divelab/Sys2Bench huggingface dataset:
Question: v, w, x, y, and z are five positive integers for which v≤w≤x≤y≤z. If the average (arithmetic mean) of the five numbers is 30 and their median is 25, which is the smallest possible value of z?
Options:
A)30
B)35
C)37
D)38
E)40
Rationale: sum=150
mid value = 25
minimize 'z'. So, 25 25 25 37 38
answer: D
Answer: D
Question: Sachin is younger than Rahul by 7 years. If the ratio of their ages is 7:9, find the age of Sachin
Options:
A)23.5
B)24.5
C)12.5
D)14.5
E)None of these
Rationale: Explanation:
If Rahul age is x, then Sachin age is x-7,
so (x-7)/x = 7/9
=> 9x-63 = 7x
=> 2x = 63
=> x = 31.5
So Sachin age is 31.5 - 7 = 24.5
Option B
Answer: B
Question: Three workers have a productivity ratio of 4 to 3 to 2. All three workers are working on a job for 4 hours. At the beginning of the 5th hour, the slowest worker takes a break. The slowest worker comes back to work at the beginning of the 9th hour and begins working again. The job is done in ten hours. What was the ratio of the work performed by the fastest worker as compared to the slowest?
Options:
A)12 to 1
B)6 to 1
C)5 to 1
D)1 to 6
E)3 to 10
Rationale: The fastest worker who does 4 units of job worked for all 10 hours, so he did 4*10=40 units of job;
The slowest worker who does 2 unit of job worked for only 4+2=6 hours (first 4 hours and last 2 hours), so he did 2*6=12 units of job;
The ratio thus is 12 to 40, or 3 to 10.
Answer: E.
Answer: E
Question: In an examination, a student's average marks were 63. If he had obtained 20 more marks for his Geography and 2 more marks for his history, his average would have been 65. How many subjects were there in the examination?
Options:
A)12
B)11
C)13
D)14
E)10
Rationale: Explanation:
Let the number of subjects = x
Then, total marks he scored for all subjects = 63x
If he had obtained 20 more marks for his Geography and 2 more marks for his history, his average would have been 65
=> Total marks he would have scored for all subjects = 65x
Now we can form the equation as 65x - 63x = additional marks of the student = 20 + 2 = 22
=> 2x = 22
=> x = 22/2 = 11
Answer: Option B
Answer: B
Question: If y and g are distinct prime numbers less than 10, which of the following cannot be the product of y and g?
Options:
A)6
B)9
C)10
D)14
E)15
Rationale: If y and g are distinct prime numbers less than 10 prime numbers less than 10 are 2, 3, 5, 7
all except 9 is product of any two numbers picked from above set.
Ans: B
Answer: B
Question: In a partnership, A invests 1/6 of the capital for 1/6 of the time, B invests 1/3 of the capital for 1/3 of the time and C, the rest of the capital for the whole time. Out of a profit of Rs.4600, B’s share is:
Options:
A)Rs.650
B)Rs.800
C)Rs.960
D)Rs.1000
E)Rs.1200
Rationale: Suppose A invests x/6 for y/6 months.
B invests x/3 for y/3 months.
C invests x – x/6 + x/3 i.e x/2 for y months.
Therefore, A : B : C = x/6 * y/6 : x/3 * y/3 : x/2 * y = 1/36 : 1/9 : 1/2 = 1 : 4 : 18.
Therefore, B’s share = Rs. 4600 * 4/23
= Rs.800.
ANSWER:B
Answer: B
Question: if
2345 =62
6571 =73
then
8355 =?
Options:
A)93
B)94
C)95
D)96
E)97
Rationale: 2345
=(2*3)+(4*5)
=6+20
=26 reverse 62
6571
=(6*5)+(7*1)
=30+7
=37 reverse 73
so
8355
=(8*3)+(5*5)
=24+25
=49 reverse 94
ANSWER:B
Answer: B
Question: Loren bought a roll of cloth and sold it for a 5% profit based on the selling price. If Loren`s profit was $45.5 total on the cloth, how much did it cost her to buy the cloth?
Options:
A)$455.
B)$525.5.
C)$675.
D)$810.5.
E)$864.5
Rationale: If the roll was sold for a 5% profit based on the cost, it means that of the total selling price, 95% was the cost, and 5% was the profit.
Selling price = 5% profit + 95% cost
5% profit = $45.5
Find: Cost - ?
Profit: 5% - $45.5
Cost: 95% - x
We cross multiply the values to find x:
x = (95∗45.5)/5(95∗45.5)/5 = $864.5
Answer: E
Answer: E
Question: If n is an integer, f(n) = f(n-1) - n and f(4)=12. What is the value of f(6)?
Options:
A)1
B)0
C)-1
D)2
E)4
Rationale: Since f(n)=f(n-1)-n then: f(6)=f(5)-6 and f(5)=f(4)-5.
As given that f(4)=12 then f(5)=12-5=7 --> substitute the value of f(5) back into the first equation: f(6)=f(5)-6=7-6=1.
Answer: A.
Questions on funtions to practice:
Answer: A
Question: What should come in place of the question mark (X) in the following equation ?
60% of X + 2/3 of 39 = 44
Options:
A)50
B)60
C)30
D)20
E)None of these
Rationale: Explanation:
60% of X + 2/3 of 39 = 44
i.e. 3/5 of X + 2/3 of 39 = 44 (60% = 3/5)
3/5 * X + 2/3 * 39 = 44
3/5 * X + 26 = 44
3/5 * X = 18
X = 18 * 5/3
X = 30
ANSWER:C
Answer: C
Question: Of the teams competing in the world archery championships, Thirty percent are from Europe. Half as many are from the United States and one twentieth are from Africa. What fraction of teams are from neither Europe, the US or Africa.
Options:
A)10/20
B)15/20
C)13/15
D)17/20
E)13/17
Rationale: Assume 100 total people.
30% of 100 = 30 --->Europeans
1/2 of 30 ---> 15 Americans
1/20 of 100 ---> 5 Africans
Now you would add them all up, and minus it by the total (100). 100 - 50= 50. So, 50 people out of 100 are not EU, US or Africans. 50/100 is also equal to 10/20.
So therefore, the answer is A.
Answer: A
Question: 3 boys and 7 girls can complete John work in 10 days. 4 boys and 6 girls need 8 days to complete the same work . In how many days will 10 girls complete the same work?
Options:
A)10 days
B)20 days
C)40 days
D)60 days
E)70 days
Rationale: Work done by 4 boys and 6 girls in 1 day = 1/8
Work done by 3 boys and 7 girls in 1 day = 1/10
Let 1 man does m work in 1 day and 1 woman does w work in 1 day. The above equations can be written as
4m + 6w = 1/8 ---(1)
3m + 7w = 1/10 ---(2)
Solving equation (1) and (2) , we get m=11/400 and w=1/400
Amount of work 10 girls can do in John day = 10 × (1/400) = 1/40
Ie, 10 girls can complete the work in 40 days
C
Answer: C
Question: Reena took a loan of Rs. 1400 with simple interest for as many years as the rate of interest. If she paid Rs. 432 as interest at the end of the loan period, what was the rate of interest?
Options:
A)8.55%
B)5.55%
C)4.55%
D)6.55%
E)7.55%
Rationale: Let rate = R% and time = R years.
Then, (1400 * R * R) / 100 = 432
14R2 = 432
R2 = 30.8 => R = 5.55
ANSWER:B
Answer: B
Question: A metal company's old machine makes bolts at a constant rate of 100 bolts per hour. The company's new machine makes bolts at a constant rate of 150 bolts per hour. If both machines start at the same time and continue making bolts simultaneously, how many minutes will it take the two machines to make a total of 550 bolts?
Options:
A) 36
B) 72
C) 120
D) 132
E) 180
Rationale: Old Machine
100 bolts in 60 mins
so,
5/3 bolts in 1 min
New Machine
150 bolts in 60 mins
so,
5/2 bolts in 1 min
together,
5/3 + 5/2 =
25/6 bolts in 1 min
so, for 550 bolts
550 * 6 / 25 = 132 mins
Ans D
Answer: D
Question: Find the cost of fencing around a circular field of diameter 20 m at the rate of Rs.1.50 a meter?
Options:
A)287
B)94.2
C)156
D)158
E)267
Rationale: 2 * 22/7 * 10 = 62.8
62.8 * 1 1/2 = Rs.94.2
Answer: B
Answer: B
Question: A man buys an article for Rs. 27.50 and sells it for Rs 28.60. Find his gain percent
Options:
A)4%
B)2%
C)1%
D)3%
E)5%
Rationale: CP = 27.50
SP = 28.60
Gain = 28.60 - 27.50 = 1.10
gain % = gain/cost*100
(1.10/27.50*100)% = 4%
ANSWER A
Answer: A
Question: A photo-mat shop charges $0.55 for the first photo inside a film, and 20% cents less for each additional photo. How many photos can we develop with $52.58 if each film contains 36 photos?
Options:
A)4 films and 12 photos
B)5 films and 6 photos
C)5 films and 14 photos
D)6 films and 4 photos
E)2 films and 28 photos
Rationale: 1st photo = 0.55
Subsequent = 0.55*0.6=0.33
Price of 1 full film=0.55+0.33*35=12.1
Price of 4 full film = 12.1*4=48.4
52.58-48.4=4.18
4.18=0.55+0.33x
x=11
52.58--->2 full films and 1+11=28 photos
Answer: E
Answer: E
Question: Meena wrote all the numbers from 1 to 59,999 inclusive. How many digits did she write in total?
Options:
A)248,889
B)268,889
C)288,889
D)308,889
E)328,889
Rationale: 1-9=>1*9 digits
10-99=>2*90=180 (numbers between 10-99 is 90 where each has 2 digits)
100-999=>3*900=2700
1000-9999=>4*9000 = 36,000
10000-59999=>5*50,000 = 250,000
The answer is 288,889
The answer is C.
Answer: C
Question: A company declared a semi-annual dividend of 12%. Find the annual dividend of Sam owing 2000 shares of the company having a par value of Rs. 10 each.
Options:
A)4000
B)4200
C)4400
D)4800
E)5000
Rationale: semi-annual dividend = 10×12/100 = Rs.1.2
Total semi-annual dividend = 2000 × 1.2 = Rs.2400
Total annual dividend = 2 × Rs.2400 = Rs.4800
Answer is D.
Answer: D
Question: A number when divided by the sum of 555 and 445 gives two times their difference as quotient and 30 as the remainder. The number is
Options:
A)1220
B)1250
C)22030
D)220030
E)NOne
Rationale: Sol.
Required number = (555 + 445) x 2 x 110 + 30
= 220000 + 30
= 220030.
Answer D
Answer: D
Question: A train running at a speed of 36 km/h passes an electric pole in 14 seconds. In how many seconds will the whole train pass a 370-meter long platform?
Options:
A)45
B)47
C)49
D)51
E)53
Rationale: Let the length of the train be x meters.
When a train crosses an electric pole, the distance covered is its own length x.
speed = 36 km/h = 36000 m / 3600 s = 10 m/s
x = 14 * 10 = 140 m.
The time taken to pass the platform = (140 +370)/ 10 = 51 seconds
The answer is D.
Answer: D
Question: The amount of water (in ml) that should be added to reduce 6 ml. Lotion, containing 50% alcohol, to a lotion containing 30% alcohol, is?
Options:
A)8 ml
B)5 ml
C)4 ml
D)6 ml
E)1 ml
Rationale: 3 3
30% 70%
30% ----- 3
70% ------? => 7 - 3 = 4ml
Answer:C
Answer: C
Question: A 300 meter long train crosses a platform in 33 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform?
Options:
A)287m
B)278m
C)350m
D)228m
E)250m
Rationale: Speed = [300 / 18] m/sec = 50/3 m/sec.
Let the length of the platform be x meters.
Then, x + 300 / 33
= 50/3
3(x + 300)
= 1650 è x
= 250m.
Answer:E
Answer: E
Question: There are 4 prime numbers in ascending order. The multiplication of 1st 3 is 385 and that of last 3is 1001. what is the last number is
Options:
A)10
B)15
C)16
D)13
E)18
Rationale: Explanation:
abcbcd=3851001=>ad=513
abcbcd=3851001=>ad=513
So d = 13
D
Answer: D
Question: Two taps can separately fill a cistern 4 minutes and 6 minutes respectively and when the waste pipe is open, they can together fill it in 8 minutes. The waste pipe can empty the full cistern in?
Options:
A)7
B)8
C)6
D)9
E)3.4
Rationale: 1/4 + 1/6 - 1/x = 1/8
x = 24/7 = 3.4
Answer: E
Answer: E
Question: In a digital circuit which was to implement (A B) + (A)XOR(B), the designer implements (A B) (A)XOR(B) What is the probability of error in it ?
Options:
A)25%
B)35%
C)75%
D)45%
E)55%
Rationale: A	B	AB	A XOR B	(AB)+(A XOR B)	(AB) (A XOR B)
0	0	0	0	0	0
0	1	0	1	1	0
1	0	0	1	1	0
1	1	1	0	1	0
so, we are getting 3 wrong answers out of 4
probability of error is 3/4=75%
ANSWER:C
Answer: C
Question: In a consumer survey, 85% of those surveyed liked at least one of three products: 1, 2, and 3. 46% of those asked liked product 1, 30% liked product 2, and 20% liked product 3. If 5% of the people in the survey liked all three of the products, what percentage of the survey participants liked more than one of the three products?
Options:
A)6
B)10
C)15
D)20
E)25
Rationale: Use the forumla ;
Total = Group1 + Group2 + Group3 - (sum of 2-group overlaps) - 2*(all three) + Neither
100 = 46 + 30 + 20 - ( sum of 2) -2(5) +15
100 = 101-( sum of 2)
1 = sum of 2
so more than 1 = 6
A
Answer: A
Question: If the sides of a triangle are 32 cm, 27 cm and 12 cm, what is its area?
Options:
A)120 cm2
B)112 cm2
C)162 cm2
D)666 cm2
E)886 cm2
Rationale: The triangle with sides 32 cm, 27 cm and 12 cm is right angled, where the hypotenuse is 32 cm.
Area of the triangle = 1/2 * 27 * 12 = 162 cm2
Answer: C
Answer: C
Question: 65% of the employees of a company are men. 60% of the men in the company speak French and 40% of the employees of the company speak French. What is % of the women in the company who do not speak French?
Options:
A)4%
B)10%
C)97.14%
D)90.14%
E)20%
Rationale: No of employees=100(say)
Men=65
Women=35
Men speaking french=0.60*65=39
Employees speaking french=0.4*100=40
Therefore women speaking French=40-39=1
And women not speaking French=35-1=34
% of women not speaking French=34/35*100=97.14%
Answer C
Answer: C
Question: How many two digit numbers of distinct digits can be formed by using digits 3, 4, 5, 6 and 7 such that the numbers are divisible by 9?
Options:
A)1
B)2
C)3
D)4
E)6
Rationale: CONCEPT: A number will be divisible by 9 if sum of all the digits of the number is divisible by 9
Here the Possible sum of the two distinct digits can be 9 only in order to satisfy the given condition
If sum of Digits = 9, No. = 36, 45, 54, 63 --- 4 Cases
Answer: option D
Answer: D
Question: Today is Monday. After 61 days, it will be:
Options:
A)Wednesday
B)Saturday
C)Tuesday
D)Thursday
E)sunday
Rationale: EXPLANATION
Each day of the week is repeated after 7 days.
So, after 63 days, it will be Monday.
After 61 days, it will be Saturday.
Answer B
Answer: B
Question: The cost of 3 pens and 5 pencils is Rs.150. Also the cost of one pen and one pencil is in the ratio of 5:1 respectively. What is the cost of one dozen pens?
Options:
A)Rs.200
B)Rs.250
C)Rs.300
D)Rs.450
E)None of these
Rationale: Explanation:
Let the cost of one pen is ‘5x’ and pencil is ‘x’
3 X 5x + 5x = Rs.150
15x + 5x = Rs.150
X = 150/20 = 7.50
:. Cost of 1 pen = 5x = 5 x 7.50 = 37.50
:. Cost of 12 pens, i.e. (one dozen) = 37.50x 12 = Rs.450
Answer: Option D
Answer: D
Question: A certain galaxy is known to comprise approximately 6 x 10^11 stars. Of every 50 million of these stars, one is larger in mass than our sun. Approximately how many stars in this galaxy are larger than the sun?
Options:
A)800
B)1,250
C)8,000
D)12,000
E)80,000
Rationale: 6*10^11
50 mln = 5*10^7
we divide 10^11 by 10^7 and we get (10^4)*6 = 60,000 and divide by 5. the result is 12,000
D
Answer: D
Question: If a certain number is divided by 12, the quotient, dividend, and divisor, added together, will amount to 64. What is the number?
Options:
A)18
B)28
C)48
D)38
E)59
Rationale: Let x = the number sought.
Then x/12 + x + 12 = 64.
And x - 624/13 = 48.
Answer: A
Question: 6^4− 4^4 = ?
Options:
A)20
B)52
C)104
D)520
E)1040
Rationale: We can write the above in terms of
(a+b) (a-b)
6^4−4^4= (6^2)2 - (4^2)2 = (6^2−4^2)*(6^2+4^2) =
(36−16)*(36+16) => 20*52 = 1040
Ans option E.
Answer: E
Question: If A:B = 1/2: 1/3 B:C = 1/2:1/3 then A:B:C?
Options:
A)9:6:4
B)2:3:3
C)1:2:6
D)2:3:5
E)6:5:9
Rationale: A:B = 1/2:1/3 = 3:2
B:C = 1/2:1/3 = 3:2
--------------------
A:B:C = 9:6:4
ANSWER A
Answer: A
Question: If x-y=8, which of the following must be true?
I. Both x and y are positive
II. If x is positive, y must be positive
III. If x is negative, y must be negative
Options:
A)I only
B)II only
C)III only
D)I and II
E)II and III
Rationale: The best way to approach such questions is to plug in values for x and y
Given: x-y=8
I. Both x and y are positive:
Let x=10 and y=2
x-y=8
But,
Let x=6 and y=-2
x-y=8
Therefore, NOT TRUE
II. If x is positive, y must be positive
Let x=10 and y=2
x-y=8
But,
Let x = 6 and y=-2
x-y=8
Therefore, NOT TRUE
III. If x is negative, y must be negative
If x is negative, for the expression x-y=8 to be true, y must be a -ve number. Otherwise, the sum of two negative numbers will yield another negative number!
Therefore, TRUE
Ans: 'C'
Answer: C
Question: A student completes a 3 part exam as follows. The student completes sections A in 4 minutes and takes an equal time to complete the two remaining sections. What is the ratio of time spent on section C to section A if the total duration is 1 hour?
Options:
A)10:3
B)9:2
C)7:1
D)8:3
E)11:2
Rationale: The time spent on section B and section C is 28 minutes each.
The ratio of C to A is 28:4 = 7:1
The answer is C.
Answer: C
Question: The average of 11 numbers is 10.9. If the average of first six is 10.5 and that of the last six is 11.1 the sixth number is?
Options:
A)9.7
B)10
C)10.5
D)11.5
E)12
Rationale: Explanation:
1 to 11 = 11 * 10.9 = 119.9
1 to 6 = 6 * 10.5 = 63
6 to 11 = 6 * 11.1 = 66.6
63 + 66.6 = 129.6 – 119.9 = 9.7
6th number = 9.7
Option A
Answer: A
Question: Bill spends two days driving from Point A to Point B . On the first day, he drove 2 hours longer and at an average speed 5 miles per hour faster than he drove on the second day. If during the two days he drove a total of 680 miles over the course of 18 hours, what was his average speed on the second day, in miles per hour?
Options:
A)20
B)25
C)28
D)30
E)35
Rationale: First recognize that we have TWO pieces of information regarding the time Bill spent driving each day.
On day 1, Bill drove 2 hours longer than he drove on day 2.
So, let x = # of driving hours on day 2
Then x + 2 = # of driving hours on day 1
Bill drove a TOTAL of 18 hours
So, x + (x + 2) = 18
Simplify: 2x + 2 = 18
Solve, x = 8
So, Bill drove 10 hours on day 1 and he drove 8 hours on day 2
Now let's solve the question by starting with a word equation.
Let x = speed driven on day 2
So, x + 5 = speed driven on day 1
(Distance traveled on day 1) + (Distance traveled on day 2) = 680
Distance = (rate)(time)
We get: (x+ 5)(10) + (x)(8) = 680
Expand: 10x + 50 + 8x = 680
Simplify: 18x + 50 = 680
18x = 630
x = 35 (mph)
ANSWER:E
Answer: E
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.70400?
Options:
A)89100
B)81028
C)27772
D)29889
E)22312
Rationale: 70400* 9/8 * 9/8 = 89100.Answer:A
Answer: A
Question: John can divide his herd into 5 equal parts and also to 6 equal parts, but not to 9 equal parts. What could be the number of cows John has in his herd?
Options:
A)180
B)336
C)456
D)120
E)155
Rationale: On first look B, C,E are not divisible either by 5 or 6 - ruled out.
A,D divisible by both 5,6, but 180 is divisible by 9.
Answer : D
Answer: D
Question: If x is an integer and 2.134 × 10^x is less than 21000, what is the greatest possible value for x?
Options:
A)7
B)6
C)5
D)4
E)3
Rationale: If x=4
2.134 × 10^4 = 21340 > 21000
So, x = 3
Answer : E
Answer: E
Question: What is the ratio between perimeters of two squares one having 11 times the diagonal then the other?
Options:
A)3: 8
B)3: 6
C)3: 7
D)11: 1
E)3: 3
Rationale: d = 11d d = d
a√2 = 11d a√2 = d
a = 11d/√2 a = d/√2 => 11: 1
Answer:D
Answer: D
Question: 1/2-[(2/7*7/32)+1]+9/16=
Options:
A)29/16
B)19/16
C)15/16
D)9/13
E)0
Rationale: 1/2 - [(2/7*7/32) + 1] + 9/16 =
1/2 - [(1/16) + 1] + 9/16 =
1/2 - [17/16] + 9/16 =
8/16 - 17/16 + 9/16 = 0
The answer is E.
Answer: E
Question: Two boys starting from the same place walk at a rate of 5kmph and 5.5kmph respectively. What time will they take to be 10.5km apart, if they walk in the same direction?
Options:
A)15 hours
B)16 hours
C)17 hours
D)18 hours
E)21 hours
Rationale: The relative speed of the boys = 5.5kmph â€“ 5kmph
= 0.5 kmph
Distance between them is 10.5 km
Time = Distance/Speed
Time= 10.5km / 0.5 kmph = 21 hrs
answer :E
Answer: E
Question: If the sum of two numbers is 55 and the H.C.F. and L.C.M. of these numbers are 5 and 120 respectively, then the sum of the reciprocals of the numbers is equal to:
Options:
A)11/122
B)11/120
C)11/121
D)11/140
E)11/111
Rationale: Explanation:
Let the numbers be a and b.
Then, a + b = 55 and ab = 5 x 120 = 600.
The required sum
Answer: B) 11/120
Answer: B
Question: A and B starts a business with Rs.8000 each, and after 7 months, B withdraws half of his capital . How should they share the profits at the end of the 18 months?
Options:
A)18:11
B)22:13
C)23:12
D)36:25
E)11:10
Rationale: A invests Rs.8000 for 18 months, but B invests Rs.8000 for the first 7 months and then withdraws Rs.4000. So, the investment of B for remaining 11 months is Rs.4000 only.
A : B
8000*18 : (8000*7) + (4000*11)
144000 : 100000
A:B = 36:25
ANSWER:D
Answer: D
Question: The number 50 is divided into two equal parts, the ratio of the largest part to the smallest is 2/3, then the largest part is?
Options:
A)30
B)35
C)40
D)45
E)20
Rationale: assume two numbers are x and y
x/y = 2/3.. 2x = 3y ----1
The number 50 is divided into two equal parts. If you make equal parts there is no question of Largest part and Smallest Part. So assuming 50 is devided in to two parts.
x+ y = 50 ---- 2
simplyfy 1 and 2 x =30 and y = 20
ANSWER:A
Answer: A
Question: How many W ways can you group 3 people from 4 sets of twins if no two people from the same set of twins can be chosen?
Options:
A)3
B)16
C)28
D)32
E)56
Rationale: Ways to select 3 people from 8 people (4 twins x 2) = 8C3 = 56
Ways to select 1 twin + 1 people = 4C1*6C1 = 24
Ways to select a group 3 people from 4 sets of twins if no two people from the same set of twins can be chosen W= 56 - 24 = 32
Ans: D
Answer: D
Question: Two boys starting from the same place walk at a rate of 5kmph and 5.5kmph respectively. What time will they take to be 8.5km apart, if they walk in the same direction?
Options:
A)67 hours
B)47 hours
C)17 hours
D)27 hours
E)16 hours
Rationale: Explanation:
In this type of questions we need to get the relative speed between them,
The relative speed of the boys = 5.5kmph â€“ 5kmph
= 0.5 kmph
Distance between them is 8.5 km
Time = Distance/Speed
Time= 8.5km / 0.5 kmph = 17 hrs
Answer: C
Answer: C
Question: The speed of the boat in still water in 12 kmph. It can travel downstream through 60 kms in 3 hrs. In what time would it cover the same distance upstream?
Options:
A)8 hours
B)6 hours
C)4 hours
D)15 hours
E)6 hours
Rationale: Still Water=12km/hr
Downstream=60/3=20km/hr
Upstream=>> still water=(u+v/2) =>> 12=u+20/2 = 4km/hr
So time taken in upstream = 60/4 =15hrs
ANSWER:D
Answer: D
Question: Two stations A and B are 110 km apart on a straight line. One train starts from A at 6 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet?
Options:
A)11
B)10
C)9
D)12
E)15
Rationale: Suppose they meet x hours after 6 a.m.
Distance covered by A in x hours = 20x km.
Distance covered by B in (x - 1) hours = 25(x - 1) km.
Therefore 20x + 25(x - 1) = 110
45x = 135
x = 3.
So, they meet at 9 a.m.
Answer: C
Answer: C
Question: 3889 + 12.952 - ? = 3854.002
Options:
A)47.59
B)48.95
C)49.85
D)47.95
E)49.75
Rationale: Let 3889 + 12.952 - x = 3854.002.
Then x = (3889 + 12.952) - 3854.002
= 3901.952 - 3854.002
= 47.95.
Answer is D.
Answer: D
Question: A car gets 20 kilometers per gallon of gasoline. How many gallons of gasoline would the car need to travel 180 kilometers?
Options:
A)8.5 gallons
B)9 gallons
C)6.5 gallons
D)5.5 gallons
E)6 gallons
Rationale: Each 20 kilometers, 1 gallon is needed. We need to know how many 20 kilometers are there in 180 kilometers?
180 / 20 = 9 * 1 gallon = 9 gallons correct answer B
Answer: B
Question: the probability of a student possessing a ball point pen in exam is 3/5 & possessing an ink pen is 2/3. find his probability of possessing at least one of them
Options:
A)10/15
B)11/15
C)12/15
D)13/15
E)14/15
Rationale: the probability of a student possessing a ball point pen in exam is 3/5 .
the probability of a student not possessing a ball point pen in exam is 2/5 & possessing an ink pen is 2/3.
& not possessing an ink pen is 1/3.
his probability of possessing none of them =2/5*1/3=2/15
his probability of possessing one of them =1-2/15 = 13/15
ANSWER:D
Answer: D
Question: Camel and carriage for Rs. 5000. He SP the camel at a gain of 20% and the carriage at a loss of 10%. If he gains 3% on the whole, then find the CP of the camel?
Options:
A)Rs.2166.67
B)Rs.2145.67
C)Rs.2157
D)Rs.2167.1
E)Rs.2178.34
Rationale: Now, in this numerical, there is no common loss and gain %.
Hence, solve it making equations.
Let cost price of camel be x.
As cost of camel and carriage = Rs 5000
Cost of carriage = Rs. (5000 – x)
After selling camel he gains 20% and on carriage a loss of 10%. But on the whole he gains 3%.
Therefore,
20% of x – 10 % of (5000 – x) = 3 % of 5000
20 × x – 10 × (5000 – x) = 3 × 5000
100 100 100
x – (5000 – x) = 150
5 10
10x – (5000 – x) × 10 = 150 × 10
5 10
2x-5000+x=1500
3x=1500+5000
x=2166.67
The cost of camel = Rs.2166.67
Option (A) is the correct answer
Answer: A