mathewhe/aqua_rat huggingface dataset:
Question: Z is a set of positive numbers. The median of Z is greater than the mean of Z. Which of the following E must be true?
I. At least 50% of the numbers in Z are smaller than the median.
II. Less than 50% of the numbers in Z are greater than the median.
III. The median of Z is greater than the average of the largest and smallest numbers in Z.
(A) I only
(B) II only
(C) III only
(D) I and III only
(E) E=None of the above
Rationale: Condition 3 can be invalidated by: (1, 3, 4, 5)--median is equal to average of 1 and 5 and average is greater than 3.
Then, don't conditions 1 and 2 have to occur simultaneously? I reasoned this based on the word... maybe that's incorrect.
Even if not, we can rule them both out. So, E.
Answer: (E) E=None of the above
Question: A, B and C can do a piece of work in 7 days, 14 days and 28 days respectively. How long will they taken, if all the three work together?
(A) 3 days
(B) 4 days
(C) 5 days
(D) 6 days
(E) 7 days
Rationale: Explanation:
1/7 + 1/14 + 1/28 = 7/28 = 1/4 => 4 days
Answer: B
Answer: (B) 4 days
Question: What least no. must be subtracted from 101054 so that remaining no.is divisible by 10?
(A) 6
(B) 4
(C) 8
(D) 5
(E) 3
Rationale: Explanation:
On dividing 101054 by 10 we get the remainder 4, so 4 should be subtracted
Option B
Answer: (B) 4
Question: In triangle PQR, the angle Q = 90 degree, PQ = 7 cm, QR = 8 cm. X is a variable point on PQ. The line through X parallel to QR, intersects PR at Y and the line through Y, parallel to PQ, intersects QR at Z. Find the least possible length of XZ
(A) 5.6 cm
(B) 2.4 cm
(C) 4.8 cm
(D) 2.16 cm
(E) 3.2 cm
Rationale: Look at the diagram below:
Now, in case when QY is perpendicular to PR, two right triangles PQR and PQY are similar: QY:QP=QR:PR --> QY:7=8:10 --> QY=5.6.
Answer: A.
Answer: (A) 5.6 cm
Question: What is y if y + 2x = 10 and x = 3?
(A) A)10
(B) B)8
(C) C)6
(D) D)4
(E) E)2
Rationale: y = 10 - 2x
y = 10 - 8.
y = 2
Answer : D
Answer: (D) D)4
Question: The H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 13 and 14. The larger of the two numbers is:
(A) 276
(B) 299
(C) 322
(D) 345
(E) 367
Rationale: the numbers are (23 x 13) and (23 x 14).
Larger number = (23 x 14) = 322.
Answer: Option C
Answer: (C) 322
Question: Find the average of all numbers between 1 and 13 which are divisible by 2
(A) 15
(B) 21
(C) 25
(D) 30
(E) 35
Rationale: Explanation:
Average=(2+4+6+8+10+12 )/ 2=42 / 2=21
Option B
Answer: (B) 21
Question: If x is equal to the sum of the integers from 30 to 40, inclusive, and y is the number of EVEN integers from 30 to 40, inclusive, what is the value of x+y ?
(A) 171
(B) 281
(C) 391
(D) 591
(E) 601
Rationale: sum s= n/2{2a+(n-1)d} = 11/2{2*30+ (11-1)*1} =11*35=385 =X
number of even number =( 40-30)/2 +1 = 6= Y
X+Y = 385+6 =391
C
Answer: (C) 391
Question: There are 24 students in a seventh grade class. They decided to plant birches and roses at the school's backyard. While each girl planted 3 roses, every three boys planted 1 birch. By the end of the day they planted 2424 plants. How many birches were planted?
(A) 2
(B) 5
(C) 8
(D) 6
(E) 4
Rationale: Let x be the number of roses. Then the number of birches is 24−x, and the number of boys is 3×(24−x). If each girl planted 3 roses, there are x3girls in the class.
We know that there are 24 students in the class. Therefore x3+3(24−x)=24
x+9(24−x)=3⋅24
x+216−9x=72
216−72=8x
1448=x1
x=18
So, students planted 18 roses and 24 - x = 24 - 18 = 6 birches.
correct answer is D)6
Answer: (D) 6
Question: A and B started a partnership business investing capital in the ratio of 3 : 5. C joined in the partnership after six months with an amount equal to that of B. At the end of one year, the profit should be distributed among A, B and C in --- proportion.
(A) 10 : 5 : 4
(B) 5 : 3 : 4
(C) 3 : 4: 5
(D) 6 : 10 : 5
(E) None of these
Rationale: Explanation :
Initial investment capital ratio of A and B = 3 : 5
Hence we can assume that initial capital of A and B are 3x and 5x respectively.
Amount that C invest after 6 months = 5x (Since it is equal to B's investment)
Ratio in which profit should be distributed after 1 year = 3x*12 : 5x * 12 : 5x*6
=> 3*12 : 5*12 : 5*6
= 6 : 10 : 5. Answer : Option D
Answer: (D) 6 : 10 : 5
Question: A dealer purchases 15 articles for Rs. 25 and sells 12 articles for Rs. 36. Find the profit percentage?
(A) 80%
(B) 50%
(C) 59%
(D) 40%
(E) 53%
Rationale: L.C.M of 15 and 12
= 60
CP of 60 articles
= Rs. 100 (25 * 4)
SP of 60 articles
= Rs. 180 (36 * 5)
Profit percentage
= (180 - 100)/100 * 100 = 80%
Answer: A
Answer: (A) 80%
Question: In a fuel station the service costs $1.75 per car, every liter of fuel costs 0.65$. Assuming that a company owns 12 cars and that every fuel tank contains 60 liters and they are all empty, how much money total will it cost to fuel all cars?
(A) 320$
(B) 380$
(C) 420$
(D) 450$
(E) 489$
Rationale: Total Cost = ( 1.75*12 ) + ( 0.65 * 12 * 60 ) = 21 + 468 => 489
Hence answer will be (E) 489
Answer: (E) 489$
Question: If x and y are positive integers, which of the following CANNOT be the greatest common divisor of 35x and 20y?
(A) 5
(B) 5(x – y)
(C) 20x
(D) 20y
(E) 35x
Rationale: Looking at the list of answer choices, there are some that we can quickly eliminate...
IF
X = 1
Y = 1
Then we have 35 and 20, so the GCD = 5
Eliminate A.
X = 20
Y = 1
Then we have 700 and 20, so the GCD = 20
Eliminate D.
X = 1
Y = 35
Then we have 35 and 700, so the GCD = 35
Eliminate E.
With the remaining 2 answers, we have to think a little more.
To get a simple example of 5(X-Y) to be the GCD, we probably need 35X to be ODD
IF...
X = 3
Y = 2
Then we have 105 and 40, so the GCD = 5
5(X-Y) = 5(3-2) = 5
This can ALSO be the GCD
Eliminate B.
ANSWER:C
Answer: (C) 20x
Question: The sum of three numbers is 98. If the ratio of the first to the second is 2 : 3 and that of the second to the third is 5 : 8,then the second number is :
(A) 20
(B) 30
(C) 38
(D) 48
(E) None of these
Rationale: A : B = 2 : 3 = 2 × 5 : 3 × 5 = 10 : 15
and B : C = 5 : 8 = 5 × 3 : 8 × 3 = 15 : 24
Therefore, A : B : C = 10 : 15 : 24
∴ A : B : C = 10 : 15 : 24
Let the number be 10x, 15x and 24x.
Then, 10x + 15x + 24x = 98
or 49x = 98 or x = 2
⇒ Second number = 15x = 15 × 2 = 30
Answer B
Answer: (B) 30
Question: In an election between two candidates, one got 55% of the total valid votes, 20% of the votes were invalid. If the total number of votes was 6500, the number of valid votes that the other candidate got, was:
(A) 2800
(B) 2700
(C) 2900
(D) 2340
(E) 2300
Rationale: D
Number of valid votes = 80% of 6500 = 5200.
Valid votes polled by other candidate = 45% of 5200
= (45/100 x 5200) = 2340.
Answer: (D) 2340
Question: How many terminating zeroes R does 200! have?
(A)  40
(B)  48
(C)  49
(D)  55
(E)  64
Rationale: You have 40 multiples of 5, 8 of 25 and 1 of 125. This will give 49 zeros.C
Answer: (C)  49
Question: 75 men working 8 hours per day dig 50 m deep. How many extra men should be put to dig to a depth of 70 m working 6 hours per day?
(A) 75
(B) 45
(C) 55
(D) 65
(E) 35
Rationale: (75 * 8)/50
= (x * 6)/70
=> x =140
140 â€“ 65
= 65
Answer: D
Answer: (D) 65
Question: Rates for having a manuscript typed at a certain typing service are $10 per page for the first time a page is typed and $5 per page each time a page is revised. If a certain manuscript has 100 pages, of which 30 were revised only once, 20 were revised twice, and the rest required no revisions, what was the total cost of having the manuscript typed?
(A) $1250
(B) $1350
(C) $1150
(D) $1360
(E) $1370
Rationale: 50 pages typed 1x
30 pages typed 2x (original + one revision)
20 pages typed 3x (original + two revisions)
50(10)+30(10+5)+20(10+5+5)=500+450+400=1350
Answer - B
Answer: (B) $1350
Question: The water level in a reservoir has been dropping at the rate of 14 inches per day. Exactly 5 days ago, the water level was at w inches. What will be the water level exactly 3 days from now if the rate at which the level is dropping remains the same?
(A) w − 126
(B) w − 56
(C) w − 112
(D) w + 14
(E) w + 126
Rationale: Drop=14 inches/day
5 Days ago=w, means now it's equal w-70 and in 3 days = w-70-42=w-112
Answer C
Answer: (C) w − 112
Question: If the sum of two numbers is 60 and the H.C.F and L.C.M of these numbers are 3 and 120 respectively, then the sum of the reciprocal of the numbers is equal to:
(A) 2/9
(B) 4/5
(C) 1/6
(D) 6/6
(E) 3/9
Rationale: Let the numbers be a and b.
Then, a + b = 60 and ab = 3 * 120 =360.
Required sum = 1/a + 1/b = (a + b)/ab = 60/360 = 1/6.
ANSWER:C
Answer: (C) 1/6
Question: A certain bus driver is paid a regular rate of $15 per hour for any number of hours that does not exceed 40 hours per week. For any overtime hours worked in excess of 40 hours per week, the bus driver is paid a rate that is 75% higher than his regular rate. If last week the bus driver earned $976 in total compensation, how many total hours did he work that week?
(A) 56
(B) 51
(C) 59
(D) 54
(E) 52
Rationale: For 40 hrs = 40*15=600
Excess = 976-600=376
For extra hours =.75(15)=11.25+15=26.25
Number of extra hrs =376/26.25=14.3=14 approx.
Total hrs =40+14=54
Answer D
Answer: (D) 54
Question: The mean of 20 values was 150. It was detected on rechecking that one value 160 was wrongly copied as 135 for the computation of the mean. Find the correct mean.
(A) 151
(B) 149
(C) 151.25
(D) 148
(E) None of the above
Rationale: Corrected mean = 150×20−135+160/20
= 3000−135+160/20
=3025/20=151.25
Answer C
Answer: (C) 151.25
Question: If the true discount on s sum due 2 years hence at 14% per annum be Rs. 168, the sum due is ?
(A) Rs.948
(B) Rs.876
(C) Rs.768
(D) Rs.658
(E) NONE OF THESE
Rationale: Explanation:
P.W. =(100*T.D)/R*T = (100*168)/14*2 = 600.
Sum = (P.W. + T.D.) = Rs. (600 + 168) = Rs. 768.
ANSWER IS C
Answer: (C) Rs.768
Question: To fill a tank, 10 buckets of water is required. How many buckets of water will be required to fill the same tank if the capacity of the bucket is reduced to two-fifth of its present ?
(A) 25
(B) 50
(C) 75
(D) 100
(E) 125
Rationale: Let the capacity of 1 bucket = x.
Then, the capacity of tank = 10x.
New capacity of bucket = 2/5 x
Therefore, Required number of buckets = (10x)/(2x/5)
= (10x) x 5/2x
= 50/2
= 25
Answer is A.
Answer: (A) 25
Question: The youngest of 4 children has siblings who are 3, 5, and 8 years older than she is. If the average (arithmetic mean) age of the 4 siblings is 21, what is the age of the youngest sibling?
(A) 17
(B) 18
(C) 19
(D) 21
(E) 22
Rationale: Total age of the 4 sibling is 21 x 4 = 84 years ..
We already have the total age of all the children is 4y + 16
So, 4y + 16 = 84
Or, 4y = 68
Or, y = 17
So, Age of the youngest child is 17 years.
ANSWER:A
Answer: (A) 17
Question: The average temperature on Wednesday in Chicago, St. Louis, and Pittsburgh was 27Â°C. The average temperature that same day of St. Louis, Pittsburgh, and Jersey City was 30Â°C. If temperature in Jersey City was 32Â°C, what was the temperature on Wednesday in Chicago?
(A) 22Â°C
(B) 23Â°C
(C) 24Â°C
(D) 25Â°C
(E) 26Â°C
Rationale: Solution: Average temperature for Chicago, St. Louis and Pittsburgh = 27Â°C
Total temperature = 3*27 = 81
Average temperature for St. Louis, Pittsburgh and Jersey City = 30Â°C
Total temperature = 3*30 = 90
Temperature in Jersey City = 32Â°C
Now,
(Chicago+St. Louis+Pittsburgh)-(St. Louis+Pittsburgh+Jersey City) = 81-90
Chicago - Jersey City = -9
Chicago = Jersey City - 9 = 23Â°C
Answer: Option B
Answer: (B) 23Â°C
Question: At what rate of compound interest per annum will a sum of Rs. 1200 become Rs. 1348.32 in 2 years
(A) 3%
(B) 4%
(C) 5%
(D) 6%
(E) None of these
Rationale: Explanation:
Let Rate will be R%
1200(1+R100)2=134832100(1+R100)2=134832120000(1+R100)2=1123610000(1+R100)=106100=>R=6%
Answer: D
Answer: (D) 6%
Question: A train speeds past a pole in 15 seconds and a platform 110 meters long in 25 seconds. What is the length of the train?
(A) 100 m
(B) 125 m
(C) 130 m
(D) 150 m
(E) 165 m
Rationale: Let the length of the train be x meters.
The speed of the train is x / 15.
Then, x + 110 = 25*(x / 15)
10x = 1650
x = 165 meters
The answer is E.
Answer: (E) 165 m
Question: There are 3 numbers A, B and C. If A:B = 3/4, B:C = 4/5, C:D = 5/6, then A:D will be?
(A) 1 : 2
(B) 2 : 3
(C) 3 : 5
(D) 3 : 7
(E) 3 : 8
Rationale: Sol. A : B = 3 : 4, B : C = 4 : 5, C : D = 5 : 6
∴A∶B∶C∶D= 3 : 4 : 5 : 6.
Thus, A : D = 3 : 6 or, 1 : 2
A
Answer: (A) 1 : 2
Question: A train 500 m long can cross an electric pole in 20 sec and then find the speed of the train?
(A) 17 Kmph
(B) 78 Kmph
(C) 90 Kmph
(D) 18 Kmph
(E) 19 Kmph
Rationale: Length = Speed * time
Speed = L/T
S = 500/20
S = 25 M/Sec
Speed= 25*18/5 (To convert M/Sec in to Kmph multiply by 18/5)
Speed = 90 Kmph
Answer: C
Answer: (C) 90 Kmph
Question: Two spherical balls lie on the ground touching. If one of the balls has a radius of 3 cm, and the point of contact is 5 cm above the ground, what is the radius of the other ball?
(A) 3 cm
(B) 9 cm
(C) 12 cm
(D) 15 cm
(E) none of the these
Rationale: similar triangle properties..
2/r+3 = 3/r-3
giving r = 15.
Answer: D
Answer: (D) 15 cm
Question: Three workers have a productivity ratio of 1 to 3 to 5. 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?
(A) 25 to 3
(B) 6 to 1
(C) 5 to 1
(D) 1 to 6
(E) 1 to 5
Rationale: The fastest worker who does 5 units of job worked for all 10 hours, so he did 5*10=50 units of job;
The slowest worker who does 1 unit of job worked for only 4+2=6 hours (first 4 hours and last 2 hours), so he did 1*6=6 units of job;
The ratio thus is 50 to 6, or 25 to 3.
Answer: A
Answer: (A) 25 to 3
Question: The sum and the product of two numbers are 24 and 23 respectively, the difference of the number is?
(A) 1
(B) 6
(C) 7
(D) 8
(E) 22
Rationale: Explanation:
x + y = 24
xy = 23
(x- y)2 = (x + y)2 - 4xy
(x- y)2 = 576- 92 => (x - y) = 22
Answer: E
Answer: (E) 22
Question: Of the 700 employees of Company X, 70 percent have been with the company for at least ten years. If y of theselong-termmembers were to retire and no other employee changes were to occur, what value of y would reduce the percent oflong-termemployees in the company to 60 percent ?
(A) 200
(B) 160
(C) 112
(D) 80
(E) 25
Rationale: Original (Long-Term is 70%)
Total = 700
Long-Term = .7(700) = 490
New (Long-Term is 60%)
New Total = 800 - y
New Long-Term =490 - y
490 - y = .6 (800 - y)
y = 25
Answer: E
Answer: (E) 25
Question: In a certain store, the profit is 1150% of the cost. If the cost increases by 25% but the selling price remains constant, approximately what percentage of the selling price is the profit?
(A) 30%
(B) 70%
(C) 900%
(D) 250%
(E) 120%
Rationale: Let C.P. = Rs. 100. Then, profit = Rs. 1150, S.P. = Rs. 1250
New C.P. = 125% of Rs. 100 = Rs. 125.
New S.P. = Rs. 1250
Profit = 1250 - 125 = Rs. 1125
Required percentage = 1125/1250 * 100 = 900%
ANSWER:C
Answer: (C) 900%
Question: At a certain food stand, the price of each apple is 40¢ and the price of each orange is 60¢. Mary selects a total of 10 apples and oranges from the food stand, and the average (arithmetic mean) price of the 10 pieces of fruit is 54¢. How many oranges must Mary put back so that the average price of the pieces of fruit that she keeps is 45¢?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: If the average price is 54, then Mary has 7 oranges and 3 apples (a ratio of 7:3).
For the average price to be 45, the ratio should be 1:3.
Mary must put back 6 oranges.
The answer is E.
Answer: (E) 6
Question: Two pipes can fill a tank in 15 minutes and 12 minutes. The outlet pipe can empty the tank in 20 minutes. If all the pipes are opened when, the tank is empty, then in how many minutes will it take to fill the tank?
(A) 12
(B) 13
(C) 11
(D) 10
(E) 9
Rationale: Part of tank filled by all three pipes in one minute =
1/15 + 1/12 – 1/20 = (8+10-6) / 120
= 18-6 / 120
= 1/10
So, the tank becomes full in 10 minutes.
ANSWER:D
Answer: (D) 10
Question: Jake can dig a well in 16 days. Paul can dig the same well in 24 days. Jake, Paul and Hari together dig the well in 8 days. Hari alone can dig the well in
(A) 48
(B) 99
(C) 22
(D) 27
(E) 92
Rationale: Explanation: Simple one. Let the total work to be done is 48 meters. Now Jake can dig 3 mts, Paul can dig 2 mts a day. Now all of them combined dug in 8 days so per day they dug 48/8 = 6 mts. So Of these 8 mts, Hari capacity is 1 mt.
So he takes 48 /1 = 48 days to complete the digging job.
Answer:A
Answer: (A) 48
Question: A train 150 m long pass a telegraph pole in 5 seconds. Find the speed of the train
(A) 66 km/hr
(B) 108 km/hr
(C) 72 km/hr
(D) 79.2 km/hr
(E) None
Rationale: Sol.
Speed = [150/5] m/sec = [30 * 18/5] km/hr = 108 km/hr.
Answer B
Answer: (B) 108 km/hr
Question: A ship sails 4 degrees north, then 15 S. then 17 N. then 19 S. and has finally 11 degrees of south latitude. What was her latitude at starting ?
(A) 0
(B) 1
(C) 2
(D) 3
(E) None of these
Rationale: Let x = the latitude sought.
Then marking the northings +, and the southings -;
By the statement x + 4 - 15 + 17 - 19 = -11
And x =2.
Answer C
Answer: (C) 2
Question: A certain number of men can do a work in 65 days working 6 hours a day. If the number of men are decreased by one-fourth, then for how many hours per day should they work in order to complete the work in 40 days?
(A) 33
(B) 13
(C) 88
(D) 77
(E) 12
Rationale: Let the number of men initially be x. we have M1 D1 H1= M2 D2 H2
So, x * 65 * 6 = (3x)/4 * 40 * h2
=> h2 = (65 * 6 * 4)/(3 * 40) = 13.
Answer: B
Answer: (B) 13
Question: The sale price sarees listed for Rs.400 after successive discount is 10% and 8% is?
(A) 338
(B) 277
(C) 331.2
(D) 882
(E) 212
Rationale: 400*(90/100)*(92/100) = 331.2
Answer: C
Answer: (C) 331.2
Question: The average age of a class of 36 students is 16 yrs. if the teacher's age is also included, the average increases by one year. Find the age of the teacher
(A) 45 Years
(B) 53 Years
(C) 49 Years
(D) 52 Years
(E) 54 Years
Rationale: Total age of students is 36X16 = 576 Years Total age inclusive of teacher = 37X (16+1) = 629 So, Teacher's age i629-576= 53Yrs There is a shortcut for these type of problems Teacher's age is 16+(36X1) =53 YearsAnswer : B
Answer: (B) 53 Years
Question: An analyst will recommend a combination of 3 industrial stocks, 2 transportation stocks, and 2 utility stocks. If the analyst can choose from 5 industrial stocks, 3 transportation stocks, and 4 utility stocks, how many different combinations of 7 stocks are possible?
--
(A) 180
(B) 19
(C) 60
(D) 12
(E) 720
Rationale: 5C3 * 4C2 * 3C2 = 10*6*3 = 180.
Answer: A.
Answer: (A) 180
Question: In the first 10 overs of a cricket game, the run rate was only 3.2. What should be the run rate in the remaining 30 overs to reach the target of 282 runs?
(A) 6.25
(B) 5.5
(C) 7.4
(D) 8.3
(E) 6.2
Rationale: Explanation:
Runs scored in the first 10 overs = 10 × 3.2 = 32
Total runs = 282
Remaining runs to be scored = 282 - 32 = 250
Remaining overs = 30
Run rate needed = 250/30=8.3
Answer: Option D
Answer: (D) 8.3
Question: There is a 30% increase in the price of an article in the first year, a 20% decrease in the second year and a 10% increase in the next year. If the final price of the article is Rs.3432 , then what was the price of the article initially?
(A) Rs.2000
(B) Rs.4000
(C) Rs.3000
(D) Rs.5000
(E) Rs.6000
Rationale: Let the price of the article, four years age be Rs. 100 in the 1st year, price of the article = 100 + 30 = Rs. 130. In the 2nd year, price = 130 - 20% of 130 = 130 - 26 = Rs. 104.
In the 3rd year, price = 104 + 10% of 104 = 104 + 10.4 = Rs. 114.40.
But present price of the article is Rs. 3432
for 114.4 ---> 100 ; 2288 ---> ?
Required price = (3432 * 100)/114.4 = 30 * 100 = Rs.3000.
Answer:C
Answer: (C) Rs.3000
Question: If 4% more is gained by selling an article for Rs. 350 than by selling it for Rs. 340, the cost of the article is
(A) 250
(B) 231
(C) 200
(D) 288
(E) 111
Rationale: Explanation:
Let C.P. be Rs. x.
Then, 4% of x = 350 - 340 = 10
x/25 = 10 => x = 250
Answer: A
Answer: (A) 250
Question: Calculate Tony''s average score in an exam if he obtained the following marks 53, 87, 89, 80 and 78 out of 100 in different subjects.
(A) 73.4
(B) 74.4
(C) 75.4
(D) 76.4
(E) 77.4
Rationale: Explanation:
(53+87+89+80+78)/5=77.4
Answer: Option E
Answer: (E) 77.4
Question: In a police selections, the weight of Arun is marked as 64 kg instead of 48 kg. Find the percentage of correction required.
(A) 30%
(B) 25%
(C) 24%
(D) 29%
(E) 34%
Rationale: Explanation :
% correction = (64-48)/64 X 100 = 25%
Answer : B
Answer: (B) 25%
Question: Express a speed of 36 kmph in meters per second?
(A) 10
(B) 88
(C) 66
(D) 81
(E) 121
Rationale: 36 * 5/18 = 10 mps
Answer: A
Answer: (A) 10
Question: If 375*s is a perfect square then s can be which of the following numbers?
(A) 21
(B) 35
(C) 54
(D) 15
(E) 150
Rationale: My solution:
For a number to be a perfect square all the prime factors must be in pairs. So,
Prime factors of 375 are 5*5 *5 * 3
1) 21 = 3 * 7
2) 35 = 5 * 7
3) 54 = 2 * 3 * 3 * 3
4) 15 = 3 * 5
5) 150 = 2 * 3 * 5 * 5
So only answer choice D completes the pairing of 3, 5 . It adds a3, a5, and a7to the prime factors of 375 (3*5*5*5) and makes it a perfect square.D
Answer: (D) 15
Question: What is the are of an equilateral triangle of side 2 cm?
(A) √3
(B) 64√9
(C) 64√4
(D) 64√3
(E) 64√2
Rationale: Area of an equilateral triangle = √3/4 S2
If S = 2, Area of triangle = √3/4 * 2 * 2 = √3 cm2;
Answer: A
Answer: (A) √3
Question: The average age of 20 students of a class is 20 years. Out of these, the average age of 5 students is 14 years and that of the other 9 students is 16 years, The age of the 20th student is
(A) 186
(B) 120
(C) 152
(D) 220
(E) 220
Rationale: Explanation:
Age of the 20th student = [20 * 20 - (14 * 5 + 16 * 9)] = (400-214) = 186 years.
Answer: A
Answer: (A) 186
Question: The probability that A can solve the problem is 2/3 and B can solve it is 3/4. If both of them attemp the problem, then what is the probability that the problem get solved ?
(A) 9/12
(B) 10/12
(C) 11/12
(D) 1
(E) 2
Rationale: Explanation :
The event is defined as:
A solves the problem AND B does not solve the problem
OR
A doesn't solve the problem AND B solves the problem
OR
A solves the problem AND B solves the problem
Numerically this is equivalent to:
(2/3) x (1/4) + (1/3) x (3/4) + (2/3) x (3/4) = 11/12
Answer : C
Answer: (C) 11/12
Question: The sum of four consecutive even numbers is 84. What would be the smallest number?
(A) 33
(B) 88
(C) 70
(D) 123
(E) 18
Rationale: Let the four consecutive even numbers be 2(x - 2), 2(x - 1), 2x, 2(x + 1)
Their sum = 8x - 4 = 84 => x =11
Smallest number is: 2(x - 2) = 18.
Answer: E
Answer: (E) 18
Question: A man spend 1/5 of his salary on food , 1/10 of his salary on house rent and 3/5 salary on clothes. he still has $15000 left with him. find salary..
(A) $150000
(B) $18000
(C) $180000
(D) $1800
(E) None
Rationale: [1/(x1 / y1 + x2/y2 + x3/y3)] * Total amount= Balance amount
[1-(1/5 + 1/10 + 3/5)} * total salary= $15000, = [1-9/10] * Total salary = $15000, Total salary = $15000*10 = $150000, correct answer (A)
Answer: (A) $150000
Question: By selling 99 pens, a trader gains the cost of 33 pens. Find his gain percentage?
(A) 33 1/3%
(B) 68 1/3%
(C) 28 1/3%
(D) 18 1/3%
(E) 11 1/3%
Rationale: Explanation:
Let the CP of each pen be Rs. 1.
CP of 99 pens = Rs. 99
Profit = Cost of 33 pens = Rs. 33
Profit% = 33/99 * 100 = 33 1/3%
Answer: A
Answer: (A) 33 1/3%
Question: A thief steals at a car at 3.30 p.m. and drives it at 60 km/hr. The theft is discovered at 3 p.m. and the owner sets off in another car at 75 km/hr. When will he overtake the thief?
(A) 1 p.m
(B) 3 p.m
(C) 4 p.m
(D) 5 p.m
(E) 6 p.m
Rationale: E
6 p.m
Suppose the thief is overtaken x hrs after 3.30 p.m.
Then, distance covered by the owner in (x - 1/2) hrs.
60x = 75(x - 1/2) => x = 5/2 hrs.
So, the thief is overtaken at 6 p.m.
Answer: (E) 6 p.m