divelab/Sys2Bench huggingface dataset:
Question: If W is the set of all the integers between 49 and 76, inclusive, that are either multiples of 3 or multiples of 2 or multiples of both, then W contains how many numbers?
Options:
A)19
B)91
C)41
D)18
E)14
Rationale: Official Solution:
Number of multiples of 3
Step 1. Subtract the extreme multiples of 3 within the range (The greatest is 75, the smallest is 51): 75 - 51 = 24
Step 2. Divide by 3: 24 / 3 = 8
Step 3. Add 1: 8 + 1 = 9.
So there are 9 multiples of 3 within the range: examples are 51, 54, 57, 60, etc.
Number of multiples of 2
Step 1. Subtract the extreme multiples of 2 within the range (The greatest is 76, the smallest is 50): 76 - 50 = 26
Step 2. Divide by 2: 26 / 2 = 13
Step 3. Add 1: 13 + 1 = 14.
So there are 14 multiples of 2 within the range: examples are 50, 52, 54, 56, 58, 60 etc.
Add the 9 multiples of 3 and the 14 multiples of 2: 9+14=23.However, by adding the multiples of 2 and the multiples of 3, we are effectively counting several numbers twice: for example, 54 and 60 are parts of both the lists above. So we can't just take 9+14=23. Find the Number of multiples of 6 (which are the double counted, as 6 is divisible by both 2 and 3), and subtract it from 23:
Step 1. Subtract the extreme multiples of 6 within the range (The greatest is 72, the smallest is 54): 72 - 54 = 18
Step 2. Divide by 6: 18 / 6 = 3
Step 3. Add 1: 3 + 1 = 4.
So there are 4 multiples of 6 within the range: we counted 4 numbers twice.
Subtract the 4 multiples of 6 from the sum of the multiples of 2 and 3:
= 9 + 14 - 4
= 23 - 4
= 19
Therefore, the final number of multiples of 2, 3 or 6 is 19.
Hence, this is the correct answer. (A)
Answer: A
Question: Marcela, Karla, Isabel, and Viviana all got their math tests back. The average of Marcela, Karla, and Isabel's grades was an 85%. The average of Karla, Isabel, and Viviana's grades was a 78%. If Viviana got a 75%, what did Marcela get?
Options:
A)90%
B)92%
C)96%
D)88%
E)98%
Rationale: Solution: Average grade for Marcela, Karla, and Isabel = 85%
Total grade points= 3*85 = 255
Average grade for Karla, Isabel and Viviana = 78%
Total grade points = 3*78 = 234
Viviana got a 75%.
Now,
(Marcela+Karla+Isabel) - (Karla+Isabel+Viviana) = 255-234
Marcela-Viviana = 21
Marcela's score= Viviana's + 21 = 96%
Answer: Option C
Answer: C
Question: If 6 parallel lines in a plane is intersected by a family of another 8 parallel lines, how many parallelograms are there in the network thus formed?
Options:
A)80
B)63
C)420
D)160
E)1260
Rationale: parallelogram can formed by 2 horizontal and 2 vertical lines
for horizontal 6c2
for vertical 8c2
total parallelogram is 6 c2*8c2=15*28
=420
ANSWER:C
Answer: C
Question: Here are 6 periods in each working day of a school. In how many ways can one organize 5 subjects such that each subject is allowed at least one period?
Options:
A)1023
B)6000
C)1980
D)1800
E)1450
Rationale: 5 subjects can be arranged in 6 periods in 6P5 ways.
Any of the 5 subjects can be organized in the remaining period (5C1 ways).
Two subjects are alike in each of the arrangement. So we need to divide by 2! to avoid overcounting.
Total number of arrangements
= 6P5× 5C1 /2!=1800
Option D
Answer: D
Question: A dealer offers a cash discount of 20%. Further, a customer bargains and receives 20 articles for the price of 15 articles. The dealer still makes a profit of 20%. How much percent above the cost price were his articles marked?
Options:
A)100%
B)80%
C)75%
D)66+2/3%
E)50%
Rationale: Marked Price (M) = Cost Price (C) + Mark up...(EQN. A)
Selling price = 20% Discount over M = 0.8*M
Given that, a customer bargains and receives 20 articles for the price of 15 articles--> *a further loss of 25% to the dealer--> BUT a NET PROFIT of 20% over cost price (C)
0.75 * 0.8 * M = 1.2 * C
Hence, M/C = 2/1 = 200%
From Eqn. A , (C + Mark up)/C = 200% --> Mark up / C = 100%
Ans. A
Answer: A
Question: The avg. age of a group of 28 students is 20 years.If 4 more students join the group,the avg age increases by 1 year.The avg age of the new student is?
Options:
A)22 years
B)23 years
C)24 years
D)25 years
E)28 years
Rationale: Total age of 28 students=28*20=560
If total age of 4 students=x
Then, (560+x)/(28+4) =(20+1), x=112
So average age of new students=112/4= 28 years
ANSWER:E
Answer: E
Question: There are 15 teams in the hockey league, and each team faces all the other teams 10 times each. How many games are played in the season?
Options:
A)650
B)750
C)850
D)950
E)1050
Rationale: The number of ways to choose two teams is 15C2 = 15*14/2 = 105
The total number of games in the season is 10*105 = 1050.
The answer is E.
Answer: E
Question: The ratio of the amount of the oil bill for the month of February to the amount of the oil bill for the month of January was 3:2. If the oil bill for February had been $10 more, the corresponding ratio would have been 5:3. How much was the oil bill for January?
Options:
A)$60
B)$80
C)$100
D)$120
E)$140
Rationale: 3:2 = 9:6 and 5:3 = 10:6.
An increase in $10 increases the ratio by 1:6.
Therefore, January's bill was 6($10) = $60.
The answer is A.
Answer: A
Question: The speed at which a man can row a boat in still water is 16 kmph. If he rows downstream, where the speed of current is 4 kmph, what time will he take to cover 100 metres?
Options:
A)23
B)27
C)28
D)12
E)18
Rationale: Speed of the boat downstream = 16 +4 = 20 kmph= 20 * 5/18 = 5.55 m/sHence time taken to cover 100 m = 100/5.55= 18 seconds.Answer:E
Answer: E
Question: A reduction of 40% in the price of bananas would enable a man to obtain 64 more for Rs.40, what is reduced price per dozen?
Options:
A)3
B)4
C)5
D)6
E)7
Rationale: 40*(40/100) = 16 --- 64
? --- 12 => Rs.3
Answer:A
Answer: A
Question: Four car rental agencies A, B, C and D rented a plot for parking their cars during the night. A parked 15 cars for 12 days, B parked 12 cars for 20 days, C parked 18 cars for 18 days and D parked 16 cars for 15 days. If A paid Rs. 1260 as rent for parking his cars, what is the total rent paid by all the four agencies?
Options:
A)2388
B)2778
C)6888
D)6150
E)2771
Rationale: The ratio in which the four agencies will be paying the rents = 15 * 12 : 12 * 20 : 18 * 18 : 16 * 15
= 180 : 240 : 324 : 240 = 45 : 60 : 81 : 60
Let us consider the four amounts to be 45k, 60k, 81k and 60k respectively.
The total rent paid by the four agencies = 45k + 60k + 81k + 60k= 246k
It is given that A paid Rs. 1260
45k = 1260 => k = 28
246k = 246(28) = Rs. 6888
Thus the total rent paid by all the four agencies is Rs. 6888.
Answer: C
Answer: C
Question: The difference between C.I. and S.I. on an amount of Rs. 15,000 for 2 years is Rs. 96. What is the rate of interest per annum?
Options:
A)8
B)10
C)12
D)14
E)16
Rationale: [15000 * (1 + R/100)2 - 15000] - (15000 * R * 2)/100 = 96
15000[(1 + R/100)2 - 1 - 2R/100] = 96
15000[(100 + R)2 - 10000 - 200R]/10000 = 96
R2 = (96 * 2)/3 = 64 => R = 8
Rate = 8%
ANSWER:A
Answer: A
Question: In how many ways can five different rings be worn on four fingers of one hand?
Options:
A)10
B)5
C)15
D)16
E)18
Rationale: Required number of ways = ways of selecting 4 objects out of 5 given objects
= 5C4 = 5*4*3*2/24= 5
Answer B
Answer: B
Question: John has a boat that can go 20 km/hr with the current, and 16 km/hr against the current. How fast is John's rate?
Options:
A)10 Km/Hr
B)6 Km/Hr
C)2 Km/Hr
D)8 Km/Hr
E)4 Km/hr
Rationale: with current = 20
against current - 16
s=?
s=(20-16)/2= 4/2 = 2
Answer = C
Answer: C
Question: A company has 3 directors and 3 managers. How many different committees with 5 people can be chosen having at least 1 director?
Options:
A)500
B)720
C)4500
D)6
E)55
Rationale: atleast one means exactly one and more than one.
different committees with 5 people can be chosen having at least 1 director is
(3c2*3c3) + (3c3*3c2) = 6;
Hence D.
Answer: D
Question: The probability of pulling a blue ball out of a glass jar is 1/X. The probability of pulling a blue ball out of a glass jar and breaking the jar is 1/Y. What is the probability of breaking the jar?
Options:
A)X/Y.
B)1/(XY)
C)Y/X.
D)1/(X+Y).
E)1/(X-Y).
Rationale: pulling a blue ball out of a glass jar and breaking the jar both are independent events.
For 2 independent events, we know, P(a) * P(b) = P(a∩b)
If Prob of pulling a blue ball out of a glass jar = P(a) and Prob of breaking the jar = P(b)
1/x * P(b) = 1/y ---> P(b) = x/y
Hence, answer should be A.
Answer: A
Question: After distributing the sweets equally among 25 children, 8 sweets remain. Had the number of children been 28, 22 sweets would have been left after equal distribution. What was the total number of sweets ?
Options:
A)328
B)348
C)358
D)Data inadequate
E)None
Rationale: when divided equally among 25 children, 8 sweets remain.
when divided equally among 28 children, 22 sweets remain.
ANSWER:C
Answer: C
Question: Walking 7/6 of his usual rate, a boy reaches his school 4 min early. Find his usual time to reach the school?
Options:
A)28 min
B)25 min
C)24 min
D)30 min
E)40 min
Rationale: Speed Ratio = 1:7/6 = 6:7
Time Ratio = 7:6
1 -------- 7
4 --------- ? 28 m
ANSWER A
Answer: A
Question: Suganya and Suriya are partners in a business. Suganya invests Rs. 38,000 for 8 months and Suriya invests Rs.40,000 for 10 months. Out of a profit of Rs.31,570. Suganya's share is
Options:
A)Rs.1435
B)Rs.12,628
C)Rs.1685
D)Rs.18,942
E)None
Rationale: Solution
Ratio of their shares	=(35000Ã—8):(42000Ã—10)
= 2 : 44.
Suganya's share	= Rs.(31570 Ã—2/44)
= Rs.1435.
Answer A
Answer: A
Question: A box contains 5 pairs of shoes (10 shoes in total). If two shoes are selected at random, what it is the probability that they are matching shoes?
Options:
A)1/190
B)1/20
C)1/9
D)1/10
E)1/9
Rationale: The problem with your solution is that we don't choose 1 shoe from 10, but rather choose the needed one AFTER we just took one and need the second to be the pair of it. So, the probability would simply be: 1/1*1/9(as after taking one at random there are 9 shoes left and only one is the pair of the first one)=1/9
Answer: C.
Answer: C
Question: A wheel that has 3 cogs is meshed with a larger wheel of 21 cogs. When the smaller wheel has made 21 revolutions, then the number of revolutions made by the larger wheel is:
Options:
A)3
B)10
C)6
D)8
E)7
Rationale: Explanation :
Let the required number of revolutions made by larger wheel be x.
Then, More cogs, Less revolutions (Indirect Proportion)
21:3::21:x => 21 * x = 21 * 3
=> x = (21 * 3)/21
=> x = 3
Answer : A
Answer: A
Question: An Olympic diver received the following scores: 4, 3, 5, 2. The standard deviation of her scores is in which of the following ranges?
Options:
A)4.01 to 4.99
B)1.01 to 1.99
C)3.01 to 3.99
D)5.01 to 5.99
E)2.01 to 2.99
Rationale: 4+3+7+2/4=4
∣4−4∣^2 =0^2 = 0
∣3−4∣^2 =1^2 = 1
∣7−4∣^2 =3^2 = 9
∣2−4∣^2 =2^2 = 4
sqrt 14/4 =1.87
Answer : B
Answer: B
Question: A and B take part in 100 m race. A runs at 5 kmph. A gives B a start of 8 m and still beats him by 8 seconds. The speed of B is:
Options:
A)1.33 kmph
B)4.14 kmph
C)2.33 kmph
D)2.88 kmph
E)4.44 kmph
Rationale: Explanation:
A's speed = \fn_jvn {\color{Black} \left ( 5\times \frac{5}{18} \right )m/sec} = \fn_jvn {\color{Black}\frac{25}{18}m/sec}
Time taken by A to cover 100 m = \fn_jvn {\color{Black}(100\times \frac{18}{15})sec} = 72sec
\fn_jvn {\color{Black} \therefore } Time taken by B to cover 92 m = (72 + 8) = 80 sec.
\fn_jvn {\color{Black} \therefore } B's speed =\fn_jvn {\color{Black} \left ( \frac{92}{80}\times \frac{18}{5} \right )kmph} =4.14kmph
Answer: B
Answer: B
Question: Find the number of square tiles to cover the floor of a room measuring 4 m * 9 m leaving 0.25 m space around the room. A side of square tile is given to be 25 cms?
Options:
A)197
B)476
C)169
D)260
E)256
Rationale: 3 1/2 * 8 1/2 = 1/4 * 1/4 * x => x
= 476
Answer:B
Answer: B
Question: A, B, C and D enter into partnership. A subscribes 1/3 of the capital B 1/4, C 1/5 and D the rest. How much share did A get in a profit of Rs.2460?
Options:
A)Rs.800
B)Rs.810
C)Rs.820
D)Rs.900
E)Rs.920
Rationale: Option C
Answer: C
Question: The diagonals of a rhombus are 12 cm and 15 cm. Find its area?
Options:
A)30
B)45
C)90
D)120
E)180
Rationale: Area=0.5 x 12 x 15
=90 cmÂ²
Answer: C
Answer: C
Question: Which of the following inequalities is equivalent to 10 + 2x > 100 + 5x?
Options:
A) x < -30
B) x > -30
C) x > -20
D) x < -10
E) x > -11
Rationale: You can work with the inequality in the same way as you do when you have the equal to sign. You can take terms to the other side by flipping their sign, you can multiply/divide the inequality by the same term on both sides of the equation etc.
The only important thing to note is the following:
When you multiply/divide by a negative number, the sign of the inequality flips.
To illustrate,
10 + 2x > 100 + 5x
-90 > 5x - 2x (Correct)
-90 > 3x (Correct)
-30 > 3x (Correct)
the correct option is A
Answer: A
Question: In what ratio P:Q should the Mixture P of milk and water in the ratio of 6:1 be mixed with another Mixture Q of milk and water in the ratio 3:4 so that the resultant mixture contains equal quantities of milk and water?
Options:
A)1:3
B)1:4
C)1:5
D)2:5
E)3:4
Rationale: (6/7)*P +(3/7)*Q = (1/7)*P+(4/7)*Q
5P=Q
P/Q = 1/5
The answer is C.
Answer: C
Question: If k = 2n - 1, where n is an integer, what is the remainder of k^2/8?
Options:
A)1
B)3
C)5
D)7
E)Cannot be determined from the information given.
Rationale: Let us assume that k = 4(n)(n-1)
This is divisible by 8.
So k+1 when divided by 8 will give reminder 1.
For example, consider n = 2
We have 4*2*1 + 1 = 9
When we divide this by 8 we get reminder 1.
ANSWER:A
Answer: A
Question: In the first 7 overs of a cricket game, the run rate was only 4.2. What should be the rate in the remaining 30 overs to reach the target of 282 runs?
Options:
A)6.25
B)8.42
C)8.3
D)8.1
E)6.21
Rationale: Required run rate
= [282 - (4.2 * 7)]/30
= 252.60/40
= 8.42
Answer:B
Answer: B
Question: Guna has 8 flavors of ice cream in him parlor. How many options are there for Thilak to pick a one-flavor, two-flavor, three-flavor, four-flavor, five-flavor, six-flavor,seven-flavor or eight-flavor order?
Options:
A)223
B)395
C)448
D)774
E)835
Rationale: 8C1 + 8C2+ 8C3+8C4+8C5+8C6+8C7+8C8 = 395.
Answer: B
Answer: B
Question: Of the employees in a company, 40 % are female who have a master degree. If 40 % of the female employees do not have a master degree, what percent of the employees in the company are female?
Options:
A)66.67%
B)67.67%
C)68.67%
D)65.67%
E)64.67%
Rationale: Let E be total no. of employees and F be total no of female employees.
Question asked what is F/E X 100%?
No. of female employees with Masters = 0.4 x E (From the question)
No. of female employees without masters = 0.4 x F (From the question)
Therefore No. of female employees with masters = F - 0.4 F = 0.6 F
The 2 expressions equal each other therefore 0.6F = 0.4E; F/E = 0.4/0.6 = 66.67%
Ans: A
Answer: A
Question: . In digging a pond 23 m * 12 m * 8 m the volumes of the soil extracted will be?
Options:
A)3323
B)2300
C)2877
D)2208
E)2111
Rationale: 23 * 12 * 8 = 2208
Answer: D
Answer: D
Question: A house wife saved $3.50 in buying an item on sale. If she spent $32.50 for the item, approximately how much percent she saved in the transaction?
Options:
A)8%
B)9%
C)10%
D)11%
E)12%
Rationale: Actual price = 32.50+3.50 = $36
Saving = 3.50/36 * 100 = 10% approximately
Answer is C
Answer: C
Question: The average age of 15 students of a class is 15 years. Out of these, the average age of 8 students is 14 years and that of the other 6 students is 16 years. The age of the 15th student is
Options:
A)9 years
B)11 years
C)17 years
D)21 years
E)25 years
Rationale: Solution
Age of the 15th student	=[15x15-(14x8+16x6)]
= (225 - 208)
= 17 years.
Answer C
Answer: C
Question: A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
Options:
A)338
B)240
C)287
D)267
E)191
Rationale: Speed = (54 * 5/18) m/sec = 15 m/sec. Length of the train = (15 x 20)m = 300 m. Let the length of the platform be x meters. Then, (x + 300)/36 = 15 ==> x + 300 = 540 ==> x = 240 m.
Answer: B
Answer: B
Question: A and B enter into partnership with capital as 7:9. At the end of 8 months, A withdraws. If they receive the profits in the ratio of 8:9 find how long B's capital was used?
Options:
A)5
B)6
C)4
D)7
E)9
Rationale: 7 * 8 : 9 * x = 8:9 => x= 7.Answer: D
Answer: D
Question: When 200 is divided by positive integer x, the remainder is 3. What is the remainder when 297 is divided by x?
Options:
A)2
B)3
C)4
D)6
E)8
Rationale: f200/x leaves a reminder 3 then (200-3) i.e. 197 is divisible by x
So (200+197)/x leaves a reminder rem(200/x)+rem(197/x)=> 3+0=3
Answer :B
Answer: B
Question: What is the difference between the C.I. on Rs. 5000 for 1 1/2 years at 4% per annum compounded yearly and half-yearly?
Options:
A)2.04
B)2.09
C)2.03
D)2.02
E)2.01
Rationale: C.I. when interest is compounded yearly
= [5000 * (1 + 4/100) * (1 + (1/2 * 4)/100]
= 5000 * 26/25 * 51/50 = Rs. 5304
C.I. when interest is compounded half-yearly
= [5000 * (1 + 2/100)2]
= (5000 * 51/50 * 51/50 * 51/50) = Rs. 5306.04 Difference = (5306.04 - 5304) = Rs. 2.04.Answer: A
Answer: A
Question: If x + y = 2 and x^2 - xy - 10 - 2y^2 = 0, what does x − 2y equal?
Options:
A)0
B)1
C)2
D)5
E)10
Rationale: If x + y = 2 and x^2 - xy - 10 - 2y^2 = 0, what does x − 2y equal?
A. 0
B. 1
C. 2
D. 5
E. 10
Since x + y = 2 we have y=2-x.
So 0= x^2 - xy - 10 - 2y^2 = x^2 - x(2-x) - 10 - 2(2-x)^2 = x^2 -2x+x^2 -10-8+8x-2x^2 = x=6x-18. ---> x=3 ---> y= -1 --->x-2y=5
The answer is (D).
Answer: D
Question: A milk man has 20 liters of milk. If he mixes 5 liters of water, which is freely available, in 20 liters of pure milk.If the cost of pure milk is Rs.18 per liter,then the profit of the milkman, when he sells all the mixture at cost price is:
Options:
A)20%
B)25%
C)33.33%
D)18%
E)None of these
Rationale: Explanation:
when the water is freely available and all the water is sold at the price of the milk, then the water gives the profit on the cost of 20 liters of milk.
Therefore, profit percentage = 25 %. Answer: B
Answer: B
Question: In a 1000 m race, A beats B by 10 m and B beats C by 100 m. In the same race, by how many meters does A beat C?
Options:
A)A)109m
B)B)829m
C)C)822m
D)D)929m
E)E)132mj
Rationale: By the time A covers 1000 m, B covers (1000 - 10) = 990 m.
By the time B covers 1000 m, C covers (1000 - 100) = 900 m.
So, the ratio of speeds of A and C =
1000/990 * 1000/900 = 1000/891 So, by the time A covers 1000 m, C covers 891 m.
So in 1000 m race A beats C by 1000 - 891 = 109 m.
Answer:A
Answer: A
Question: If integers ending in zero are excluded, what is the unit digit of the product of the even integers from 402 to 498, inclusive?
Options:
A)2
B)3
C)4
D)5
E)6
Rationale: 402 x 404 x 406 x 408 => unit digit 4
412 x 414 x 416 x 418 => unit digit 4
492 x 494 x 496 x 498 => unit digit 4
So we have 10 numbers ending by 4 to multiply.
Given that 4 x 4 = 16, we have 5 numbers ending by 6 to multiply
Given that 6 x 6 = 36, we have 3 numbers ending by 6 to multiply
So the unit digit is 6
Answer: E.
Answer: E
Question: A sum of Rs. 2900 amounts to Rs. 3422 in 3 years. Had the rate of interest be 4% higher then what would the sum amount in the same time period?
Options:
A)Rs. 3770
B)Rs. 3683
C)Rs. 3596
D)Data inadequate
E)None of these
Rationale: 3422=2900+(2900*R*3/100)
R=6
If R is 4 more.
Then R=10
Sum=2900+(2900*10*3/100)
Sum=3770
ANSWER:A
Answer: A
Question: A person crosses a 600m long street in 3 minnutes. What is his speed in km per hour?
Options:
A)5.8km/hr
B)7.2km/hr
C)9km/hr
D)12km/hr
E)3km/hr
Rationale: Speed = 600/3*60 = 3.33m/sec
=3.33*18/5
=12km/hr
Answer is D
Answer: D
Question: The average of 9 observations was 8, that of the 1st of 5 being 10 and that of the last 5 being 8. What was the 5th observation?
Options:
A)18
B)12
C)15
D)17
E)19
Rationale: Explanation:
1 to 9 = 8 * 9 = 72
1 to 5 = 5 * 10 = 50
5 to 9 = 5 * 8 = 40
5th = 50 + 40 = 90 – 72 = 18
Option A
Answer: A
Question: A man spends 1/3rd of his salary on food. he spends 1/4th on rent and 1/5th on cloths. If he is left with 1760, then who much salary does he earn
Options:
A)8223
B)8123
C)8323
D)8423
E)8523
Rationale: let total salary be x
A/Q
=> x = (x/3)+(x/4)+(x/5)+ 1760
=> x - 47x/60 = 1760
=> 13x/60 = 1760
=> x = 1760*60/13
=> x = 8123(approax)
ANSWER:B
Answer: B
Question: How many seconds will a 1200 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)26 sec
B)65 sec
C)55 sec
D)19 sec
E)72 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 = 1200 * 3/50
= 72 sec.
Answer:E
Answer: E
Question: Two buses start at the same time, one from P to Q and the other from Q to P. If both buses reach after 4 hours and 16 hours at Q and P respectively after they cross each other, what would be the ratio of speeds of the bus starting from P and that of the one starting from point Q?
Options:
A)2 : 1
B)1 : 2
C)2 : 2
D)1 : 4
E)5 : 2
Rationale: Hint:
SP / SQ = √tQ / √tP
SP and SQ are speeds of two the buses at points P and Q respectively.
tP = 18 hrs and tQ = 4 hrs
SP / SQ = √16 / √4
Therefore, ratio of speeds	Sp/ SQ = 4/2 = 2/1
One bus travels at a speed twice of the other bus.
ANSWER IS A
Answer: A
Question: The average age of a husband and his wife was 20 years at the time of their marriage. After five years they have a one-year old child. The average age of the family now is :
Options:
A)11
B)18
C)19
D)287
E)17
Rationale: Explanation:
Sum of the present ages of husband, wife and child = (20 * 2 + 5 * 2) + 1 = 51 years.
Required average = (51/3) = 17 years.
Answer: E) 17
Answer: E
Question: The speed of a motor boat itself is 20 km/h and the rate of flow of the river is 4 km/h. Moving with the stream the boat went 120 km. What distance will the boat cover during the same time going against the stream?
Options:
A)60 km
B)85 km
C)70 km
D)80 km
E)90 km
Rationale: distance=speed*time;
120=(20+4)*t;
t=5 hrs;
D=(20-4)*5;
D=80 km
ANSWER:D
Answer: D
Question: We run a business that rents out canoes and kayaks. A canoe rental costs $11 per day, and a kayak rental costs $16 dollars per day. One day, our business rents out 4 canoes for every 3 kayaks and receives a total of $460 in revenue. How many more canoes than kayaks were rented out?
Options:
A)8
B)7
C)6
D)5
E)4
Rationale: Let x be the number of canoes.
Then 3x/4 is the number of kayaks.
11x+(3x/4)*16=460
11x+12x=460
23x=460
x=20 (canoes)
3x/4=15 (kayaks)
There were 20-15 = 5 more canoes rented out.
The answer is D.
Answer: D
Question: A 14% stock yielding 8% is quoted at?
Options:
A)165
B)170
C)175
D)180
E)185
Rationale: Assume that face value = Rs.100 as it is not given
To earn Rs.8, money invested = Rs.100
To earn Rs.14, money invested = 100×14/8 = Rs.175
ie, market value of the stock = Rs.175
Answer is C.
Answer: C
Question: In how many different ways can the letters of the word "AIM" be rearrangement?
Options:
A)4
B)2
C)7
D)9
E)6
Rationale: Option 'E'
The total number of arrangements is
3P3 = 3! = 6
Answer: E
Question: HOW MANY KGS OF TEA WORTH RS.25/KG MUST BE BLENDED WITH 30 KGS OF TEA WORTH RS.30/KG SO THAT BY SELLING THE BLENDED VARIETY AT RS.30/KG THERE SHOULD BE A GAIN OF 15%
Options:
A)36
B)108
C)32
D)42
E)45
Rationale: (x+30)*30=(115/100)(25x+30*30)
Solving we get 108.
Answer is B.
Answer: B