mathewhe/aqua_rat huggingface dataset:
Question: A box contains 10 apples, 9 of which are red. An apple is drawn from the box and its color is noted before it is eaten. This is done a total of n times, and the probability that a red apple is drawn each time is less than 0.5. What is the smallest possible value of n?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: When you choose (and then eat) the first apple, the probability of that apple being red is 9/10. So if we do the activity 1 times, the probability of it being red is 9/10.
For 2 times, it is (9/10)*(8/9)
For 3 times, it is (9/10)*(8/9)*(7/8)
You can notice that the numerator of the first term cancels with the denominator of the second. So we can see that the probability becomes 0.5 when the last term is 5/6 & it becomes less than 0.5 when the last term is 4/5.
9 accounts for n=1, so 4 will account for n=6,
Answer.D
Answer: (D) 6
Question: The toll T, in dollars, for a truck using a certain bridge is given by the formula T = 1.50 + 1.50( x − 2), where x is the number of axles on the truck. What is the toll for an 18-wheel truck that has 2 wheels on its front axle and 4 wheels on each of its other axles?
(A)  $ 2.50
(B)  $ 3.00
(C)  $ 3.50
(D)  $ 6.00
(E)  $ 5.00
Rationale: Number of wheels in truck = 18
Number of wheels on its front axle =2
number of wheels remaining = 16
number of axles remaining axles = 16/4 = 4
Total number of axles = 5
T = 1.50 + 1.50( x − 2)
= 1.50 + 1.5*3
= 1.5 +4.5 = 6 $
Answer D
Answer: (D)  $ 6.00
Question: If two of the four expressions x + y , x + 7y , x - y , and 7x - y are chosen at random, what is the probability that their product will be of the form of x^2-(by)^2, where b is an integer?
(A) 1/3
(B) 1/8
(C) 1/2
(D) 1/6
(E) 1/5
Rationale: Total number of expressions if 2 are multiplied = 4C2 = 4!/2!*2! = 6
now we have to find the expressions that are in form of x^2 - (by)^2
one is (x+y)(x-y) = x^2 - (1y)^2
If you see any other combination we are always going to have one term of xy since 7x and 7y are there, so there can be only one type of combination like this.
therefore, probablity is 1/6
Answer : D
Answer: (D) 1/6
Question: Triangle ATriangle B are similar triangles with areas 2268 units square and 2527 units square respectively. The ratio of there corresponding height would be
(A) 9:10
(B) 18:19
(C) 23:27
(D) 13:17
(E) 15:23
Rationale: Let x be the height of triangle A and y be the height of triangle of B.
since triangles are similar, ratio of area of A and B is in the ratio of x^2/y^2
Therefore, (x^2/y^2)=2268/2527
(x^2/y^2)=(18*18*7)/(19*19*7)
(x^2/y^2)=18^2/19^2
x/y=18/19
Ans=B
Answer: (B) 18:19
Question: Rajesh calculated his average over the last 24 tests and found it to be 76. He finds out that the marks for three tests have been inverted by mistake. The correct marks for these tests are 87, 79 and 98. What is the approximate percentage difference between his actual average and his incorrect average?
(A) 0
(B) 9
(C) 8
(D) 7
(E) 5
Rationale: No Change
Incorrect value is: 78, 97, 89
correct values are: 87, 79, 98
difference between correct and incorrect value is= 9 + 9 -18=0
Answer:A
Answer: (A) 0
Question: Given that -1 ≤ v ≤1, -2 ≤ u ≤ -0.5 and -2 ≤ z ≤ -0.5 and w = vz/u, then which of the following is necessarily true ?
(A) -0.5 ≤ w ≤ 2
(B) -4 ≤ w ≤ 4
(C) -4 ≤ w ≤ 2
(D) -2 ≤ w ≤ 0.5
(E) None of these
Rationale: Explanation :
We try to get an upper bound on the value of w.
After taking a look at the options we figure it out that if we take v=-1,z=-2 and u=-0.5.
we get the lower bound as -4.
If we take v=1, z=-2 and u=-0.5 we have the upper bound as 4.
Hence, the right option is 2.ie -4 ≤ w ≤ 4
Answer : B
Answer: (B) -4 ≤ w ≤ 4
Question: A certain restaurant offers 6 kinds of cheese and 2 kinds of fruit for its dessert platter. If each dessert platter contains an equal number of kinds of cheese and kinds of fruit, how many different dessert platters could the restaurant offer?
(A) 8
(B) 12
(C) 15
(D) 21
(E) 27
Rationale: As dessert platter should contain equal number of kinds of cheese and fruits, desert can contain:
A. 2 kinds of cheese and 2 kinds of fruits --> 6C2*2C2=15*1=15
B. 1 kind of cheese and 1 kind of fruit --> 6C1*2C1=6*2=12
A+B=15+12=27
Answer: E.
Answer: (E) 27
Question: Mars travels around the sun at a speed of approximately 15 miles per second. The approximate speed is how many miles per hour?
(A) 48,000
(B) 51,000
(C) 54,000
(D) 57,000
(E) 60,000
Rationale: 15 * 3600 = 54,000
The answer is C.
Answer: (C) 54,000
Question: Find a a prime number from below options?
(A) 84
(B) 97
(C) 98
(D) 100
(E) 102
Rationale: Clearly, 97 is a prime number.
B
Answer: (B) 97
Question: A car gets 40 kilometers per gallon of gasoline. How many gallons of gasoline would the car need to travel 160 kilometers?
(A) 4
(B) 5.5
(C) 6.5
(D) 7.5
(E) 8.5
Rationale: Each 40 kilometers, 1 gallon is needed. We need to know how many 40 kilometers are there in 160 kilometers?
160 ÷ 40 = 4 × 1 gallon = 4 gallons
correct answer A
Answer: (A) 4
Question: On a summer camp, 25% of the campers paid $120 each, 30% paid $80 each and the rest paid $65 each. What percentage of the total amount paid came from the campers who paid $80?
(A) 18%
(B) 21%
(C) 35%
(D) 33.3%
(E) 37.5%
Rationale: let the total no of campers be 100
total amount = (25*120)+(30*80)+(40*65) = 3000+2400+2600= $8000
required percentage = (28/80)*100 =35%
C
Answer: (C) 35%
Question: A bottle contains a certain solution. In the bottled solution, the ratio of water to soap is 3:4, and the ratio of soap to salt is four times this ratio. The solution is poured into an open container, and after some time, the ratio of water to soap in the open container is halved by water evaporation. At that time, what is the ratio of water to salt in the solution?
(A) 3:8
(B) 3:9
(C) 3:4
(D) 3:12
(E) 4:12
Rationale: Water:soap = 3:4
Soap:Salt=12:16
=> For 12 soap, salt = 16
=> For 4 Soap, salt = (16/12)*4 = 16/12=64/12=18/3=6/1
So, water:soap:salt = 3:4:6 = 3:4:6
After open container, water:soap:salt = 1.5:4:6
So, water:salt = 1.5:6 = 3:12
ANSWER:D
Answer: (D) 3:12
Question: Sari and Ken climb up a mountain. At night, they camp together. On the day they are supposed to reach the summit, Sari wakes up at 07:00 and starts climbing at a constant pace. Ken starts climbing only at 09:00, when Sari is already 700 meters ahead of him. Nevertheless, Ken climbs at a constant pace of 500 meters per hour, and reaches the summit before Sari. If Sari is 50 meters behind Ken when he reaches the summit, at what time did Ken reach the summit?
(A) 13:00
(B) 13:30
(C) 14:00
(D) 15:00
(E) 15:30
Rationale: Both Sari and Ken climb in the same direction.
Speed of Sari = 700/2 = 350 meters/hr (since she covers 700 meters in 2 hrs)
Speed of Ken = 500 meters/hr
At 8:00, distance between Ken and Sari is 700 meters. Ken needs to cover this and another 50 meters.
Time he will take = Total distance to be covered/Relative Speed = (700 + 50)/(500 - 350) = 5 hrs
Starting from 9:00, in 5 hrs, the time will be 14:00
Answer (C)
Answer: (C) 14:00
Question: Every year an amount increases by 1/8th of itself. How much will it be after two years if its present value is Rs.51200?
(A) 81000
(B) 81028
(C) 27772
(D) 29889
(E) 64800
Rationale: 51200* 9/8 * 9/8 = 64800.Answer:E
Answer: (E) 64800
Question: Look at this series: 2, 1, (1/2), (1/4), ... What number should come next?
(A) (1/3)
(B) (1/8)
(C) (2/8)
(D) (1/16)
(E) (1/32)
Rationale: Answer: Option B
This is a simple division series; each number is one-half of the previous number.
In other terms to say, the number is divided by 2 successively to get the next result.
4/2 = 2
2/2 = 1
1/2 = 1/2
(1/2)/2 = 1/4
(1/4)/2 = 1/8
Answer: (B) (1/8)
Question: A cyclist rides a bicycle over a route which is 1/3 uphill, 1/3 level, and 1/3 downhill. If the cyclist covers the uphill part of the route at the rate of 12 km per hour and the level part at the rate of 18 km per hour, what rate in km per hour would the cyclist have to travel the downhill part of the route in order to average 18 km per hour for the entire route?
(A) 24
(B) 30
(C) 36
(D) 42
(E) 48
Rationale: Let V be the speed on the downhill section.
Let D be the distance of each of the three equal sections.
Total time T = T1+T2+T3 and 3D/T = 18 km/hour
3D / (D/12 + D/18 + D/V) = 18
1/6 = 1/12 + 1/18 + 1/V
1/V = 1/36 and so V = 36 km/h
The answer is C.
Answer: (C) 36
Question: Solution P is 20 percent lemonade and 80 percent carbonated water by volume; solution Q is 45 percent lemonade and 55 percent carbonated water by volume. If a mixture of PQ contains 67.5% percent carbonated water, what percent of the volume of the mixture is P?
(A) 25%
(B) 40%
(C) 50%
(D) 60%
(E) 75%
Rationale: 67.5% is 12.5%-points below 80% and 12.5%-points above 55%.
So the ratio of solution P to solution Q is 1:1.
Mixture P is 1/2 = 50% of the volume of mixture PQ.
The answer is C.
Answer: (C) 50%
Question: A trader bought a car at 20% discount on its original price. He sold it at a 40% increase on the price he bought it. What percent of profit did he make on the original price?
(A) 72%
(B) 82%
(C) 12%
(D) 22%
(E) 42%
Rationale: Original price = 100
CP = 80
S = 80*(140/100) = 112
100 - 112 = 12%
Answer: C
Answer: (C) 12%
Question: The ratio between the present ages of P and Q is 6:7.If Q is 4 years old than P,what will be the ratio of the ages of P and Q after 4 years ?
(A) 3:4
(B) 3:5
(C) 4:3
(D) None of these
(E) Cannot be determined
Rationale: Solution
Let P's age and Q's age be 6x years and 7x years respectively.
Then,7x-6x = 4 ⇔ x = 4.
∴ Required ratio = (6x + 4) : (7x + 4)=28 : 32 =7: 8. Answer D
Answer: (D) None of these
Question: The smallest number which when diminished by 7, is divisible 12, 16, 18, 21 and 28 is:
(A) 1008
(B) 1015
(C) 1022
(D) 1032
(E) 1048
Rationale: Required number = (L.C.M. of 12,16, 18, 21, 28) + 7
= 1008 + 7
= 1015
Answer: Option B
Answer: (B) 1015
Question: A train is moving at a speed of 132 km/hr. If the length of the train is 110 metres, how long will it take to cross a railway platform 165 metres long?
(A) 7½ sec
(B) 10 sec
(C) 12 ½ sec
(D) 15 sec
(E) 18 sec
Rationale: Speed of train = 132 *(5/18) m/sec = 110/3 m/sec.
Distance covered in passing the platform = (110 + 165) m = 275 m.
Time taken =275 *(3/110) sec =15/2 sec = 7 ½ sec
Answer : A.
Answer: (A) 7½ sec
Question: WINK, Inc. follows a certain procedure that requires two tasks to be finished independently in order for a job to be done. On any given day, there is a 1/8 probability that task 1 will be completed on time, and a 3/5 probability that task 2 will be completed on time. On a certain day, what is the probability that task 1 will be completed on time, but task 2 will not?
(A) 1/20
(B) 3/40
(C) 13/40
(D) 7/20
(E) 13/22
Rationale: P(1 and not 2)=1/8*(1-3/5)=1/20.
Answer: A.
Answer: (A) 1/20
Question: The variables m and n are positive integers. When m is divided by 18, there is a remainder of 12, and when n is divided by 24, there is a remainder of 14. Which of the following are possible values of m + n?
I. 70
II. 50
III. 92
(A) I only
(B) III only
(C) I and II
(D) I only III
(E) II and III
Rationale: m = 18k + 12 --> Values are 12, 30, 48, 66, 84
n = 24k + 14 --> Values are 14, 38, 62, 86
I. 70--> Not possible
II. 50 --> 12 + 38-->Possible
III. 92 --> 30 + 622 --> Possible
Answer: E
Answer: (E) II and III
Question: When n is divided by 5 the remainder is 3. What is the remainder when (n + 2)^2 is divided by 5?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: n = 5x+3, for some integer x
(n+2)^2=(5x+5)^2=5y, for some integer y
When we divide this by 5, the remainder is 0.
The answer is A.
Answer: (A) 0
Question: A man sells a horse for Rs.800 and loses something, if he had sold it for Rs.980, his gain would have been double the former loss. Find the cost price of the horse?
(A) 287
(B) 279
(C) 267
(D) 860
(E) 298
Rationale: CP = SP + 1CP = SP - g
800 + x = 980 - 2x
3x = 180 => x
= 60
CP = 800 + 60
= 860
Answer:D
Answer: (D) 860
Question: The ratio between the speeds of two Bullet trains is 7:6. If the second Bullet train runs 440 kms in 4 hours, then the speed of the first train is:
(A) 89.25 km/hr.
(B) 37.25 km/hr.
(C) 128.3 km/hr.
(D) 94.25 km/hr.
(E) 96.25 km/hr.
Rationale: Let the speed of two bullet trains be 7x and 6x km/hr.
Then, 6x = (440/4) = 110
x = (110/6) = 18.33
Hence, speed of first bullet train = (7 x 18.33) km/hr = 128.3 km/hr.
C
Answer: (C) 128.3 km/hr.
Question: In a Private Company 20 Nos. staffs are employed. In a Festival season their Boss give festival allowance to all. He says his accountant to calculate for 30 days @ 100. Also he says balance payment will give to driver and cleaning staff and to be adjust from petty cash. He had given Rs.65000/- to the accountant. How much amount will taken from Petty cash?
(A) 1000
(B) 3000
(C) 3500
(D) 2500
(E) 2250
Rationale: For 20 staffs: 300*100*20 = 60000
for driver and cleaning staff: 300*100*2 =6000
From petty Cash : 1000
Answer is 1000
Answer: (A) 1000
Question: An order was placed for the supply of a carpet whose breadth was 6 m and length was 1.44 times the breadth. What be the cost of a carpet whose length and breadth are 40% more and 25% more respectively than the first carpet. Given that the ratio of carpet is Rs. 45 per sq m?
(A) Rs.4082.87
(B) Rs.4082.42
(C) Rs.4082.97
(D) Rs.4082.40
(E) Rs.4082.19
Rationale: Length of the first carpet
= (1.44)(6) = 8.64 cm
Area of the second carpet
= 8.64(1 + 40/100) 6 (1 + 25/100)
= 51.84(1.4)(5/4) sq m
= (12.96)(7) sq m
Cost of the second carpet
= (45)(12.96 * 7) = 315 (13 - 0.04)
= 4095 - 12.6
= Rs.4082.40
Answer:D
Answer: (D) Rs.4082.40
Question: A gambler has won 40% of his 30 poker games for the week so far. If, all of a sudden, his luck changes and he begins winning 80% of the time, how many more games must he play to end up winning 60% of all his games for the week?
(A) 20
(B) 25
(C) 30
(D) 35
(E) 40
Rationale: Let x be the number of additional games the gambler needs to play.
0.4(30) + 0.8x = 0.6(x+30)
0.2x = 6
x = 30
The answer is C.
Answer: (C) 30
Question: Find the no.of ways of arranging the 10 boys around a round tabele?
(A) 9!
(B) 10!
(C) 8!
(D) 7!
(E) 6!
Rationale: Ans.(9!)
Sol. Total number of persons = (10-1)! =9!
Answer: (A) 9!
Question: Angelo and Isabella are both salespersons. In any given week, Angelo makes $560 in base salary plus 8 percent of the portion of his sales above $1,000 for that week. Isabella makes 10 percent of her total sales for any given week. For what amount of weekly sales would Angelo and Isabella earn the same amount of money?
(A) 23,500
(B) 24,000
(C) 25,500
(D) 26,500
(E) 27,500
Rationale: Let the weekly sales of both = x
560+(x−1000)8/100=10/100x
x = 24000
ANSWER:B
Answer: (B) 24,000
Question: With a uniform speed a car covers the distance in 8 hours. Had the speed been increased by 5 km/hr, the same distance could have been covered in 7 1/2 hours. What is the distance covered?
(A) 187 km
(B) 480 km
(C) 278 km
(D) 297 km
(E) 600 km
Rationale: Let the distance be x km. Then,
x/(7 1/2) - x/8 = 5
2x/15 - x/8 = 5 => x = 600 km.
Answer:E
Answer: (E) 600 km
Question: Shan starts from Barabanki to Fatehpur, 1 hour after Ajay starts. Shahrukh meets Kajol 1.5 hours after Shahrukh starts. If the speed of Shan is at least 20km/hour fasterthan the speed of Kajol. What is the min speed of Shan to overtake Ajay, before he meets Kajol?
(A) 40.5 km/h
(B) 45.67 km/h
(C) 50.7 km/h
(D) 68.5 km/h
(E) 67.5 km/h
Rationale: Let t be the time after Kajol starts, when she meets Ajay, then
\inline t=\frac{300}{(x+y)}
This should be less than 2.5 or (x+y)>120
Since y= \inline \frac{3x}{2} \inline \Rightarrow y>72
This (y>72) is greater than 67.5 km/h and hence Shahrukh will always overtake Ajay before he meets Kajol.
E)
Answer: (E) 67.5 km/h
Question: 1600 men have provisions for 28 days in the temple. If after 4 days, 300 men leave the temple, how long will the food last now?
(A) 25 1/2 days
(B) 29 1/2 days
(C) 28 1/2 days
(D) 27 1/2 days
(E) 26 1/2 days
Rationale: 1600 ---- 28 days
1600 ---- 24
1200 ---- ?
1600*24 = 1300*x
x =29 1/2 days
ANSWER:B
Answer: (B) 29 1/2 days
Question: There is a 10% chance that Tigers will not win at all during the whole season. There is a 5% chance that Federer will not play at all in the whole season. What is the greatest possible probability that the Tigers will win and Federer will play during the season?
(A) A)55%
(B) B)60%
(C) C)70%
(D) D)72%
(E) E)95%
Rationale: There is a 10% chance that Tigers will not win at all during the whole season
We can infer that there is 90% chance Tigers will win .
Similarly There is a 5% chance that Federer will not play at all in the whole season
We can also infer that there is 95% chance that Federer will play.
Answer E
Answer: (E) E)95%
Question: When I was born, my mother was 23 years of age. After 6 years, when my sister was born, my father was 34 years of age. what is the difference between the ages of my parents?
(A) 17 years
(B) 11 years
(C) 6 years
(D) 5 years
(E) 8 years
Rationale: When age of Son=0 ,Mother=23
After 6 years, Son=6 ,Mother=23+6=29 ,Father=34
So difference between ages of Mother & Father=34-29=5
ANSWER:D
Answer: (D) 5 years
Question: On a trip, a cyclist averaged 11 miles per hour for the first 22 miles and 10 miles per hour for the remaining 20 miles. If the cyclist returned immediately via the same route and took a total of 9 hours for the round trip, what was the average speed (in miles per hour) for the return trip?
(A) 7.6
(B) 7.8
(C) 8
(D) 8.2
(E) 8.4
Rationale: The time to go 42 miles was 22/11+20/10=2+2=4 hours.
The average speed for the return trip was 42 miles/5 hours= 8.4 mph.
The answer is E.
Answer: (E) 8.4
Question: Average of five numbers is 27. If one number is excluded the average becomes 25. The excluded number is
(A) 35
(B) 45
(C) 55
(D) 65
(E) 67
Rationale: Explanation:
Number is (5*27) - (4*25) = 135-100 = 35
Answer: Option A
Answer: (A) 35
Question: At a certain college, 70 percent of the students taking physical education class who were injured reported their injury, while 20 percent of the students who were injured in physical education class didn't report their injury. What percent of the students taking physical education class were injured?
(A) 87.5%
(B) 60.5%
(C) 40%
(D) 75.5%
(E) 80%
Rationale: Statement: 70% of students taking Pysical Education class (PE) Admitted to being Injured (AI). Of the students who took PE who were Injured (I), 20% declined to admit injury (notAI). [Note: A Venn Diagram is useful to visualize the problem.]
Solution: Sample space is 100%.
PE = 100%
AI/PE = 70%
notAI/I = 20% => 100% - 20% => AI/I = 80%
I/PE = (70)/(80)% = 80%
Answer: A
Answer: (A) 87.5%
Question: A train 200 m long is running with a speed of 54 kmph. In what will it pass a car whose speed at 36 kmph in the direction opposite to that in which the train is going
(A) 8 sec
(B) 10 sec
(C) 12 sec
(D) 14 sec
(E) 15 sec
Rationale: Explanation:
Speed of the train relative to man = (54 + 36) kmph
= 90 ×5/18 m/sec = 25 m/sec.
Time taken by the train to cross the car = Time taken by it to cover 200 m
at 25 m / sec = (200 ×1/25) sec = 8 sec
Answer: Option A
Answer: (A) 8 sec
Question: If the ratio of ages of two friends is 4:3 and sum of their ages is 70 years then what is the age of older friend?
(A) 30 years
(B) 35 years
(C) 40 years
(D) 25 years
(E) 45 years
Rationale: Sum of thier ages is 70 in ratio 4:3
So 40+30 gives us 70. Wich is 4:3 so, older guy is having 40.
ANSWER:C
Answer: (C) 40 years
Question: In a group of 100 cars, 47 cars do not have air conditioning. If at least 53 cars have racing stripes, what is the greatest number of cars that could have air conditioning but not racing stripes?
(A) 45
(B) 47
(C) 49
(D) 51
(E) 53
Rationale: Lets assume AC=53(includesonly AC carsandcars with AC and racing stripes)
lets assume RS(racing stripes)>=53(includescars with AC and racing stripesandonly racing stripes).
Now since we want to maximize(only AC) we have to see to it thatcars with AC and racing stripesis minimal(assume 0) But since RS>=53.. we have to assign atleast 6 tocars with AC and racing stripes.
Hence AC=53-6=47.
The answer is B
Answer: (B) 47
Question: 1,000^2 + 1,001^2 +1,002^2 + 1,003^2 + 1,004^2 =
(A) 6,030,053
(B) 6,030,054
(C) 6,030,055
(D) 6,020,030
(E) 6,030,057
Rationale: Interesting problem.
I think key is to notice that all the given answer choices differs in last two digits. Therefore, our entire focus should be to figure out how the given terms contribute to last two digits of total.
1000^2 -> 00
1001^1 -> 01
.
.
.
1004^2 -> 16
Total -> *30
Answer D.
Answer: (D) 6,020,030
Question: The simple interest at x% for x years will be Rs. x on sum of:
(A) x
(B) 100x
(C) [100/x]
(D) [x/100]
(E) None
Rationale: Sol.
Sum = [100 * S.I. / R * T] = Rs. [100 * x / x * x] = Rs. [100/x].
Answer C
Answer: (C) [100/x]
Question: The standard deviation of a normal distribution of data is 2, and 3 standard deviations below the mean is greater than 45. What is a possible value for the mean of the distribution?
(A) 52
(B) 47
(C) 48
(D) 49
(E) 50
Rationale: The standard deviation ({SD}) = 2;
3 standard deviations below the mean is greater than 45:
{Mean} - 3*{SD} > 45;
{Mean} - 6 > 45;
{Mean} > 51.
Answer: A.
Answer: (A) 52
Question: Four 6 faced dice are thrown together. The probability that all the three show the same number on them is?
(A) 1/32
(B) 1/216
(C) 1/33
(D) 1/38
(E) 1/34
Rationale: The three dice can fall in 6 * 6 *6 * 6 = 1296 ways.
Hence the probability is 6/1296
= 1/216
Answer: B
Answer: (B) 1/216
Question: Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is?
(A) 3/7
(B) 3/2
(C) 3/5
(D) 3/4
(E) 3/1
Rationale: Let the speeds of the two trains be x m/sec and y m/sec respectively. Then, length of the first train = 27 x meters, and length of the second train = 17 y meters. (27 x + 17 y) / (x + y) = 23 ==> 27 x + 17 y = 23 x + 23 y ==> 4 x = 6 y ==> x/y = 3/2.Answer: B
Answer: (B) 3/2
Question: Michele invests 300 of her money in a mutual fund that quickly goes sour, losing 25% of its value each day for a week. Which of the following COULD be the value of Michele’s investment at the close-of-business any day that week?
(A) $40.10
(B) $133.00
(C) $250.05
(D) $1575.00
(E) $10000.00
Rationale: Suppose she invests n$ in the starting then in the subesequent days the money left after the day will be
n/2, n/4, n/8, n/16, n/32
So, answer will be A
Answer: (A) $40.10
Question: How many 4 digit numbers can be formed with the digits 0, 1, 2, 3, 4, 5, 6 and 4?
(A) a. 220
(B) b. 249
(C) c. 432
(D) d. 216
(E) e. 288
Rationale: Taking Question with it's same language as given
To make number divisible by 5, the unit digit should be either 0 or 5 only
Case 1: If unit digit is fixed as zero
With two6s The choice to fill the remaining three digits = 3C2 x 5 = 15
With all remaining 3 digits different, The choice to fill the remaining three digits = 6 x 5 x 4= 120
Total Such cases = 120+15 = 135
Case 2: If unit digit is fixed as Five
With two6s and one0The choice to fill the remaining three digits = 2 [6605 or 6065]
With two6s and without0The choice to fill the remaining three digits = 3C2 x 4 = 12
With all remaining 3 digits different, and one0The choice to fill the remaining three digits = 2 (ways to place zero) x 5 x 4= 40
With all remaining 3 digits different, and without0The choice to fill the remaining three digits = 3 x 5 x 4= 60
Total Such cases = 2+12+40+60 = 114
Total numbers = 135+114 = 216
ANSWER OPTION D
Answer: (D) d. 216
Question: A man can row 40km upstream and 55km downstream in 13 hours also, he can row 30km upstream and 44km downstream in 10 hours.find the speed of the man in still water and the speed of the current.
(A) 1 lmph
(B) 2 kmph
(C) 4 kmph
(D) 5 kmph
(E) 3 kmph
Rationale: let rate upstream=x km/hr and rate downstream=y km/hr.
Then,40/x +55/y =13â€¦(i) and 30/x +44/y =10
Multiplying (ii) by 4 and (i) by 3 and subtracting ,we get:11/y=1 or y=11.
Substituting y=11 in (i),weget:x=5.
Rate in still water =1/2(11+5)kmph=8kmph.
Rate of current=1/2(11-5)kmph=3kmph
ANSWER E
Answer: (E) 3 kmph