euro 20.70
Let the amount taxable purchases be Euro x.
Then, 6% of x = 30/100
x = (30/100 x 100/6) = 5.
Cost of tax free items = Euro [26 - (5 + 0.30)] = Euro 20.70
Answer: E
Question: A set of numbers has an average of 40. If the largest element is 4 greater than 3 times the smallest element, which of the following values cannot be in the set?
Options:
A) 85
B) 90
C) 125
D) 50
E) 55
Rationale: Ans: C
Solution: we are given the relation between smallest and the largest term. so let the smallest a and largest be 3a+4
so the avg = 50
which tells us that any value of a must be less than 40
so a<50 means, largest value 3a+4 <(3*40)+4
=largest value must be <124
so 125 can not be the value in the set.
Answer: C
Question: How many numbers can be formed from 1, 2, 3, 4, 5 (without repetition), when the digit at the unit’s place must be greater than that in the ten’s place?
Options:
A)54
B)60
C)50
D)2 x 4!
E)51 / 3
Rationale: The digit in the unit’s place should be greater than that in the ten’s place. Hence if digit 5 occupies the unit place then remaining four digits need not to follow any order. Hence the required numbers = 4!. However, if digit 4 occupies the unit place then 5 cannot occupy the ten’s position. Hence digit at the ten’s place will be one among 1, 2 or 3. This can happen in 3 ways. The remaining 3 digits can be filled in the remaining three places in 3! ways. Hence, in all we have (3 x 3!) numbers ending in 4. Similarly, if we have 3 in the unit’s place, the ten’s place can be either 1 or 2. This can happen in 2 ways. The remaining 3 digits can be arranged in the remaining 3 places in 3! ways. Hence, we will have (2 x 3!) numbers ending in 3. Similarly, we can see that there will be 3! numbers ending in 2 and no number ending with 1.
Hence, the total number of numbers = 4! + (3 x 3!) + (2 x 3!) + 3!
= 4! + 6 x 3! = 24 + (6 x 6) = 60
ANSWER:B
Answer: B
Question: Find the length of the longest pole that can be placed in a room 12 m long 8m broad and 9m high.
Options:
A)13
B)14
C)15
D)16
E)17
Rationale: Length of longest pole = Length of the diagonal of the room
= sqrt(12^2+8^2+9^2= sqrt(289)= 17 m.
Answer is E.
Answer: E
Question: The speed of a boat in upstream is 60 kmph and the speed of the boat downstream is 80 kmph. Find the speed of the boat in still water and the speed of the stream?
Options:
A)10 kmph
B)23 kmph
C)75 kmph
D)56 kmph
E)46 kmph
Rationale: Speed of the boat in still water
= (60+80)/2
= 70 kmph. Speed of the stream
= (80-60)/2
= 10 kmph.
Answer:A
Answer: A
Question: In how many ways can a group of 22 friends be seated round 2 tables if one of the tables can seat 12 and the other can seat 10 people?
Options:
A)15C5 * 9! *4!
B)15C3 * 8! *3!
C)15C4 * 9! *3!
D)22C2 * 11! *9!
E)26C5 * 10! *4!
Rationale: 12 people can be selected from 22 people in 22C12 ways.
Remaining 10 people can be selected from 10 people in 10C10 ways.
Now, arranging 12 people on a round table = (12-1) ! = 11!
Arranging 10 people on a round table = (10-1) ! = 9!
Hence, total number of ways = 22C12 * 11! * 10C10 * 9!
= 22C2 * 11! * 9!
D
Answer: D
Question: A coin is tossed live times. What is the probability that there is at the least one tail?
Options:
A)31/32
B)31/38
C)31/30
D)31/37
E)31/31
Rationale: Let P(T) be the probability of getting least one tail when the coin is tossed five times.
= There is not even a single tail.
i.e. all the outcomes are heads.
= 1/32 ; P(T) = 1 - 1/32 = 31/32
Answer:A
Answer: A
Question: Two trains 170 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is?
Options:
A)10.6 sec
B)18.8 sec
C)14.8 sec
D)10.88 sec
E)11.88 sec
Rationale: Relative speed = 60 + 40 = 100 km/hr.
= 100 * 5/18 = 250/9 m/sec.
Distance covered in crossing each other = 170 + 160 = 330 m.
Required time = 330 * 9/250 = 297/25= 11.88 sec.
Answer: E
Answer: E
Question: Henry got a weekly raise of $963. If he gets paid every other week, write an integer describing how the raise will affect his paycheck.
Options:
A)693
B)396
C)963
D)691
E)961
Rationale: Let the 1st paycheck be x (integer).
Henry got a weekly raise of $ 963.
So after completing the 1st week she will get $ (x+963).
Similarly after completing the 2nd week she will get $ (x + 963) + $ 963.
= $ (x + 963 + 963)
= $ (x + 1926)
So in this way end of every week her salary will increase by (C)$ 963.
Answer: C