divelab/Sys2Bench huggingface dataset:
Question: Amy, Max and Nim, each have a basket full of apples. The number of apples each have is in the ratio 7:8:9 respectively. what could be the product of the number of apples.
Options:
A)4032
B)5012
C)1033
D)4123
E)5102
Rationale: The ratio is in in the order of consecutive positive integers. Therefore, the product of the numbers will be divisible by both 2 and 3.
4032 -> even number, 4+0+3+2=6 ->divisible by 3.
Answer:A
Answer: A
Question: A bicyclist's wheel has a circumference of 4 meters. if the bicyclist covers 40 meters in 5 hours at a constant speed, how many rotations does the wheel make per hour at that speed?
Options:
A)2
B)3
C)4
D)5
E)6
Rationale: The bicyclist covers y meters in t hrs. So he covers y/t meters in one hour.
To cover y/t meters, the bicycle's wheel went round and round that is, multiple times, the wheel completed one circumference on the road. How many times did it complete one full rotation. Since the circumference is x, the number of times it completes the circumference is y/xt.
given : x=4; y=40 and t=5
hence y/xt =40/4*5=2
Answer (A)
Answer: A
Question: How many perfect squares less than 1000 end with the digit 6?
Options:
A)3
B)4
C)5
D)6
E)7
Rationale: 4:16
6:36
14:196
16:256
24:576
26:676
ANSWER:D
Answer: D
Question: 5 friends went to a restaurant and decided to pay the bill amount equally. But 4 of them could pay Rs. 50 each as a result 5th has to pay Rs. 40 extra than his share. Find the amount paid by him.
Options:
A)130
B)110
C)50
D)100
E)None
Rationale: Explanation:
Average amount paid by 4 persons = Rs. 50
Increase in average due to Rs. 40 paid extra by the 5th men = Rs. 40/4= Rs. 10
Therefore, Average expenditure of 6 friends = Rs. 50 + Rs. 10 = Rs. 60
Therefore, Amount paid by the 6th men = Rs. 60 + Rs. 40 = Rs. 100
Correct Option: D
Answer: D
Question: A glass was filled with 40 ounces of water, and 0.01 ounce of the water evaporated each day during a 20-day period. What percent of the original amount of water evaporated during this period?
Options:
A)0.005%
B)0.02%
C)0.5%
D)5%
E)20%
Rationale: We are given that 0.01 ounces of water evaporated EACH DAY. Furthermore, we know that this process happened over a 20-DAY PERIOD. To calculate the total amount of water that evaporated during this time frame we need to multiply 0.01 by 20. This gives us:
0.01 x 20 = 0.2 ounces
Finally, we are asked for “What percent” of the original amount of water evaporated during this period. To determine this percentage, we have to make sure we translate the expression correctly. We can translate it to:
(Amount Evaporated/Original Amount) x 100%
(0.2/40) x 100%
= 0.5%
Answer C
Answer: C
Question: If two resistors, A(R1) and B(R2) stand in parallel with each other in electrical wire, the total resistor appears as R1R2/(R1+R2). If three resistors, A(R1), B(R2), and C(2R2) stand in parallel in electrical wire, what is the ratio D of the resistors’ sum of A and C to the resistors’ sum of A and B?
Options:
A)2(R1+R2):(R1+2R2)
B)(R1+R2):(R1+2R2)
C)(2R1+R2):(R1+2R2)
D)2(R1+R2):(2R1+R2)
E)2(R1-R2):(R1+2R2)
Rationale: two resistors A (r1) and B (r2).
total or sum of two resistors appear as
r1r2/r1+r2. It is looks like inversion of sum of rates.
1/r1+1/r2= r1+r2/r1r2.
same way sum of A(r1) and c(2r2)=1/r1+1/2r2
=2r2+r1/r12r2.
inversion rate = r12r2/2r2+r1.
ratio D of sum of a and c/sum of a and b=2r2r1/2r2+r1*r1+r2/r1r2
=2(r1+r2)/2r2+r1.A
Answer: A
Question: The speed of a car increases by 2 kms after every one hour. If the distance travelling in the first one hour was 35 kms. what was the total distance travelled in 12 hours?
Options:
A)456 kms
B)482 kms
C)552 kms
D)556 kms
E)500 kms
Rationale: Explanation:
Total distance travelled in 12 hours =(35+37+39+.....upto 12 terms)
This is an A.P with first term, a=35, number of terms,
n= 12,d=2.
Required distance = 12/2[2 x 35+{12-1) x 2]
=6(70+23)
= 552 kms.
ANSWER IS C
Answer: C
Question: The dimensions of a field are 20 m by 5 m. A pit 10 m long, 4 m wide and 3 m deep is dug in one corner of the field and the earth removed has been evenly spread over the remaining area of the field. What will be the rise in the height of field as a result of this operation ?
Options:
A)1m
B)5m
C)4m
D)2m
E)3m
Rationale: The volume of the earth removed is 10*4*3 = 120 m^3.
The remaining area of the field is 20*5 - 10*4 = 60 m^2.
120 m^3 of the earth evenly spread over the area of 60 m^2 will rise the height by (height) = (volume)/(area) = 120/60 = 2 m.
Answer: D
Answer: D
Question: 79 laboratories raise the bacterium, the laboratory have 48 culture dishes on average, which has about 25,073 bacteria each. How many bacteria are there approximately?
Options:
A)10^7
B)10^9
C)10^8
D)10^10
E)10^11
Rationale: 79 laboratories raise the bacterium, the laboratory have 48 culture dishes on average, which has about 25,073 bacteria each. How many bacteria are there approximately?
A. 10^7
B. 10^8
C. 10^9
D. 10^10
E. 10^11
-> Due to approximately, 79=80, 48=50, 25,073=25,000 are derived, which makes (79)(48)(25,075)=(80)(50)(25,000)=10^8. The answer is C.
Answer: C
Question: Each shelf of a bookcase contained 11 books. If the librarian took out 32 books and rearranged the remaining books so that all shelves but the last one contained 7 books and that last shelf contained 3 books, how many shelves does the bookcase have?
Options:
A)5
B)6
C)7
D)8
E)9
Rationale: Let x be the number of shelves.
11x - 32 = 7(x-1) + 3
4x = 28
x = 7
The answer is C.
Answer: C
Question: Five kg of butter was bought by a shopkeeper for 300. One kg becomes unsaleable. He sells the remaining in such a way that on the whole he incurs a loss of 10%. At what price per kg was the butter sold?
Options:
A)67.5
B)52.5
C)60
D)72.5
E)None of these
Rationale: Let S.P. = x per kg
∴ S.P. of 4 kg = 4x
∴ 4x = 100−40/100×300
⇒ x = 270⁄4 = 67.50
Answer A
Answer: A
Question: If C = 2D+1 where C is an Integer then which of the following is true?
Options:
A)C is always Odd
B)C is always Even
C)C is a non multiple of 2
D)C= 1
E)C is even if D is a non integer and a multiple of 0.5
Rationale: E
Answer: E
Question: A man can row upstream at 7kmph and downstream at 10kmph. Find man's rate in still water ?
Options:
A)8.5km/hr
B)6.7km/hr
C)5km/hr
D)1.5km/hr
E)2.6km/hr
Rationale: Rate in still water = 1/2 (10+7) = 8.5km/hr
Answer is A
Answer: A
Question: A man can row a boat at 20 kmph in still water. If the speed of the stream is 5 kmph, what is the time taken to row a distance of 60 km downstream?
Options:
A)12/5 hours
B)80/13 hours
C)30/73 hours
D)30/13 hours
E)50/13 hours
Rationale: Speed downstream = 20 + 5 = 25 kmph.
Time required to cover 60 km downstream
= d/s = 60/25
= 12/5 hours.
Answer:A
Answer: A
Question: In how many ways can 5 boysand 2 girls be arranged at a table if 2 girls are never together?
Options:
A)240
B)340
C)430
D)450
E)480
Rationale: Total ways of arranging 7 person in a circle = 6! = 720 ways
If we consider two women as one, then we have 5+1=6 persons. Arranging these six persons in circle will take = 5! = 120 ways
And two women can arrange themselves in 2! ways
Total ways in which two women sit together in circle = 5!*2! = 240 ways
Total ways in which two women doesn’t sit together in circle = 6! - 5!*2! = 720 - 240 = 480 ways
E
Answer: E
Question: A man can do a piece of work in 5 days, but with the help of his son he can do it in 4 days. In what time can the son do it alone ?
Options:
A)2 days
B)6 days
C)12 days
D)20 days
E)None of these
Rationale: Explanation:
In this type of question, where we have one person work and together work done. Then we can easily
get the other person work just by subtracting them. As
Son's one day work =
(1/4−1/5)=(5−4)/20=1/20
So son will do whole work in 20 days
Answer: D
Answer: D
Question: In the storage room of a certain bakery, the ratio of sugar to flour is 5 to 6, and the ratio of flour to baking soda is 10 to 1. If there were 60 more pounds of baking soda in the room, the ratio of flour to baking soda would be 8 to 1. How many pounds of sugar are stored in the room?
Options:
A)600
B)1200
C)1500
D)1600
E)2000
Rationale: Sugar:Flour = 5:6 = 25:30;
Flour:Soda = 10:1 = 30:3;
Thus we have that Sugar:Flour:Soda = 25x:30x:3x.
Also given that 30x/(3x+60) = 8/1 --> x=80 --> Sugar = 25x = 2,000.
Answer: E.
Answer: E
Question: What profit percent is made by selling an article at a certain price, if by selling at 2/3rd of that price, there would be a loss of 30%?
Options:
A)20%
B)29%
C)70%
D)27%
E)5%
Rationale: SP2 = 2/3 SP1
CP = 100
SP2 = 70
2/3 SP1 = 70
SP1 = 105
100 --- 105 => 5%
Answer: E
Answer: E
Question: A farmer has 3,000 seeds which is enough for him to plant seeds every day for 50 days. After 10 days he loses some of the seeds and the remaining seeds is now enough for him to plant for the same period of 50 days as before. How many seeds did he lose?
Options:
A)200
B)600
C)1,000
D)900
E)700
Rationale: 3,000 ---- 50
3,000 ---- 40
x = 50
x*50 = 3,000*40
x = 2,400
3,000
-------
600
Answer = B
Answer: B
Question: What will come in place of the x in the following Number series? 3, 6, 12, x , 33
Options:
A)33
B)37
C)39
D)21
E)43
Rationale: (D)
The pattern is + 3, + 6, + 9, +12 â€¦â€¦â€¦..
So the missing term is = 12 + 9= 21
Answer: D
Question: If 50% of x is 30 less than 25% of 1500, then x is?
Options:
A)690
B)860
C)560
D)875
E)880
Rationale: 50% of x = x/2 ; 25% of 1500 = 25/100 * 1500 = 375
Given that, x/2 = 375 - 30 => x/2 = 345 => x = 690.
Answer: A
Answer: A
Question: $600 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)$240
Rationale: A:(B+C) = 2:3
A's share = 600*2/5 = $240
Answer is E
Answer: E
Question: A sum of 14,800 amounts to 19,800 in 3 years at the rate of simple interest. What is the rate of interest?
Options:
A)12%
B)11%
C)16%
D)15%
E)18%
Rationale: B
11%
S.I. = (19800 - 14800) = 5000.
Rate = (100 x 5000)/(14800x3)% = 11%
Answer: B
Question: A basket contains 8 apples, of which 1 is spoiled and the rest are good. If we select 2 apples from the basket simultaneously and at random, what is the probability that the 2 apples selected will include the spoiled apple?
Options:
A)1/2
B)1/3
C)1/4
D)1/5
E)1/6
Rationale: The total number of ways to choose 2 apples is 8C2 = 28
The number of ways that include the spoiled apple is 7C1 = 7
P(the spoiled apple is included) = 7/28 = 1/4
The answer is C.
Answer: C
Question: A can complete a project in 20 days and B can complete the same project in 30 days. If A and B start working on the project together and A quits 5 days before the project is completed, in how many days will the project be completed?
Options:
A)18 days
B)27 days
C)26.67 days
D)15 days
E)12 days
Rationale: Let X = the number of days taken to complete the project.
The amount of work done by A is (x-10) * (1/20).
The amount of work done by B is (x) * (1/30).
(1/20)*(x-5) + (1/30)*(x) = 1
(x/20) + (x/30) - (5/20) = 1
5x/60 = 5/4
x = 60/4
x = 15
Therefore, the answer is D: 15.
Answer: D
Question: The sum of the heights of two high-rises is x feet. If the first high rise is 37 feet taller than the second, how tall will the second high rise be after they subtract an antenna with a height of z feet to the top?
Options:
A)(x+z)/2 + 37
B)2x−(37+z)
C)(x−37)/2 + z
D)x/2 - 37 + z
E)(x−37)/2 + z
Rationale: I will note h1 the height of high-rise 1 and h2 the height of high-rise 2. SO:
h1 + h2 = x
and h1 = h2 + 37 =>
Q: h2 + z = ?
h2 + h2 + 37 = x => 2h2 = x-37 =? h2 = (x-37)/2
=> h2 - z = (x-37)/2 + z, CORRECT ANSWER E
Answer: E
Question: There are 12 cans in the refrigerator. 7 of them are red and 5 of them are blue. In how many ways we can remove 11 cans so that at least one red and at least one blue cans to remain the refrigerator.
Options:
A)4
B)490
C)493
D)455
E)445
Rationale: Ways to pick 1 cans so that at least one red and at least one blue cans to remain the refrigerator =
total ways to pick 1 can out of 12 - ways to pick 1 red out of 7 red - ways to pick 1 blue out of 5 blue
12C1âˆ’7C1âˆ’5C1=12âˆ’7âˆ’1=4
ANSWER:A
Answer: A
Question: What is the area of the given rectangle?
I.	Perimeter of the rectangle is 60 cm.
II.	Breadth of the rectangle is 12 cm.
III.	Sum of two adjacent sides is 30 cm.
Options:
A)I only
B)II only
C)I and II only
D)II and III only
E)II and either I or III
Rationale: EXPLANATION
From I and II, we can find the length and breadth of the rectangle and therefore the area can be obtained.
So, III is redundant.
Also, from II and III, we can find the length and breadth and therefore the area can be obtained.
So, I is redundant.
Correct answer is “II and either I or III”.
Answer E
Answer: E
Question: How many seconds will a train 100 meters long take to cross a bridge 150 meters long if the speed of the train is 54 kmph?
Options:
A)22 sec
B)77 sec
C)16.7 sec
D)18 sec
E)17 sec
Rationale: D = 100 + 150 = 250
S = 54 * 5/18 = 15 mps
T = 250/15 = 16.7 sec
Answer:C
Answer: C
Question: If d + xy = d and x is not equal to 0, which of the following must be true?
Options:
A)x=0
B)x+y=0
C)x<y
D)y=0
E)x=d
Rationale: d + xy = d --> xy=0. Since x is not equal to 0, thus y = 0.
Answer: D.
Answer: D
Question: In a fuel station the service costs $1.75 per car, every liter of fuel costs 0.65$. Assuming that a company owns 12 cars and that every fuel tank contains 60 liters and they are all empty, how much money total will it cost to fuel all cars?
Options:
A)320$
B)389$
C)420$
D)450$
E)489$
Rationale: Total Cost = ( 1.75*12 ) + ( 0.65 * 12 * 60 ) =489
Hence answer will be (E)
Answer: E
Question: (1-1/n)+( 1-2/n)+(1-3/n)+…… up to n terms=?
Options:
A)1/2n
B)1/2(n-1)
C)1/2n(n-1)
D)none of these
E)cannot be determined
Rationale: Solution: Given sum=(1+1+1+…. to n terms)-(1/n+2/n+3/n+…. to n terms)
= n-(n(n+1)/2)/n
= n-(n+1)/2=1/2(n-1).
Answer B
Answer: B
Question: In a fraction, if numerator is added by 2 and denominator by 1 it results 1, and if numerator added again by 4 and denominator by 2 it results 1/2. Find the fraction?
Options:
A)3/4
B)5/4
C)7/4
D)9/4
E)11/4
Rationale: x+2/y+1 =1 i.e, x-y+1=0;--------(1)
x+4/y+2 =1/2 i.e., 2x-y+6=0;---------(2)
solving 1 and 2...we get x= -5 and y= -4
answer is 5/4...
ANSWER:B
Answer: B
Question: LCM of two numbers is 7700 and HCF is 11. If one number is 308 then other number is
Options:
A)269
B)285
C)300
D)275
E)None of these
Rationale: Option D
Answer: D
Question: There are two numbers whose sum is 72. One number is twice the other. What are the
numbers?
Options:
A)32-55
B)24-48
C)35-42
D)20-40
E)33-55
Rationale: Read the problem. It is about numbers.
The question at the end asks, “What are the numbers?”
Create a let statement.
Let x smaller number
2x= larger number
Reread the problem. It states that the sum of the two numbers is 72.
Translate the problem into an equation and solve.
x+2x=72
3x=72
x=24
2x=48
The answers are: The smaller number is 24 and the larger number is 48.
Is this sensible? Yes, because the sum of 24 and 48 is 72.
correct answer B
Answer: B
Question: In a certain brick wall, each row of bricks above the bottom row contains one less brick than the row just below it. If there are 5 rows in all and a total of 100 bricks in the wall, how many bricks does the bottom row contain ?
Options:
A)18
B)16
C)17
D)15
E)19
Rationale: The bottom row has x bricks
x+x-1+x-2+x-3+x-4 = 100
5x-10=100
5x=90
x= 18
Answer:A
Answer: A
Question: In track last week, the boys ran 15 laps. The girls ran 5 more
laps. Each lap is a one-fifth of a mile. How many miles did the girls run?
Options:
A)2 miles
B)3 miles
C)4 miles
D)5 miles
E)6 miles
Rationale: The girls ran 15 + 5 = 20 laps. 20 x 1/5 = 20/5, which reduces to 4.
The girls ran 4 miles
correct answer C
Answer: C
Question: A father said to his son, "I was as old as you are at present at the time of your birth." If the father's age is 38 years now, the son's age five years back was?
Options:
A)16 years
B)14 years
C)18 years
D)19 years
E)15 years
Rationale: Let the son's present age be x years.
Then, (38 - x) = x
2x = 38 => x = 19
Son's age 5 years back = (19 - 5)
= 14 years.
Answer: B
Answer: B
Question: P is able to do a piece of work in 15 days and Q can do the same work in 20 days. If they can work together for 4 days, what is the fraction of work left?
Options:
A)4/5
B)2/7
C)8/15
D)7/5
E)2/8
Rationale: Explanation :
Amount of work P can do in 1 day = 1/15
Amount of work Q can do in 1 day = 1/20
Amount of work P and Q can do in 1 day = 1/15 + 1/20 = 7/60
Amount of work P and Q can together do in 4 days = 4 × (7/60) = 7/15
Fraction of work left = 1 – 7/15= 8/15
ANSWER:C
Answer: C
Question: 3*14 + 3*15 + 3*18 + 11 = ?
Options:
A)125
B)126
C)130
D)148
E)152
Rationale: 3*14 + 3*15 + 3*18 + 11 = 42 + 45 + 54 + 11 = 152
The answer is E.
Answer: E
Question: A man can row upstream at 25 kmph and downstream at 37 kmph, and then find the speed of the man in still water?
Options:
A)86
B)67
C)31
D)15
E)17
Rationale: US = 25
DS = 37
M = (37 + 25)/2
= 31
Answer: C
Answer: C
Question: A number exceeds 20% of itself by 40. The number is
Options:
A)50
B)60
C)80
D)320
E)None
Rationale: Explanation:
Let the answer be 'a'
Then a−20/100a=40⇒5a−a=200
⇒a=50⇒a=50
Correct Option: A
Answer: A
Question: Calculate the time it will take for a train that is 120 meter long to pass a bridge of 160 meter length, if the speed of the train is 40 km/hour ?
Options:
A)21.2 seconds
B)25.2 seconds
C)29.2 seconds
D)35.2 seconds
E)11.2 seconds
Rationale: Speed = 40 Km/hr = 40*(5/18) m/sec = 11.1111 m/sec
Total distance = 120+160 = 280 meter
Time = Distance/speed
= 280 * (1/11.1111) = 25.2 seconds
Answer: B
Answer: B
Question: The least value of expression 2log10 x - logx (1/100) for x>1 is:
Options:
A)2
B)3
C)4
D)5
E)6
Rationale: 2log10 x = logx1/100 x = log10 10^-2/log10 x
=2log10 x + 2/log10 x
=2[log10 x - 1/log10 x]
since x>1=>log10 x >0
log10 x+ 1/log10^x>=2=> for x = 10, 2[log10 x + 1/log 10 x] > 4
Hence least value is 4
ANSWER C
Answer: C
Question: A person covered one-fourth of the total distance at 22 kmph and remaining distance at 24 kmph. What is the average speed for the total distance?
Options:
A)21 (1/8)
B)21 (1/15)
C)23 (7/15)
D)29 (1/15)
E)21 (4/15)
Rationale: Let the total distance be x km
total time taken = (x/4)/22 + (3x/4)/24 = 15x/352
Average speed = x/(15x/352) = 23 (7/15)kmph.
Answer: C
Answer: C
Question: 24 oz of juice P and 25 oz of juice E are mixed to make smothies X and Y . The ratio of p to E in smothie X is 4 is to 1 and that in Y is 1is to 5.How many ounces of juice P are contained in the smothie X?
Options:
A)5
B)10
C)15
D)20
E)25
Rationale: Easy way to solve this question is start from the answer and then conform the information provided in the question.
we can start from option D i.e 20 ... as a quantity of juice P in X because it is the only one option that gets divided by 4 is 20 ... since in the X the juice P to E ratio is 4:1
this gives us that quantity of juice P in X = 20 therefore quantity of Juice E will be 5 ... hence ratio = 4:1
This will lead to quantity of juice P in X = 4 and quantity of Juice E = 20 ... hence ratio 1:5
if we calculate total Juice P = 24 and total of juice V = 25
it fits because totals are same as what mentioned in the question ...
thus ans is D
Answer: D
Question: Rich has 3 green, 2 red and 3 blue balls in a bag. He randomly picks 5 from the bag without replacement. What is the probability T that of the 5 drawn balls, Rich has picked 1 red, 2 green, and 2 blue balls?
Options:
A)T=8/28
B)T=9/28
C)T=10/28
D)T=10/18
E)T=11/18
Rationale: (3c2*2c1*3c2)/8c5
=(3*2*3)/ (8*7*6/3*2)
=18/56
=9/28
B
Answer: B
Question: How many different subsets of the set {10, 14, 13, 24} are there that contain an odd number of elements?
Options:
A) 3
B) 6
C) 8
D) 10
E) 12
Rationale: Answer = C = 8
{10}
{14}
{13}
{24}
{10, 14, 13}
{14, 13, 24}
{10, 13, 24}
{10, 14, 24}
Answer: C
Question: Working alone at their respective constant rates, A can complete a task in ‘a’ days and B in ‘b’ days. They take turns in doing the task with each working 2 days at a time. If A starts they finish the task in exactly 12 days. If B starts, they take half a day more. How long does it take to complete the task if they both work together?
Options:
A)4
B)4.5
C)6
D)8
E)6.5
Rationale: Work done by AB in a day = xy respectively.
When A starts:
No. of days when A works = 6No. of days when B works = 6 → 6x + 6y = 1
When B starts:
No. of days when A works = 6.5No. of days when B works =5.5 → 6.5x +5.5y = 1
Solving the above two equations for xy
x = 1/12 y = 1/12
→ Total work done by AB in a day = 1/12 + 1/12 = 2/12 =1/6
→ No. of days to complete the work when both work together = 6
Answer: C
Answer: C
Question: How many possible positive integer values are there for k if -24 < 9k – 6 ≤ 3?
Options:
A)Zero
B)One
C)Two
D)Three
E)Four
Rationale: -24 < 9k – 6 ≤ 3
Add 6: -18 < 9k ≤ 9
Divide by 9: -2< k ≤ 1.
k can take only one positive integer value: 1.
Answer: B.
Answer: B
Question: hree number are in the ratio of 3 : 4 : 5 and their L.C.M. is 2400. Their H.C.F. is:
Options:
A)40
B)50
C)60
D)70
E)80
Rationale: Let the numbers be 3x, 4x and 5x.
Then, their L.C.M. = 60x.
So, 60x = 2400 or x = 40.
The numbers are (3 x 40), (4 x 40) and (5 x 40).
Hence, required H.C.F. = 40.
ANSWER :A
Answer: A
Question: John started a business, investing Rs.18000. After 3 months and 4 months respectively, Rose and Tom joined him with capitals of 12000 and 9000. At the end of the year the total profit was Rs.4125. What is the difference between Rose ’s and Tom ’s share in the profit?
Options:
A)s.340
B)s.362
C)s.375
D)s.382
E)s.390
Rationale: John : Rose : Tom
Ratio of their investments = 18000 × 12 : 12000 × 9 : 9000 × 8
= 6 : 3: 2
The difference between Rose’s and Tom’s share = 1 share
:.i.e. = Rs. 4125 × 1/11 = Rs.375.
C)
Answer: C
Question: By travelling at 80 kmph, a person reaches his destination on time. He covered two-third the total distance in one-third of the total time. What speed should he maintain for the remaining distance to reach his destination on time?
Options:
A)25 kmph
B)40 kmph
C)35 kmph
D)46 kmph
E)50 kmph
Rationale: Let the time taken to reach the destination be 3x hours. Total distance = 80 * 3x = 240x km
He covered 2/3 * 240x = 160x km in 1/3 * 3x = x hours So, the remaining 80x km, he has to cover in 2x hours. Required speed = 80x/2x
=40 kmph.
Answer: B
Answer: B
Question: On a particular mathematics exam, the student has 5 answers to choose from. If the student guesses at the answers, the probability of the student getting a correct answer on each question is 1/5. What is the least number of times that the student should guess in order to take the probability of getting a correct answer at least once to more than 50%.
Options:
A)4
B)1
C)2
D)5
E)6
Rationale: Rule of Subtraction: P(A) = 1 - P(A')
Rule of Multiplication: P(A ∩ B) = P(A) P(B)
The probability that the student gets a correct answer at least once in 2 guesses is 1- (4/5)^2 = 1 - 16/25 = 9/25 < 50%.
The probability that the student gets a correct answer at least once in 3 guesses is 1- (4/5)^3 = 1 - 64/125 = 61/125 < 50%.
The probability that the student gets a correct answer at least once in 4 guesses is 1- (4/5)^4 = 1 - 256/625 = 369/625 > 50%.
Answer: A
Answer: A
Question: Alex and Brenda both stand at point X. Alex begins to walk away from Brenda in a straight line at a rate of 8 miles per hour. One hour later, Brenda begins to ride a bicycle in a straight line in the opposite direction at a rate of R miles per hour. If R > 8, which of the following represents the amount of time, in terms of R, that Alex will have been walking when Brenda has covered twice as much distance as Alex?
Options:
A)R-4
B)R/(R+4)
C)R/(R-16)
D)8/(R-8)
E)2R - 4
Rationale: Let T be the time thatAlexwill have been walking when Brenda has covered twice as much distance as Alex.
In T hours Alex will cover 4T miles;
Since Brenda begins her journey 1 hour later than Alex then total time for her will be T-1 hours, and the distance covered in that time will be R(T-1);
We want the distance covered by Brenda to be twice as much as that of Alex: 2*8T=R(T-1) --> 16T=RT-R --> T=R/(R-16).
Answer: C.
Answer: C