divelab/Sys2Bench huggingface dataset:
Question: In a can, there is a mixture of milk and water in the ratio 4 : 5. If it is filled with an additional 4 litres of milk the can would be full and ratio of milk and water would become 6 : 5. Find the capacity of the can?
Options:
A)40
B)44
C)48
D)22
E)None of these
Rationale: Let the capacity of the can be T litres.
Quantity of milk in the mixture before adding milk = 4/9 (T - 4)
After adding milk, quantity of milk in the mixture = 6/11 T.
6T/11 - 4 = 4/9(T - 4)
10T = 396 - 176 => T = 22.
ANSWER:D
Answer: D
Question: Total dinning bill for 8 people was $211.00.If they add 15% tip and divided the bill evenly ,approximate.What was each persons find share
Options:
A)$30.14
B)45.14
C)34.66
D)32.29
E)30.33
Rationale: 211*15=3165/100=31.65
211+31.65=242.65
242.65/8=30.33
ANSWER:E
Answer: E
Question: Which of the following can be a perimeter e of a triangle inscribed in a circle of radius 1?
I. 0.001
II. 0.010
III. 0.100
Options:
A)I only
B)III only
C)II and III only
D)I, II, and III
E)Not I, II, or III
Rationale: Yes,the length of any side of a triangle must be larger than the positive difference of the other two sides, but smaller than the sum of the other two sides.
But how do you use the above property to solve the question?
The lower limit of the perimeter of an inscribed triangle in a circle of ANY radius is 0: e>0.
Answer is D.
Answer: D
Question: By selling 100 pencil, a trader gains the cost of 30 Pencil. Find his gain percentage?
Options:
A)26 1/3%
B)51 1/3%
C)30%
D)53 1/3%
E)34 1/3%
Rationale: C
30%
Let the CP of each pencil be Rs. 1.
CP of 100 pens = Rs. 100
Profit = Cost of 30 pencil = Rs. 30
Profit% = 30/100 * 100 =30%
Answer: C
Question: If $ 5,000 is invested in an account that earns 6% interest compounded semi-annually, then the interest earned after one year would be how much greater than if the $ 5,000 had been invested at 8% simple yearly interest?
Options:
A)$ 6
B)$ 8
C)$ 12
D)$ 16
E)$ 432
Rationale: ANS A
Solution
Amount (CI) = P+(1+r/n)^nt = 5000+(1+0.06/2)^2= 5406
Amount (SI) = P+PTR/100 = 5000+(5000*1*8/100)=5400
Difference = 5406-5400=6 $
A
Answer: A
Question: 80% of Ram's marks is equal to 20% of Rahim's marks which percent is equal to 30% of Robert's marks. If Robert's marks is 80, then find the average marks of Ram and Rahim?
Options:
A)70
B)97
C)87
D)90
E)75
Rationale: Given, 80% of Ram's marks = 20% of Rahim's marks = 30% of Robert's marks.
Given, marks of Robert = 80
30% of 80 = 30/100 * 8 = 24
Given, 80% of Ram's marks = 24.
=> Ram's marks = (24 * 100)/80 = 30
Also, 20% of Rahim's marks = 24
=> Rahim's marks = (24 * 100)/20 = 120
Average marks of Ram and Rahim = (30 + 120)/2 = 75.
Answer:E
Answer: E
Question: An error 12% in excess is made while measuring the side of a square. Now What is the percentage of error in the calculated area of the square?
Options:
A)6.64%
B)16.64%
C)15.64%
D)25.44%
E)10.64%
Rationale: Percentage error in calculated area
=(12+12+(12Ã—12)/100)%=25.44%
ANSWER:D
Answer: D
Question: ZYXW’ as coded as ‘ABCD’ then ‘STUV’ is coded as
Options:
A)YU
B)YY
C)U
D)H
E)W
Rationale: Here each letter is coded with its opposite letter. i.e. Z – A, Y – B, X – C, W – D. Similarly, S – H, T – G, U – F, V – E.
Answer:D
Answer: D
Question: A fort of 1000 soldiers has provisions for 25 days. After 5 days some of them left and the food was now enough for the same period of 25 days as before. How many of them left?
Options:
A)50
B)100
C)150
D)175
E)200
Rationale: 2000 ---- 50
1000 ---- 20
x ----- 25
x*25 = 1000*20
x=800
1000
-------
200
Answer: E
Answer: E
Question: There are 15 members in a family. it takes 180 days for a women to complete the work, however man completes in 120 days. They take 17days to complete the work if men work on alternate days and women work every third day. if all of them started together on the 1st day, then how many women are there in the family
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: Let the number of men be m and so the number of women = 15-m
Out of 17 days, men and women work together on 1,4,7,10,13,16th days (Total of 6 days) from the start.
Men work on alternate days, that is 1,3,5,7,9,11,13,15,17th days (Total of 9 days).
Let the total work be 360 units (LCM of 180 and 120).
1 man does 360/120 = 3 units per day
1 woman does 360/180 = 2 units per day
Based on above facts,
Total work by men + women in these 17 days = 360 units
m*9*3 + (15-m)*6*2 = 360,
27m + 180 -12m = 360, Solving m=12.
Num of men = 12 and number of women = 15-12 = 3
ANSWER:C
Answer: C
Question: Mr. Smitherly leaves Cedar Rapids at 8:00 a.m. and drives north on the highway at an average speed of 50 km per hour. Mr. Dinkle leaves Cedar Rapids at 9:00 a.m. and drives north on the same highway at an average speed of 70 km per hour. Mr. Dinkle will
Options:
A)overtake Mr. Smitherly at 9:30 a.m.
B)overtake Mr. Smitherly at 10:30 a.m.
C)overtake Mr. Smitherly at 11:30 a.m.
D)be 30 miles behind at 9:35 a.m.
E)never overtake Mr. Smitherly
Rationale: After one hour, Mr. Smitherly is ahead by 50 km.
Mr. Dinkle gains on Mr. Smitherly 20 km each hour.
2.5 hours after 9:00 a.m., Mr. Dinkle will catch Mr. Smitherly.
The answer is C.
Answer: C
Question: In how much time would the simple interest on a certain sum be 0.125 times the principal at 10% per annum?
Options:
A)1 1/4
B)1 1/6
C)1 1/5
D)1 1/3
E)1 1/9
Rationale: Let sum = x. Then, S.I. = 0.125x = 1/8 x, R = 10%
Time = (100 * x) / (x * 8 * 10) = 5/4 = 1 1/4 years.
Answer:A
Answer: A
Question: In a cinema hall for the matinee show which started at 2.30 pm and ended at 5.30 pm the vehicle parking lot had only three wheelers (auto rickshaws) and four wheelers. Today the wheels of the vehicles parked was counted and found to be 240. What could be the number of three wheelers parked therein?
Options:
A)41
B)43
C)42
D)45
E)48
Rationale: 3X+4y=240
by substitute through options 48 is correct
ANSWER:D
Answer: D
Question: Two trains are running at 40 km/hr and 20 km/hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 5 sec. What is the length of the fast train?
Options:
A)27 7/5
B)27 7/3
C)27 7/2
D)27 7/9
E)27 7/4
Rationale: Relative speed = (40 - 20) = 20 km/hr.
= 20 * 5/ 18 = 50/9 m/sec.
Length of faster train = 50/9 * 5 = 250/9
= 27 7/9 m.
Answer: D
Answer: D
Question: A train travelling at a speed of 75 mph enters a tunnel 31/2 miles long. The train is 1/4 mile long. How long does it take for the train to pass through the tunnel from the moment the front enters to the moment the rear emerges?
Options:
A)2.5 min
B)3 min
C)3.2 min
D)3.5 min
E)4 min
Rationale: Total distance = (7/2 + 1/4) miles
= 15/4 miles
time taken = 15/4*75 hrs
=1/20 hrs = 3 min
ANSWER B
Answer: B
Question: A merchant marks his goods up in such a way that the profit made on selling 30 articles is equal to the cost price of 20 articles. What is the E % profit made by the merchant?
Options:
A)66.67 %
B)50 %
C)200 %
D)100 %
E)33.33 %
Rationale: C.P of 1 article= $30(say)
C.P of 20 articles=30*20=$600
Now, C.P of 20 articles=Profit on 30 articles
Therefore, profit on 1 article=$600/30=$20
Profit E%=(20/30)*100=66.67%
Answer A
Answer: A
Question: In an exam Ashley secured 332 marks. If she secured 83 % makes, find the maximum marks
Options:
A)133
B)376
C)377
D)400
E)377
Rationale: Let the maximum marks be m.
Ashley’s marks = 83% of m
Ashley secured 332 marks
Therefore, 83% of m = 332
⇒ 83/100 × m = 332
⇒ m = (332 × 100)/83
⇒ m =33200/83
⇒ m = 400
Therefore, Ashley got 332 marks out of 400 marks.
Answer:D
Answer: D
Question: If Aaron is now twice as old as Bailey was 20 years ago, and B is Bailey's current age in years, which of the following represents the sum of Aaron and Bailey's ages 10 years from now?
Options:
A)3B-25
B)3B-16
C)3B-45
D)3B-78
E)3B-20
Rationale: B is Bailey's current age.
Let Aaron's current age be A.
given A = 2(B-20).
four years from now Aaron's age will be = 2(B-20) + 10 = 2B-30
four years from now Bailey's age will be = B+10
Sum of ages of Mason and Gunther's after 4 years = 2B-30+B+10= 3B-20
Ans : E
Answer: E
Question: How many seconds will a 900 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
Options:
A)23 sec
B)30 sec
C)49 sec
D)54 sec
E)59 sec
Rationale: Speed of train relative to man = 63 - 3
= 60 km/hr.
= 60 * 5/18
= 50/3 m/sec.
Time taken to pass the man = 900 * 3/50
= 54 sec.
Answer:D
Answer: D
Question: The length of a train and that of a platform are equal. If with a speed of 90 k/hr, the train crosses the platform in one minute, then the length of the train (in meters) is?
Options:
A)238
B)3769
C)750
D)789
E)231
Rationale: Speed = [90 * 5/18] m/sec = 25 m/sec; Time = 1 min. = 60 sec.
Let the length of the train and that of the platform be x meters.
Then, 2x/60 = 25 è x = 25 * 60 / 2 = 750
Answer: D
Answer: D
Question: If the arithmetic mean of seventy five numbers is calculated, it is 35. If each number is increased by 5, then mean of new numbers is
Options:
A)30
B)35
C)40
D)50
E)None
Rationale: Sol.
A.M. of 75 numbers = 35.
Sum of 75 numbers = (75 x 35) = 2625.
Total increase = (75x5) = 375.
Increased sum = (2625 + 375) = 3000.
Increased average = 3000 / 75 = 40.
Answer C
Answer: C
Question: Some of the 50% solution of acid was removed and this was replaced with an equal amount of 30% solution of acid. As a result, a 40% solution of acid was obtained. What fraction of the original solution was replaced?
Options:
A)1/2
B)1/3
C)2/3
D)1/4
E)2/5
Rationale: Let x be the fraction of the original solution that was replaced.
0.5*(1-x)+0.3(x)=0.4
0.2x=0.1
x=1/2
The answer is A.
Answer: A
Question: In how many ways can 4 apples (identical) be distributed among 3 children? (Some children may get no apples.)
Options:
A)20
B)25
C)30
D)15
E)10
Rationale: Generalised form for n = number of identical objects, and r = number of children is n+r-1Cr-1.
n=4 r= 3
6C2 =15
Answer : D
Answer: D
Question: A factory produces 7500 toys per week. If the workers at this factory work 5 days a week and if these workers make the same number of toys everyday, how many toys are produced each day?
Options:
A)4436 toys
B)5487 toys
C)6113 toys
D)1875 toys
E)1375 toys
Rationale: To find the number of toys produced every day, we divide the total number of toys produced in one week (of 5 days) by 5.
7500 /4 = 1875 toys
correct answer D
Answer: D
Question: A student has to secure 30% marks to get through. If he gets 80 marks and fails by 70 marks, find the maximum marks set for the examination.
Options:
A)500
B)1000
C)1200
D)1500
E)none of these
Rationale: Here, x = 30 , y = 80 and z = 70
Therefore, Maximum marks = [100( y + z )] / x.
= [100( 80 + 70 )]/30
= 500.
ANSWER:A
Answer: A
Question: Prints a page 24 pg per min .If the printed for 4 hours except 10 min.Where there
was an paper jam,how many page did it print
Options:
A)10,880
B)12,880
C)14,880
D)8,880
E)5,520
Rationale: 24 pages ------->1 min
4 hrs except 10 mints means=4*60=240-10=230 mints
i.e.,230*24=5,520 pages printed.
ANSWER:E
Answer: E
Question: Four milkmen rented a pasture. A grazed 24 cows for 3 months; B 10 for 5 months; C 35 cows for 4 months and D 21 cows for 3 months. If A's share of rent is Rs. 720, find the total rent of the field.
Options:
A)3750
B)3550
C)4250
D)2250
E)3250
Rationale: Ratio of shares of A, B, C, D = (24 x 3) : (10 x 5) : (35 x 4) : (21 x 3) = 72 : 50 : 140 : 63.
Let total rent be Rs. x. Then, A’s share = Rs. (72x)/325
(72x)/325=720 = x=(720 x 325)/72 = 3250
Hence, total rent of the field is Rs. 3250.
Answer is E.
Answer: E
Question: In a certain village, 20 litres of water are required per household per month. At this rate, if there are 10 households in the village, how long (in months) will 2000 litres of water last?
Options:
A)5
B)2
C)10
D)1
E)12
Rationale: I find it much easier to understand with real numbers, so choose (almost) any numbers to replace m,n and p:
In a certain village,m 20 litres of water are required per household per month. At this rate, if there aren 10 households in the village, how long (in months) willp2000litres of water last?
Water required is 20*10=200 (m*n)
Water available is 2000 (p)
It will last 10 months (p/m*n)
Ans : C
Answer: C
Question: In how many ways a committee, consisting of 4 men and 2 women can be formed from 6men and 4 women?
Options:
A)120
B)60
C)90
D)150
E)35
Rationale: Required number of ways = 6C4 * 4C2
= (6*5/2*1)*(4*3/2*1)
= 90
Answer is C
Answer: C
Question: Two employees X and Y are paid a total of Rs. 550 per week by their employer. If X is paid 120 percent of the sum paid to Y, how much is Y paid per week?
Options:
A)Rs.250
B)Rs.300
C)Rs.350
D)Rs.400
E)Rs.450
Rationale: Let the amount paid to X per week = x
and the amount paid to Y per week = y
Then x + y = 550
But x = 120% of y = 120y/100 = 12y/10
∴12y/10 + y = 550
⇒ y[12/10 + 1] = 550
⇒ 22y/10 = 550
⇒ 22y = 5500
⇒ y = 5500/22 = 500/2 = Rs.250
A)
Answer: A
Question: Find the product of the local value and absolute value of 4 in 20468?
Options:
A)1000
B)1200
C)1340
D)1450
E)1600
Rationale: Local value of 4 = 4 x 100 = 400
Place value of 4 = 4
There fore = 4 x 400 = 1600
E
Answer: E
Question: Linda spent 3/4 of her savings on furniture and the rest on a TV. If the TV cost her $250, what were her original savings?
Options:
A)$900
B)$800
C)$1000
D)$700
E)$100
Rationale: If Linda spent 3/4 of her savings on furnitute, the rest
4 / 4 - 3 / 4 = 1 / 4 on a TV
But the TV cost her $250. So 1 / 4 of her savings is $250. So her original savings are 4 times $250 = $100
correct answer E
Answer: E
Question: John decides to attend a basketball game with six friends. If the party of seven sits together in seven consecutive seats, and John must NOT sit in between two of his friends, how many ways can the seven friends be arranged?
Options:
A)1220
B)1000
C)540
D)1440
E)720
Rationale: John have to sit at either of the ends.
If John sits on the left most corner, then other 6 friends can be arranged in 6! = 720
John can also sit on the other end, then another 6! ways we can arrange.
So total number of ways = 720+720 = 1440
Answer : D
Answer: D
Question: Find the smallest number which when divided by 12 and 15 leaves respective remainders of 8 and 11.
Options:
A)87
B)97
C)27
D)21
E)56
Rationale: Let 'N' is the smallest number which divided by 12 and 15 leaves respective remainders of 8 and 11.
Required number = (LCM of 12 and 15) - (common difference of divisors and remainders) = (60) - (4) = 56.
ANSWER:E
Answer: E
Question: In how many ways can the letters of the word 'APPLE' be arranged ?
Options:
A)90
B)180
C)120
D)60
E)720
Rationale: The word 'APPLE' contains 5 letters, 1A, 2P, 1L.and 1E.
∴ Required number of ways = 5!/(1!)(2!)(1!)(1!) = 60.
Answer is D
Answer: D
Question: In the faculty of Reverse-Engineering, 230 second year students study numeric methods, 423 second year students study automatic control of airborne vehicles and 134 second year students study them both. How many students are there in the faculty if the second year students are approximately 80% of the total?
Options:
A)515.
B)545.
C)618.
D)649.
E)666.
Rationale: Answer is D :649
Solution : Total number of students studying both are 423 + 230 - 134 = 519 (Subtracting the 134 since they were included in the both the other numbers already).
So 80% of total is 519, so 100% is approx. 649.
Answer: D
Question: If the selling price of a mat is five times the discount offered and if the percentage of discount is equal to the percentage profit, find the ratio of the discount offered to the cost price.
Options:
A)11: 30
B)1 : 5
C)1 : 6
D)7 : 30
E)8 : 30
Rationale: Since S.P. = 5 (M.P. - S.P.) => 5 M.P. = 6 S.P.
M.P. = (6/5) S.P.
Since the percentage discount = Percentage profit,
[ { (6/5) S.P. - S.P. } / ((6/5 ) S.P) ] x100 = (S.P - C.P) / C.P x 100
Therefore, 1/6 = (S.P/C.P) – 1 => S.P = (7/6) C.P
M.P = 6/5 S.P = 6/5 x 7/6 C.P = 7/5 C.P
Therefore, Ratio of discount to C.P
= (M.P – S.P)/C.P = [{(7/5)C.P - (7/6)C.P} / C.P.]
= 7/30
Therefore the ratio is 7 : 30
ANSWER:D
Answer: D
Question: If 9 men do a work in 80 days, in how many days will 20 men do it?
Options:
A)18 days
B)36 days
C)42 days
D)48 days
E)44 days
Rationale: 9 * 80 = 20 * x
x = 36 days
ANSWER:B
Answer: B
Question: A tyre has two punctures. The first puncture along would have made the tyre flat in 9 minutes and the second alone would have done it in 6 minutes. If air leaks out at a constant rate, how long does it take both the punctures together to make it flat?
Options:
A)1 1⁄2 minutes
B)3 1⁄2 minutes
C)3 3⁄5 minutes
D)4 1⁄4 minutes
E)None of these
Rationale: 1 minute’s work of both the punctures = (1⁄9 + 1⁄6) = 5⁄18
So, both the punctures will make the tyre flat in 18⁄5 = 33⁄5 min.
Answer C
Answer: C
Question: A man can row downstream at 18 kmph and upstream at 10 kmph. Find the speed of the man in still water and the speed of stream respectively?
Options:
A)6
B)8
C)3
D)4
E)5
Rationale: Let the speed of the man in still water and speed of stream be x kmph and y kmph respectively.
Given x + y = 18 --- (1)
and x - y = 10 --- (2)
From (1) & (2) 2x = 28 => x = 14, y = 4.
Answer:D
Answer: D
Question: A train which has 440 m long, is running 45 kmph. In what time will it cross a person moving at 9 kmph in same direction ?
Options:
A)56 sec
B)44 sec
C)36 sec
D)29 sec.
E)19 sec.
Rationale: Time taken to cross a moving person = length of train/ relative speed
Time taken = 440/((45-9) (5/18)
= 440/ 36*(5/18)
= 440/10
= 44 sec
ANSWER:B
Answer: B
Question: If, 2 years ago, Jamie was half as old as he is now, how old will he be in x years?
Options:
A)x + 10
B)x + 5
C)x + 2
D)x – 5
E)x + 4
Rationale: let his age be a. a-2=a/2 hence a=4. 4 years hence, a =x+4
Answer E
Answer: E
Question: Find the curved surface area, if the radius of a cone is 35 m and slant height is 30 m?
Options:
A)1100
B)2200
C)3300
D)4400
E)5500
Rationale: Cone curved surface area = Ï€rl
22/7 Ã— 35 Ã— 30 = 110 Ã— 30 = 3300 m(power2)
Answer is C.
Answer: C
Question: The difference between C.I. and S.I. on an amount of $10,000 for 2 years is $36. What is the rate of interest per annum?
Options:
A)5%
B)6%
C)7%
D)8%
E)9%
Rationale: $36 is the interest on the first year of interest.
Let x be the interest rate.
The interest after the first year is 10000*x.
The interest on the first year's interest is 10000*x*x
10000*x^2 = 36
x = 0.06
The answer is B.
Answer: B
Question: Speed of a boat in standing water is 9 kmph and the speed of the stream is 1. 5 kmph. A man rows to a place at a distance of 105 km and comes back to the starting point. The total time taken by him is
Options:
A)16 hours
B)18 hours
C)20 hours
D)24 hours
E)28 hours
Rationale: upstream = 9kmph-1.5kmph = 7.5kmph
Downstream = 9kmph+1.5kmph = 10.5kmph
total time taken = 105/7.5 + 105/10.5 =24 hrs
ANSWER:D
Answer: D
Question: On a certain road 14% of the motorists exceed the posted speed limit and receive speeding tickets, but 20% of the motorists who exceed the posted speed limit do not receive speeding tickets. What percent of the motorists on the road exceed the posted speed limit?
Options:
A)10.5%
B)12.5%
C)17.5%
D)22%
E)30%
Rationale: Answer is C.
This question is in the OG and thus well explained by ets.
those who exceed : X
so X = 14%+0,2X
id est X = 17,5%
Answer: C
Question: Rs.1200 divided among P, Q and R. P gets half of the total amount received by Q and R. Q gets one-third of the total amount received by P and R. Find the amount received by R?
Options:
A)767
B)500
C)287
D)111
E)172
Rationale: Explanation:
Let the amounts to be received by P, Q and R be p, q and r.
p + q + r = 1200
p = 1/2 (q + r) => 2p = q + r
Adding 'p' both sides, 3p = p + q + r = 1200
=> p = Rs.400
q = 1/3 (p + r) => 3q = p + r
Adding 'q' both sides, 4q = p + q + r = 1200
=> q = Rs.300
r = 1200 - (p + q) => r = Rs.500.
Answer: B
Answer: B
Question: If 8 men or 12 women can do a piece of work in 25 days, in how many days can the same work be done by 6 men and 11 women?
Options:
A)10 days
B)11 days
C)13 days
D)15 days
E)17 days
Rationale: 8men = 12women (i.e 2men = 3women)
12women 1 day work= 1/25
soln:
6men(9women)+ 11women=20women=?
1 women 1 day work =12*25= 1/300
so, 20 women work= 20/300=1/15
ans: 15 days
ANSWER:D
Answer: D
Question: A motor boat takes 12 hours to go downstream and it takes 24 hours to return the same distance. what is the time taken by boat in still water?
Options:
A)26 h
B)16 h
C)86 h
D)96 h
E)66 h
Rationale: Explanation:
If t1 and t2 are the upstream and down stream times. Then time taken in still water is given by
\inline \frac{2\times t1\times t2}{t1+t2}=\frac{2\times 12\times 24}{36}=16h
Answer: B
Answer: B
Question: A man buys Rs. 20 shares paying 9% dividend. The man wants to have an interest of 12% on his money. The market value of each share is?
Options:
A)14
B)15
C)61
D)17
E)18
Rationale: Dividend on Rs. 20 = Rs. (9/100)x 20 = Rs.9/5.
Rs. 12 is an income on Rs. 100.
Rs.9/5 is an income on Rs.[ (100/12) x (9/5)] = Rs. 15?
Answer: B
Answer: B
Question: A and B invest money in the ratio 2:3 and they has loss of Rs.7000 at the end of year. what is the share of loss of B?
Options:
A)Rs.4200
B)Rs.3200
C)Rs.1200
D)Rs.200
E)None of the above
Rationale: et ratio of A and B be 2x & 3x
so net loss = 2x+3x= 7000
x=1400
A=2x=2(1400)=2800
B= 3x=3(1400)=4200
so, B= 4200
ANSWER:A
Answer: A
Question: A bullet train leaves Kyoto for Tokyo traveling 240 miles per hour at 12 noon. Ten minutes later, a train leaves Tokyo for Kyoto traveling 160 miles per hour. If Tokyo and Kyoto are 340 miles apart, at what time will the trains pass each other?
Options:
A)12:40pm
B)12:49pm
C)12:55pm
D)1:00pm
E)1:05pm
Rationale: Train A: going from K to T
Train B: going from T to K
First I calculated how far Train A will have travelled by the time Train B starts at 12:10:
10 minutes at 240 mph
1/6*240=40miles
They have 340-40=300 miles to travel to meet each other.
I found the combined rate of the two trains
Rate(A) + Rate(B) = 400mph
Divide Distance/Rate to find total time each will travel:
300/400>>> 45 Minutes to meet
12:10+45 minutes = 12:55 or Answer C
Answer: C
Question: A chemist mixes one liter of pure water with x liters of a 30% salt solution, and the resulting mixture is a 15% salt solution. What is the value of x?
Options:
A)1/4
B)1/3
C)1/2
D)1
E)3
Rationale: Concentration of salt in pure solution = 0
Concentration of salt in salt solution = 30%
Concentration of salt in the mixed solution = 15%
The pure solution and the salt solution is mixed in the ratio of --> (30 - 15)/(15 - 0) = 1/1
1/x = 1/1
x = 1
Answer: D
Answer: D
Question: In five football games thus far this season, Barry has run for 98, 107, 85, 89, and 91 yards. At a minimum, how many yards N will he need to gain this Sunday if he wants to keep his season average above 100 yards?
Options:
A)101
B)116
C)130
D)N=131
E)N=141
Rationale: Sorry the answer N=131 is D.
Answer: D
Question: The probability of obtaining an even prime number on each die, when a pair of dice is rolled out?
Options:
A)2/13
B)1/15
C)1/36
D)1/25
E)1/27
Rationale: The probability of getting an even prime (2) for a pair of dice is only once.
That is 1 on each die.
probability of getting 1 on a die is 1/6.
probability of getting 1 on 2 dice is 1/6 × 1/6 = 1/36
C
Answer: C
Question: A bag contains 6 red, 5 blue and 2 green balls. If 2 ballsare picked at random, what is the probability that both are red?
Options:
A)2/13
B)1/15
C)5/26
D)3/25
E)4/17
Rationale: P(Both are red),
=6C213C2=6C213C2
=5/26
C
Answer: C
Question: If the simple interest on a sum of money at 5% per annum for 3 years is Rs.1200, find the compound interest on the same sum for the same period at the same rate.
Options:
A)1251
B)1261
C)1271
D)1281
E)None
Rationale: Solution
Clearly, Rate	= 5% p.a.
Time	= 3 years
S.I	=Rs.1200.
So,Principal	=Rs.(100 x 1200/3x5)
=Rs.8000.
Amount	=Rs.[8000 x (1+5/100)³]
=Rs(8000x21/20x21/20x21/20)
= Rs.9261
C.I	=Rs.(9261-8000)
=Rs.1261.
Answer B
Answer: B