divelab/Sys2Bench huggingface dataset:
Question: In the storage room of a certain bakery, the ratio of sugar to flour is 3 to 6, and the ratio of flour to baking soda is 5 to 1. If there were 30 more pounds of baking soda in the room, the ratio of flour to baking soda would be 4 to 1. How many pounds of sugar are stored in the room?
Options:
A)30
B)50
C)60
D)45
E)70
Rationale: Sugar:Flour = 3:6 = 1:2 = 5:10
Flour:Soda = 5:1 = 10:2;
Thus we have that Sugar:Flour:Soda = 5x:10x:2x.
Also given that 10x/(2x+30) = 4/1 --> x=60 --> Sugar = 5x = 30.
Answer: A
Answer: A
Question: If money is invested at r percent interest, compounded annually, the amount of the investment will double in approximately 60/r years. If Pat's parents invested $7,000 in a long-term bond that pays 6 percent interest, compounded annually, what will be the approximate total amount of the investment 20 years later, when Pat is ready for college?
Options:
A) $20000
B) $14000
C) $12000
D) $10000
E) $9000
Rationale: Since investment doubles in 60/r years, then for r=6 it'll double in 60/6=~10 years (we are not asked about the exact amount so such an approximation will do). Thus after 20 years investment will become $7,000*2=$14,000 .
Answer: B
Answer: B
Question: A batsman scored 90 runs which included 4 boundaries and 6 sixes. What percent of his total score did he make by running between the wickets?
Options:
A)45%
B)500/11
C)42.22%
D)55%
E)35%
Rationale: Explanation :
Number of runs made by running,
=>90−(4×4+6×6).
=>90−52
=>38
Hence, the required percentage is:-
=>38/90 *100
=>42.22%
Answer : C
Answer: C
Question: Find the invalid no.from the following series 15, 16, 34, 105, 424, 2124, 12756
Options:
A)16
B)34
C)105
D)424
E)2124
Rationale: 2nd term = (1st term) * 1 + 1 = 15 *1 + 1 = 16.
3rd term = (2nd term) * 2 + 2 = 16 * 2 + 2 = 34
4th term = (3th term) *3 + 3 = 34 * 3 + 3 = 105
5th term = (4th term) * 4 + 4 = 105 * 4 + 4 = 424
6th term = (5th term) * 5 + 5 = 424 * 5 + 5 = 2125
6th term should 2125 instead of 2124.
E
Answer: E
Question: P alone can complete a piece of work in 13 days. Work done by Q alone in one day is equal to one-third of the work done by P alone in one day. In how many days can the work be completed if P and Q work together?
Options:
A)6 (1/4) days
B)39/4 days
C)7 (3/4) days
D)8 (3/4) days
E)9 (3/4) days
Rationale: Work done by P alone in one day = 1/13th of the total work done by Q alone in one day = 1/3(of that done by P in one day) = 1/3(1/13 of the total) = 1/39 of the total.
Work done by P and Q, working together in one day = 1/13 + 1/39 = 4/39 of the total
They would take 39/4 days to complete the work working together.
ANSWER:B
Answer: B
Question: A merchant sells 30 metres of cloth and gains selling price of 10 metres. Find the gain percent.
Options:
A)15 %
B)25 %
C)50 %
D)75%
E)70 %
Rationale: Here, selling price of 10 m cloth is obtained as profit.
Profit of 10 m cloth = (S.P. of 30 m cloth) – (C.P. of 30 m cloth)
Selling price of 20 m cloth = Selling Price of 30 m of cloth
Let cost of each metre be Rs. 100.
Therefore, cost price of 20 m cloth = Rs. 2000 and S.P. of 20 m cloth = Rs. Rs. 3000
Profit% =	10/20*100=50%
Profit of 50 % was made by the merchant.
ANSWER IS C
Answer: C
Question: Two kinds of Vodka are mixed in the ratio 1:5 and 5:1 and they are sold fetching the profit 10% and 20% respectively. If the vodkas are mixed in equal ratio and the individual profit percent on them are increased by 4/3 and 5/3 times respectively, then the mixture will fetch the profit of
Options:
A)21%
B)20%
C)21%18%
D)23%
E)Cannot be determined
Rationale: The profit on the first kind of vodka = x%;
The profit on the second kind of vodka = y%.
When they are mixed in the ratio 1:2 (total of 3 parts) the average profit is 10%: (x + 2y)/3 = 10.
When they are mixed in the ratio 2:1 (total of 3 parts) the average profit is 20%: (2x + y)/3 = 20.
Solving gives: x = 30% and y = 0%.
After the individual profit percent on them areincreased by 4/3 and 5/3 times respectively the profit becomes 40% and 0%,on the first and te second kinds of vodka, respectively.
If they are mixed in equal ratio (1:1), then the mixture will fetch the profit of (40 + 0)/2 = 20%.
Answer: C
Answer: C
Question: Find the one which does not belong to that group ?
Options:
A)22
B)83
C)33
D)49
E)11
Rationale: Explanation:
36 = 62, 49 = 72, 64 = 82, 81 = 92 and 100 = 102.
36, 64, 81 and 100 are squares of composite numbers, but not 49.
Answer: B
Answer: B
Question: A man can row 7 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. How far is the place?
Options:
A)3.3
B)3.4
C)3.5
D)3.6
E)3.7
Rationale: M = 7
S = 1.2
DS = 7 + 1.2 = 8.2
US = 7 - 1.2 = 5.8
x/8.2 + x/5.8 = 1
x = 3.40.Answer: B
Answer: B
Question: If log 27 = 1.416, then the value of log 9 is:
Options:
A)0.934
B)0.944
C)0.954
D)0.958
E)0.998
Rationale: log 27 = 1.416
log (3cube ) = 1.416
3 log 3 = 1.416
log 3 = 0.472
log 9 = log(3square ) = 2 log 3 = (2 x 0.472) = 0.944.
Answer: Option B
Answer: B
Question: A train, 800 meter long is running with a speed of 78 km/hr. It crosses a tunnel in 1 minute. What is the length of the tunnel (in meters)?
Options:
A)500
B)200
C)300
D)250
E)300
Rationale: Let length of the tunnel = x meter
distance = (800 + x)meter
Time = 1 =1 minute = 60 seconds
Speed = 78 km/hr=78 Ã—5/18 =65/3 m/s
800+x =60 Ã— 65/3
800+ x=1300
x=500
ANSWER: A
Answer: A
Question: Maxwell leaves his home and walks toward Brad's house at the same time that Brad leaves his home and runs toward Maxwell's house. If the distance between their homes is 40 kilometers, Maxwell's walking speed is 4 km/h, and Brad's running speed is 6 km/h, what is the distance traveled by Brad?
Options:
A)16
B)18
C)20
D)24
E)30
Rationale: Time taken = Total Distance / Relative Speed
Total Distance = 40 kms
Relative Speed (Opposite side) (As they are moving towards each other speed would be added ) = 6+ 4 = 10 kms/hr
Time taken = 40 / 10 = 4 hrs
Distance traveled by Brad = Brad's speed * time taken = 6 * 4 = 24 kms... Answer - D
Answer: D
Question: Find out the wrong term in the series 3, 6, 18, 108, 1944, 103432
Options:
A)208646
B)300458
C)103432
D)210546
E)209952
Rationale: Explanation:
Each number with in the series is the product of the two numbers that proceed it.
So, if (3 * 6 = 18) , then (108 * 1944 = 209952 ). 209952 should replace 103432.
Answer: E) 209952
Answer: E
Question: There are 11 lines in plane. How many intersections (Maximum) can be made?
Options:
A)55
B)60
C)65
D)70
E)75
Rationale: First line will cut all other 10, similarly second will cut 9, and so on
total = 10+9+8+7+6+5+4+3+2+1 = 55
ANSWER:A
Answer: A
Question: If in coded language
1 = 2
2 = 10
3 = 30
4 = 68
then
5 = ?
Options:
A)130
B)140
C)150
D)160
E)170
Rationale: 1^3 + 1= 2
2^3 + 2= 10
3^3 + 3 = 30
4^3 + 4 = 68
5^3 + 5 = 130
Ans : 130
ANSWER:A
Answer: A
Question: 2 oranges, 3 bananas and 4 apples cost Rs.15. 3 oranges 2 bananas 1 apple costs Rs.10. what is the cost of 3 oranges, 3 bananas and 3 apples?
Options:
A)30
B)15
C)10
D)20
E)40
Rationale: 2or+3ba+4ap=15--->(1)
3or+2ba+1ap=10---->(2)
(1)+(2)
5or+5ba+5ap=15+10
5(or+ba+ap)=25
or+ba+ap=25/5
or+ba+ap=5
therefore 3or+3ba+3ap===>3(or+ba+ap);
3(5)=15;
ANSWER:B
Answer: B
Question: In measuring the sides of a rectangle, one side is taken 6% in excess, and the other 5% in deficit. Find the error percent in the area calculated from these measurements.
Options:
A)0.11%
B)0.7%
C)0.4%
D)0.6%
E)0.8%
Rationale: Let x and y be the sides of the rectangle. Then, Correct area = xy.
Calculated area = (53/50) x (19/20) y = (144/143)(xy)
Error In measurement = (144/143)xy- xy = (1/143)xy
Error percentage = [(1/143)xy (1/xy)100] % = (7/10) % = 0.7%.
Answer is B.
Answer: B
Question: An agent, gets a commission of 4% on the sales of cloth. If on a certain day, he gets Rs. 12.50 as commission, the cloth sold through him on that day is worth
Options:
A)312
B)500
C)887
D)299
E)132
Rationale: Explanation:
Let the total sale be Rs. x.
Then, 4%. of x = 12.50
= (4/100 * x) = 12.5<=> x = 312.5.
Answer: A
Answer: A
Question: In a certain region, the number of children who have been vaccinated against rubella is twice the number who have been vaccinated against mumps. The number who have been vaccinated against both is twice the number who have been vaccinated only against mumps. If 8,000 have been vaccinated against both, how many have been vaccinated only against rubella?
Options:
A)2,5000
B)7,500
C)10,000
D)15,000
E)16,000
Rationale: Use a single variable as far as possible.
Number vaccinated only against mumps = x
Number vaccinated against both = 2x = 8000 (so x = 4000)
Then, number vaccinated against mumps (including both) = x + 2x = 3x
Number vaccinated against rubella = 2*3x = 6x
Then, number vaccinated against only rubella = 6x - 2x = 4x = 4*4000 = 16,000
Answer (E)
Answer: E
Question: In what time will a railway train 60 m long moving at the rate of 36 kmph pass a telegraph post on its way?
Options:
A)3
B)4
C)5
D)6
E)7
Rationale: T = 60/36 * 18/5 = 6 sec
Answer:D
Answer: D
Question: In one hour, a boat goes 13 km along the stream and 5 km against the stream. The speed of the boat in still water (in km/hr) is:
Options:
A)2
B)4
C)9
D)12
E)15
Rationale: Sol.
Speed in still water = 1/2 (13+5) kmph = 9 kmph.
Answer C
Answer: C
Question: During a trip on an expressway, Don drove a total of x miles. His average speed on a certain 5-mile section of the expressway was 30 miles per hour, and his average speed for the remainder of the trip was 50 miles per hour. His travel time for the x-mile trip was what percent greater than it would have been if he had traveled at a constant rate of 60 miles per hour for the entire trip?
Options:
A)8.5%
B)50%
C)x/12%
D)400/x%
E)500/x%
Rationale: Say x = 5 miles (so no remainder of the trip).
Time to cover x = 5 miles at 30 miles per hour = (time) = (distance)/(rate) = 5/30 = 1/6 hours = 10 minutes.
Time to cover x = 5 miles at 60 miles per hour = (time) = (distance)/(rate) = 5/50 = 1/10 hours = 5 minutes.
(Or simply, half rate will result in doubling the time.)
So, we can see that the time to cover x = 5 miles at 30 miles per hour (10 minutes) is 100% greater than the time to cover x = 5 miles at 60 miles per hour (5 minutes).
Now, plug x = 5 miles into the answer choices to see which one yields 100%. Only answer E works.
Answer: D.
Answer: D
Question: A ratio between two numbers is 8:9 and their L.C.M. is 432. The first number is
Options:
A)60
B)45
C)50
D)48
E)None
Rationale: Sol.
Let the required numbers be 8x and 9x. Then, their L.C.M. is 72x.
∴ 72x = 432⇔ x = 6. Hence, the first number is 48.
Answer D
Answer: D
Question: If an object travels at seven feet per second, how many feet does it travel in one hour?
Options:
A)30
B)300
C)720
D)25200
E)18000
Rationale: Speed = 7 feet per second.
1 Hour= 60X60 Seconds = 3600 Seconds.
Total no of feet traveled in 1 hour = 3600X7= 25200
Answer D
Answer: D
Question: Mrs. Carolina. invested $9,000; part at 5%, and part at 8%. The total interest on the investment was $630. How much did she invest at each rate?
Options:
A)x=$13,000, y =$26,000
B)x=$4,000, y =$8,000
C)x=$2,000, y =$4,000
D)x=$3,000, y =$6,000
E)x=$5,000, y =$10,000
Rationale: I approached this question like a mixture problem.
I don't like the wordingpartat 5% andpartat 8% because we have variables x and y in the answer choices and I have no idea which one is x or y.
Anyway here's how I did it.
0.05(x) + 0.08(y) = 0.07(x+y)
0.01(y) = 0.02(x)
y = 2x
Note: 0.07(x+y) because $630 is 7% of 9,000
In which answer choice is y = 2(x)
Answer D
Answer: D
Question: A five-digit number divisible by 3 is to be formed using numerical 0, 1, 2, 3, 4 and 5 without repetition. The total number E of ways this can be done is:
Options:
A)122
B)210
C)216
D)217
E)225
Rationale: We should determine which 5 digits from given 6, would form the 5 digit number divisible by 3.
We have six digits: 0, 1, 2, 3, 4, 5. Their sum=15.
For a number to be divisible by 3 the sum of the digits must be divisible by 3. As the sum of the six given numbers is 15 (divisible by 3) only 5 digits good to form our 5 digit number would be 15-0={1, 2, 3, 4, 5} and 15-3={0, 1, 2, 4, 5}. Meaning that no other 5 from given six will total the number divisible by 3.
Second step:
We have two set of numbers:
1, 2, 3, 4, 5 and 0, 1, 2, 4, 5. How many 5 digit numbers can be formed using these two sets:
1, 2, 3, 4, 5 --> 5! as any combination of these digits would give us 5 digit number divisible by 3. 5!=120.
0, 1, 2, 4, 5 --> here we can not use 0 as the first digit, otherwise number won't be any more 5 digit and become 4 digit. So, desired # would be total combinations 5!, minus combinations with 0 as the first digit (combination of 4) 4! --> 5!-4!=4!(5-1)=4!*4=96
120+96=216=E
Answer: C.
Answer: C
Question: Calculate 42120 ÷ ? = 195
Options:
A)212
B)219
C)217
D)213
E)216
Rationale: Answer
Let 42120/X = 195
Then X = 42120/195 = 216
Option: E
Answer: E
Question: The speed at which a man can row a boat in still water is 15 kmph. If he rows downstream, where the speed of current is 3 kmph, what time will he take to cover 60 metres?
Options:
A)11 seconds
B)77 seconds
C)76 seconds
D)12 seconds
E)17 seconds
Rationale: Speed of the boat downstream = 15 + 3 = 18 kmph
= 18 * 5/18 = 5 m/s
Hence time taken to cover 60 m = 60/5 = 12 seconds.
Answer:D
Answer: D
Question: 1/4 of all married couples have more than one child. 1/5 of all married couples have more than 3 children. What fraction of all married couples have 2 or 3 children?
Options:
A)1/5
B)B.1/4
C)1/20
D)3/5
E)It cannot be determined from the given information.
Rationale: Plug in simple numbers. Take 100 couples for example.
1/4 of 100 couples have more than one child = 25 couples.
1/5 of 100 couples have more than 3 kids = 20 couples.
This implies that 20 couples are a subset of 25 couples and the complement of 25 couples within those 100 couples, which equals 75 couples have either one or no kids at all.
We need to find couples that have 2 or 3 kids, so essentially, it is 25 - 20 = 5. Fraction will be 5/100 = 1/20.
Option C
Answer: C
Question: If Rs.7500 are borrowed at C.I at the rate of 4% per annum, then after 1 year the amount to be paid is?
Options:
A)8118
B)8127
C)8618
D)7800
E)8128
Rationale: A = 7500(26/25)1
= 7800
Answer: D
Answer: D
Question: Pumping alone at their respective constant rates, one inlet pipe fills an empty tank to 1/2 of capacity in 3 hours and a second inlet pipe fills the same empty tank to 2/3 of capacity in 4 hours. How many hours will it take both pipes, pumping simultaneously at their respective constant rates, to fill the empty tank to capacity?
Options:
A)3
B)3.6
C)4.2
D)4.4
E)5.5
Rationale: Time taken by First tank Fill 1/2 the tank = 3 hours
i.e. Time taken by First tank to Fill 1 complete the tank = 6 hours
Time taken by Second tank Fill 2/3 the tank = 4 hours
i.e. Time taken by First tank to Fill 1 complete the tank = (3/2)*4 = 6 hours
in 1 Hour, Both tanks together Fill the tank = (1/6)+(1/6) = 1/3 tank
i.e. Time taken by Both tank to Fill 1 complete the tank = 3 hours
A
Answer: A
Question: A man buys Rs. 48 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)s. 12
B)s. 15
C)s. 18
D)s. 21
E)s. 36
Rationale: Dividend on Rs. 48 = Rs.	9/100	x 48 =Rs.	4.32	.
Rs. 12 is an income on Rs. 100.
Rs.	4.32	is an income on Rs.100/12 x 4.32	= Rs. 36.
Answer: Option E
Answer: E
Question: A person can row at 9 kmph and still water. He takes 7 1/2 hours to row from A to B and back. What is the distance between A and B if the speed of the stream is 1 kmph?
Options:
A)60 km
B)87 km
C)33 km
D)67 km
E)20 km
Rationale: Let the distance between A and B be x km.
Total time = x/(9 + 1) + x/(9 - 1) = 7.5
=> x/10 + x/8 = 15/2 => (4x + 5x)/40 = 15/2 => x
= 33 km.
Answer:C
Answer: C
Question: Two prime numbers are considered consecutive if no other prime lies between them on the number line. If p1p1 and p2p2 are consecutive primes, with |p1–p2|>2, what is the smallest possible absolute value of the coefficient of the x term in the distributed form of the expression (x–p1)(x–p2)?
Options:
A)5
B)8
C)12
D)18
E)24
Rationale: (x−p1)∗(x−p2)=x2−(p1+p2)x+p1p2
Value of (p1+p2) will be min. for the min consecutive primes which satisfy |p1-p2|>2
So the min. value p1 & p2 can take = 7, 11
p1+p2= 7+11= 18
Answer. D
Answer: D
Question: Find the odd man out. 742, 743, 588, 853, 871, 990, 532
Options:
A)532
B)990
C)588
D)742
E)None of these
Rationale: Explanation :
In all numbers except 588, the difference of third and first digit is the middle digit. Answer : Option C
Answer: C
Question: For a certain set of numbers, if x is in the set, then x - 4 is also in the set. If the number 1 is in the set , which of the following must also be in the set ?
a) 4
b) -3
c) -6
Options:
A)a only,
B)b only,
C)c only,
D)a and b only
E)b and c only
Rationale: Notice that the question asks which of the following MUST be in the set, not COULD be in the set.
Since 1 is in the set, then so must be 1-4=-3. Similarly, since -3 is in the set, then so must be -3-3=-6. Could 4 and -1 be in the set? Certainly, but we don't know that for sure.
Answer: E.
Regarding your question: we don't know which is the source integer in the set, if it's 1, then 4 won't be in the set but if the source integer is say 7, then 4 will be in the set. So, 4 may or may not be in the set.
Answer: E
Question: Two trains of equal lengths take 12 sec and 20 sec respectively to cross a telegraph post. If the length of each train be 120 m, in what time will they cross other travelling in opposite direction?
Options:
A)17 sec
B)15 sec
C)16 sec
D)11 sec
E)18 sec
Rationale: Speed of the first train = 120/12 = 10 m/sec.
Speed of the second train = 120/20 = 6 m/sec.
Relative speed = 10 + 6 = 16 m/sec.
Required time = (120 + 120)/16 = 15 sec.
Answer:B
Answer: B
Question: The owner of a furniture shop charges his customer 15% more than the cost price. If a customer paid Rs. 6400 for a computer table, then what was the cost price of the computer table?
Options:
A)Rs.5565
B)Rs.6298
C)Rs.6290
D)Rs.6725
E)Rs.6708
Rationale: CP = SP * (100/(100 + profit%))
= 6400(100/115) = Rs.5565.
Answer: A
Answer: A
Question: A vender sold two things at same cost of 12 RS with one item at 25%profit and other at 20%loss,by this transaction he made profit or loss by how much
Options:
A)0.60 loss
B)0.70 loss
C)0.80 loss
D)0.50 loss
E)0.40 loss
Rationale: CP when profit of 25% = 9.60
CP when loss of 20% = 15
Total CP = 24.60
Total SP = 24.00
Total loss = 0.60
ANSWER:A
Answer: A
Question: If a man buys 10 lollipops for $90 and sold them for $2 dollars determine his loss.
Options:
A)50
B)60
C)70
D)80
E)90
Rationale: Cost of 10 lollipops = $90
Sold each lollipop for $2
So he sold 10 lollipops for $(10 × 2) = $20
Loss = $(90 – 20) = $70
answer :C
Therefore, loss = $ 70.
Answer: C
Question: A shopkeeper sold an article offering a discount of 4% and earned a profit of 20%. What would have been the percentage of profit earned if no discount was offered?
Options:
A)25
B)28
C)30
D)32
E)34
Rationale: Let C.P. be Rs. 100.
Then, S.P. = Rs. 120
Let marked price be Rs. x. Then, 96/100 x = 120
x = 12000/96 = Rs. 125
Now, S.P. = Rs. 125, C.P. = Rs. 100
Profit % = 25%.
ANSWER:A
Answer: A
Question: In a division sum, the quotient is 20, the divisor 66 and the remainder 55, find the dividend?
Options:
A)1375
B)1376
C)1875
D)1365
E)1345
Rationale: Explanation:
20 * 66 + 55 = 1375
Answer : A
Answer: A
Question: Aunt Marge is giving candy to each of her nephews and nieces. She has 20 pieces of candy and she gives all the candy to the children according to her wish. If Robert gets 2 more pieces than Kate, Bill gets 6 less than Mary, Mary gets 2 more pieces than Robert, and Kate gets 2 more pieces than Bill, how many pieces of candy does Kate get?
Options:
A)2
B)4
C)6
D)8
E)10
Rationale: Use the initial letter of each name as a variable:
r=k+2
b=m−6
m=r+2
k=2+bk==r−2
b=k−2=(r−2)−2=r−4
m=r+2
r+b+m+k=20
r+r−4+r+2+r−2=20
r=6
k=r−2=6−2=4
Answer: B
Answer: B
Question: Ravi purchased a refrigerator and a mobile phone for Rs. 10000 and Rs. 8000 respectively. He sold the refrigerator at a loss of 4 percent and the mobile phone at a profit of 10 percent. Overall he make a.
Options:
A)loss of Rs. 200
B)loss of Rs. 100
C)profit of Rs. 100
D)profit of Rs. 400
E)None of these
Rationale: Total C.P. = 10000+8000 = 18000
S.P. of fridge = 10000/100*96= 9600
S.P. of Mobile = 8000/100*110 = 8800
Total S.P. = 9600 + 8800 = 18400
Tota. S.P. - Total C.P. = 18400 - 18000 = 400
Answer : D
Answer: D
Question: My brother is 2 years elder to me. My father was 28 years of age when my sister was born while my mother was 26 years of age when I was born. If my sister was 1 years of age of when my brother was born, then, what was the age of my father and mother respectively when my brother was born?
Options:
A)32 yrs, 23 yrs
B)30 yrs, 25 yrs
C)35 yrs, 29 yrs
D)35 yrs, 33 yrs
E)none
Rationale: Sol.
Clearly, my brother was born 2 years before I was born and 1 years after my sister was born.
So, father's age when brother was born = (28 + 2) = 30 years.
mother's age when was born = (26 - 1) years = 25 years.
Answer B
Answer: B
Question: Two dogsled teams raced across a 200-mile course in Alaska. Team A finished the course in 2 fewer hours than team B. If team A’s average speed was 5 miles per hour greater than that of team B, what was team B’s average speed, in miles per hour?
Options:
A)12
B)15
C)18
D)20
E)25
Rationale: Let v be team B's average speed.
Time = Distance/Rate and the time difference was 2 hours.
200/v - 200/(v+5)= 2
200v + 1000 - 200v = 2(v)(v+5)
500 = (v)(v+5)
(20)(25) = (v)(v+5)
v = 20 mph
The answer is D.
Answer: D
Question: When the integer n is divided by 17, the quotient is x and the remainder is 7. When n is divided by 23, the quotient is y and the remainder is 14. Which of the following is true?
Options:
A) 23x + 17y =19
B) 17x –23y = 7
C) 17x +23y =19
D) 14x + 5y = 6
E) 5x – 14y = -6
Rationale: From the problem it follows:
n=17x+7
n=23y+14
So, 17x+7=23y+14
17x-23y=7
The answer is B
Answer: B
Question: If a person walks at 14 km/hr instead of 10 km/hr, he would have walked 20 km more. What is the actual distance travelled by him?
Options:
A)33
B)11
C)38
D)50
E)12
Rationale: Assume that the person would have covered x km if travelled at 10 km/hr
⇒Speed = DistanceTime=x10.....(Equation1)
Give that the person would have covered (x + 20) km if travelled at 14 km/hr
⇒Speed = DistanceTime=(x+20)14.....(Equation2)
From Equations 1 and 2,
x10=(x+20)1414x=10x+2004x=200x=2004=50
Answer : D
Answer: D
Question: R is the set of positive odd integers less than 40, and S is the set of the squares of the integers in R. How many elements does the intersection of R and S contain ?
Options:
A)None
B)Three
C)Four
D)Five
E)Seven
Rationale: squares < 40 {1,4,9,16,25,36}
S = {1,9,25}
R = {1,3,.....40}
Hence B.
Answer: B
Question: A straight fence is to be constructed from posts 7 inches wide and separated by lengths of chain 5 feet long. If a certain fence begins and ends with a post, which of the following couldnotbe the length of the fence in feet? (12 inches = 1 foot)
Options:
A)17
B)28
C)35
D)39
E)50
Rationale: The fence begins and ends with a post: {post = 0.5 feet}{chains = 5 feet}{post = 0.5 feet}...{chains = 5 feet}{post = 0.5 feet}
The minimum length is with 2 posts = 0.5 + 5 + 0.5 = 6 feet. To increase the fence, each time we should add{post = 0.5 feet}{chains = 5 feet}, so 5.5 feet. Thus, the lengths could be:
6 feet;
7+ 5.5 = 12.5 feet;
11.5 + 5.5 = 18 feet;
17 + 5.5 = 23.5 feet;
22.5 + 5.5 = 29feet;
28 + 5.5 = 34.5 feet;
33.5 + 5.5 = 40 feet.
...
We skipped 39 feet.
Answer: D.
Answer: D
Question: Anu normally takes 4 hours more than the time taken by Sachin to walk D km. If Anu doubles her speed, she can make it in 2 hours less than that of Sachin. How much time does Sachin require for walking D km?
Options:
A)10 hours
B)4 hours
C)8 hours
D)9 hours
E)None
Rationale: Explanation :
Let Sachin takes x hours to walk D km.
Then, Anu takes (x + 4) hours to walk D km.
With double of the speed, Anu will take (x + 4)/2 hours.
x – (x + 4)/2 = 2
=> 2x – (x + 4) = 4
=> 2x – x – 4 = 4
x = 4 + 4 = 8 hours
Answer – C
Answer: C