mathewhe/aqua_rat huggingface dataset:
Question: Rahul went to a shop and bought things worth Rs. 23, out of which 30 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?
(A) 17.7
(B) 20
(C) 22
(D) 21.4
(E) 21.5
Rationale: Total cost of the items he purchased = Rs.23
Given that out of this Rs.23, 30 Paise is given as tax
=> Total tax incurred = 30 Paise = Rs.30/100
Let the cost of the tax free items = x
Given that tax rate = 6%
∴ (23−30/100−x)6/100 = 30/100
⇒ 6(23 −0.3 −x) = 30
⇒ (23 − 0.3 − x) = 5
⇒ x = 23 − 0.3 − 5 = 17.7
A
Answer: (A) 17.7
Question: Find the SI on Rs.2400 for 8yrs 4 months at 6% per annum rate of interest ?
(A) Rs 1000
(B) Rs 1200
(C) Rs 1300
(D) Rs 1400
(E) Rs 1500
Rationale: Time period is 8 years 4 months = 8
4
12
years =
25
3
years
Simple Interest =
PTR
100
= 2400 x
25
3
x
6
100
=Rs 1200
B
Answer: (B) Rs 1200
Question: The number of people who purchased book A is twice the number of people who purchased book B. The number of people who purchased both books A and B is 500, which is twice the number of people who purchased only book B. What is the number of people B who purchased only book A?
(A) 250
(B) 500
(C) 750
(D) 1000
(E) 1500
Rationale: This is best solved using overlapping sets or a Venn Diagram. We know that A = 2B, and that 500 people purchased both A and B. Further, those purchasing both was double those purchasing B only. This gives us 250 people purchasing B only. With the 500 that pruchased both, we have a total of 750 that purchased B and this is 1/2 of those that purchased A. So, 1500 purchased A. Less the 500 that purchased both, B=1000 purchased A only. (This is much simpler to solve using the Venn diagram).
Correct answer is D. 1000
Answer: (D) 1000
Question: 65 bags of nuts are to be divided among 13 students. Each bag contains 15 nuts. How many
nuts will each student receive?
(A) 75
(B) 65
(C) 43
(D) 52
(E) 78
Rationale: 65 ÷ 13 = 5 bags per student
5 x 15 = 75 nuts per student
correct answer A
Answer: (A) 75
Question: An order was placed for the supply of a carpet whose breadth was 6 m and length was 1.44 times the breadth. What be the cost of a carpet whose length and breadth are 40% more and 25% more respectively than the first carpet. Given that the ratio of carpet is Rs. 45 per sq m?
(A) 4082.48
(B) 4082.46
(C) 4082.45
(D) 4082.4
(E) 4082.41
Rationale: Length of the first carpet = (1.44)(6) = 8.64 cm
Area of the second carpet = 8.64(1 + 40/100) 6 (1 + 25/100)
= 51.84(1.4)(5/4) sq m = (12.96)(7) sq m
Cost of the second carpet = (45)(12.96 * 7) = 315 (13 - 0.04) = 4095 - 12.6 = Rs. 4082.40
Answer:D
Answer: (D) 4082.4
Question: Jim is twice as old as Stephanie, who, four years ago, was three times as old as Kate. If, five years from now, the sum W of their ages will be 51, how old is Stephanie ?
(A) 6
(B) 10
(C) 14
(D) 20
(E) 24
Rationale: 1) take C (14y.o.), so mean that S=14, J=28, their sum itself is 42+10 years from now is 52, it is over the 51,
so eliminate C,D,E
2) take B (10y.o.),W= meaning S=10,J=20, so 20+10+10=40 and for K=10-4/3=2+9=11, finally 40+11=51. It is correct
B
Answer: (B) 10
Question: If a 5-digit numerical with local value of digits 3 is 300, 4 is 40000, 5 is 50, 6 is 6 and 7 is 7000, is multiplied by 7 then the difference between local value of 4 in the new numerical and the face value of 3 is
(A) 397
(B) 2997
(C) 49997
(D) 697
(E) 497
Rationale: According to the given local values of the 5-digit number the number is 47356
Multiplying it with 7,
47356 x 7 = 331492
(Local value of 4 in 331492) - (Face value of 3) = 400 - 3 = 397
A
Answer: (A) 397
Question: A candidate got 35% of the votes polled and he lost to his rival by 2250 votes. How many votes were cast?
(A) 7500
(B) 2888
(C) 2666
(D) 2999
(E) 2661
Rationale: 35%-----------L
65%-----------W
------------------
30%----------2250
100%---------? => 7500
Answer:A
Answer: (A) 7500
Question: 6 friends are living in 6 different flats of an apartment. Each of them was allotted a parking spot to park their cars in the ground floor. But they used to park their cars randomly in any of the 6 parking spots. In how many ways can they park their cars so that exactly 4 people park their cars in the spots allotted to them?
(A) 15
(B) 21
(C) 35
(D) 42
(E) 49
Rationale: 6C4 = 15
The remaining 2 people in each case will be parked in each other's parking spots.
The answer is A.
Answer: (A) 15
Question: Which of the following is not the square of an integer?
(A) 275625
(B) 385641
(C) 190096
(D) 432562
(E) 522729
Rationale: The square of an integer (n^2) can have only the following units digit:
0, if the units digit of n is 0;
1, if the units digit of n is 1 or 9;
4, if the units digit of n is 2 or 8.
5, if the units digit of n is 5;
6, if the units digit of n is 6 or 4;
9, if the units digit of n is 3 or 7.
The square of an integer cannot have the units digit of 2, 3, 7, or 8.
The answer is D.
Answer: (D) 432562
Question: Rary spent 2⁄5 of her money on new clothes and then deposited 1⁄2 of what remained into her savings account. If she then had $21 left, how much did she have at the start?
(A) $30
(B) $35
(C) $70
(D) $105
(E) $210
Rationale: Rary spent 2⁄5 of her money on new clothes but if you see 21 is half of 3/5 money so 210 is too huge to be correct..
solution..
let the money be x..
2/5 is used...
1/2 of remaining 3/5 is put in savings account and remaining half is 21..
so 1/2 * 3/5 *x=21..
x=21*2*5/3=70..
C
Answer: (C) $70
Question: three men invested sum. and their ratio is 5:7:6. profit is 5400.then b's share
(A) 2000
(B) 2100
(C) 2200
(D) 2300
(E) 2400
Rationale: b's share =7/18*5400=2100
ANSWER:B
Answer: (B) 2100
Question: One woman and one man can build a wall together in four hours, but the woman would need the help of two girls in order to complete the same job in the same amount of time. If one man and one girl worked together, it would take them eight hours to build the wall. Assuming that rates for men, women and girls remain constant, how many hours would it take one woman, one man, and one girl, working together, to build the wall?
(A) 5/7
(B) 1
(C) 10/7
(D) 12/7
(E) 24/7
Rationale: Solution:Let work done by man, women and girl per hour be m,w,g respectively.
Then, m+w = 1/4-->(1) , w + 2g = 1/4-->(2) and m + g =1/8-->(3).
No. of hours it would take forone woman, one man, and one girl, working together, to build the wall,n = 1/m+w+g
From (1) and (2), m=2g and from (3) g=1/24,m=1/12 and w=1/6.
So, n = 1/(7/24) = 24/7
Option, E
Answer: (E) 24/7
Question: The ratio between the radii of two spheres is 1:3. Find the ratio between their volumes?
(A) 1:28
(B) 1:27
(C) 1:18
(D) 1:21
(E) 1:12
Rationale: r1 : r2 = 1:3
r13 : r23 = 1:27
Answer: B
Answer: (B) 1:27
Question: The telephone company wants to add an area code composed of 2 letters to every phone number. In order to do so, the company chose a special sign language containing 424 different signs. If the company used 422 of the signs fully and two remained unused, how many additional area codes can be created if the company uses all 424 signs?
(A) 246
(B) 248
(C) 1692
(D) 15,128
(E) 30,256
Rationale: # of 2-letter codes possible from 424 different signs = 424*424.
# of 2-letter codes possible from 422 different signs = 422*422.
The difference = 424^2 - 422^2 = (424 - 422)(424 + 422) = 1692.
Answer: C.
Answer: (C) 1692
Question: A boy has nine trousers and 12 shirts. In how many different ways can he select a trouser and a shirt?
(A) 299
(B) 278
(C) 289
(D) 108
(E) 271
Rationale: The boy can select one trouser in nine ways.
The boy can select one shirt in 12 ways.
The number of ways in which he can select one trouser and one shirt is 9 * 12
= 108 ways.
Answer: D
Answer: (D) 108
Question: A, B and C are partners in a business. Their capitals are respectively, Rs.5000, Rs.6000 and Rs.4000. A gets 30% of the total profit for managing the business. The remaining profit is divided among three in the ratio of their capitals. In the end of the year, the profit of A is Rs.200 more than the sum of the profits of B and C. Find the total profit.
(A) 3008
(B) 3006
(C) 3004
(D) 3000
(E) 3001
Rationale: A:B:C = 5:6:4
Let the total profit = 100 - 30 = 70
5/15 * 70 = 70/3
A share = 70/3 + 30 = 160/3
B + C share = 100 - 160/3 = 140/3
A-(B+C) = 160/3 - 140/3 = 20/3
20/3 ---- 200
100 ---- ? => 3000
Answer: D
Answer: (D) 3000
Question: Three pipes of same capacity can fill a tank in 8 hours. If there are only two pipes of same capacity, the tank can be filled in.
(A) 22
(B) 12
(C) 88
(D) 99
(E) 77
Rationale: The part of the tank filled by three pipes in one hour = 1/8
=> The part of the tank filled by two pipes in 1 hour = 2/3 * 1/8 = 1/12.
The tank can be filled in 12 hours.
Answer:B
Answer: (B) 12
Question: Look at this series: 201, 202, 204, 207, ... What number should come next?
(A) 211
(B) 205
(C) 224
(D) 267
(E) 269
Rationale: In this addition series, 1 is added to the first number; 2 is added to the second number; 3 is added to the third number; 4 is added to the fourth number; and go on.
ANSWER A
Answer: (A) 211
Question: A bag contains 3 blue and 5 white marbles. One by one, marbles are drawn out randomly until only two are left in the bag. What is the probability W that out of the two, one is white and one is blue?
(A) 15/56
(B) 41/56
(C) 13/28
(D) 15/28
(E) 5/14
Rationale: The required probability W= probability of choosing 6 balls out of the total 8 in such a way that we remove 4 out of 5 white and 2 out of 3 blue balls.
Ways to select 6 out of total 8 = 8C6
Ways to select 4 out of 5 white balls = 5C4
Ways to select 2 out of 3 blue balls = 3C2
Thus the required probability = (5C4*3C2)/8C6 = 15/28.
D is thus the correct answer.
Answer: (D) 15/28
Question: The second angle of a triangle is double the first(110). The third angle is 40 less than
the first(15). Find the first angle.
(A) 35
(B) 45
(C) 55
(D) 65
(E) 75
Rationale: First x With nothing given about the firstwemake that x
Second 2x The second is double the first,
Third x−40 The third is 40 less than the first
F +S +T =180 All three angles add to 180
(x)+(2x)+(x−40)=180 Replace F , S, and T with the labeled values.
x+2x+x−40=180 Here the parenthesis are not needed.
4x−40=180 Combine like terms, x+2x+x
+40 +40 Add 40 to both sides
4x=220 The variable ismultiplied by 4
4 4 Divide both sides by 4
x=55 Our solution for x
First 55 Replace xwith 55 in the original list of angles
Second 2(55)=110 Our angles are 55, 110, and 15
Third (55)−40=15
correct answer C
Answer: (C) 55
Question: If six persons sit in a row, then the probability that three particular persons are always together is
(A) 1/5
(B) 1/8
(C) 1/5
(D) 1/3
(E) 1/1
Rationale: Six persons can be arranged in a row in 6! ways. Treat the three persons to sit together as one unit then there four persons and they can be arranged in 4! ways. Again three persons can be arranged among them selves in 3! ways. Favourable outcomes = 3!4! Required probability = 3!4!/6! = 1/5.Answer: C
Answer: (C) 1/5
Question: In how many ways the letters of the word MOUSE be arranged?
(A) 140
(B) 150
(C) 160
(D) 120
(E) 170
Rationale: Total ways of arranging the letters = 5! = 120 ways.
D)
Answer: (D) 120
Question: find the number, difference between number and its 3/5 is 58.
(A) 140
(B) 143
(C) 144
(D) 145
(E) 146
Rationale: Explanation:
Let the number = x,
Then, x-(3/5)x = 58,
=> (2/5)x = 58 => 2x = 58*5,
=> x = 145
Answer: Option D
Answer: (D) 145
Question: Two trains started at the same time, one from A to B and the other from B to A . If they arrived at B and A respectively 9 hours and 16 hours after they passed each other the ratio of the speeds of the two trains was
(A) 2:1
(B) 3:2
(C) 4:3
(D) 5:4
(E) 1:2
Rationale: Explanation:
Note : If two trains (or bodies) start at the same time from points A and B towards each other and after crossing they take a and b sec in reaching B and A respectively, then: (A's speed) : (B's speed) = (b : a)
Therefore, Ratio of the speeds of two trains = = 4 : 3. Answer: C
Answer: (C) 4:3
Question: Excluding stoppages, the speed of a bus is 60 kmph and including stoppages, it is 50 kmph. For how many minutes does the bus stop per hour?
(A) 10 min
(B) 15 min
(C) 12 min
(D) 8 min
(E) 16 min
Rationale: Due to stoppages, it covers 10 km less.
Time taken to cover 10 km = (10/60 x 60) min = 10 min
Answer : A
Answer: (A) 10 min
Question: The sum of the first 70 positive even integers is 4,970. What is the sum of the first 70 odd integers?
(A) 4500
(B) 4600
(C) 4300
(D) 4900
(E) 5000
Rationale: Sum of first n even numbers = n(n+1) =4970
Sum of first n odd numbers = n^2 = 70*70 = 4900 (here n=70)
Answer : D
Answer: (D) 4900
Question: A certain clock marks every hour by striking a number of times equal to the hour, and the time require for a stroke is exactly equal to the time interval between strokes. At 6:00 the time lapse between the beginning of the first stoke and the end of the last stroke is 22 seconds. At 11:00, how many seconds elapse between the beginning of the first stroke and the end of the last stroke?
(A) 34
(B) 38
(C) 36
(D) 40
(E) 42
Rationale: at 6'o clock, there would be 6 strikes. First strike, then a short interval, the second strike, then a short interval and so on till the 6th strike. So there would be in all 5 intervals between 6 strikes. Similarly, between 11 strikes, there would be 10 intervals.
According to the question, the time spent in the strike and the interval is same.
At 6'o clock, the 6 strikes and the 5 intervals together take 22 sec so each strike and each interval takes 2 secs.
At 11'o clock, the 11 strikes and 10 intervals will take 2*(11+10) = 42 secs
E
Answer: (E) 42
Question: In how many different ways can the letters of the word 'MATHEMATICS' be arranged so that the vowels always come together ?
(A) 10080
(B) 4989600
(C) 120960
(D) 250035
(E) None of these
Rationale: In the word 'MATHEMATICS' we treat the vowels AEAI as one letter.
Thus, we have MTHMTCS (AEAI).
Now, we have to arrange 8 letters, out of which M occurs twice, T occurs twice and the rest are different.
Number of ways of arranging these letters = 8!/(2!)(2!) = 10080.
Now, AEAI has 4 Letters in which A occurs 2 times and the rest are different.
Number of ways of arranging these letters = 4!/2! = 12.
∴ Required number of words = (10080 * 12) = 120960.
Answer is C
Answer: (C) 120960
Question: When a certain tree was first planted, it was 4 feet tall, and the height of the tree increased by a constant amount each year for the next 6 years. At the end of the 6th year, the tree was 1/6 taller than it was at the end of the 4th year. By how many feet did the height of the tree increase each year?
(A) 3/10
(B) 2/5
(C) 1/2
(D) 2/3
(E) 6/5
Rationale: Say, the tree grows by x feet every year.
Then, 4 + 6x = (1+1/6)(4+4x)
or, x = 1/2
Answer C
Answer: (C) 1/2
Question: Suppose you work for a manufacturing plant that pays you $12.50 an hour plus $0.16 for each widget you make. How many widgets must you produce in a 40 hour week to earn $620 (before payroll deductions)?
(A) 670
(B) 710
(C) 750
(D) 790
(E) 830
Rationale: total pay = 40*$12.50 + $0.16*x = 620
x = 120 / 0.16 = 750
The answer is C.
Answer: (C) 750
Question: The three competitors in a race have to be randomly chosen from a group of four men and five women. How many different such trios contain at least one woman?
(A) 50
(B) 60
(C) 70
(D) 80
(E) 90
Rationale: The total number of ways to choose three runners 9C3 = 84
The number of trios with only males is 4C3 = 4
The number of trios which include at least one woman is 80.
The answer is D.
Answer: (D) 80
Question: Find the face value of 5 in 5432100
(A) 50
(B) 5
(C) 50000
(D) 500000
(E) 5000000
Rationale: Face value is the value of digit itself
face value of 5 = 5
Answer : B
Answer: (B) 5
Question: An analyst will recommend a combination of 2 industrial stocks, 3 transportation stocks, and 3 utility stocks. If the analyst can choose from 6 industrial stocks, 3 transportation stocks, and 4 utility stocks, how many different combinations of 9 stocks are possible?
(A) 12
(B) 19
(C) 60
(D) 180
(E) 720
Rationale: 6C2 * 3C3 * 4C3 = 15*1*4 = 60.
Answer: C
Answer: (C) 60
Question: In a certain encryption pattern, HARD is coded as 1357 and SOFT is coded as 2468, What will 21448 stand for?
(A) SHAFT
(B) SHORT
(C) SHOOT
(D) SHART
(E) SHAOT
Rationale: on the behlaf of order like
h =1
a=3
r=5 and so on.
so 21448 is SHOOT
ANSWER:C
Answer: (C) SHOOT
Question: if 5x*x+14*x+k=0 having two reciprocal roots find the value of k.
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: Product of reciprocal roots =1
Product of roots of quadratic eqn ax^2+bx+c = 0 is c/a.
Hence k/5 =1
k=5
ANSWER:E
Answer: (E) 5
Question: If,
1 * 3 * 5 = 16
3 * 5 * 7 = 38
Then find,
5 * 7 * 10 =?
(A) 65
(B) 68
(C) 72
(D) 80
(E) 82
Rationale: (10 * 7) + 5 = 82
E
Answer: (E) 82
Question: A palindrome is a word or a number that reads the same forward and backward. For example, 2442 and 111 are palindromes. If 5-digit palindromes are formed using one or more of the digits 1, 2, 3, and 4, how many palindromes are possible?
(A) 32
(B) 64
(C) 96
(D) 128
(E) 256
Rationale: There are 4 choices for each of the first three digits.
The number of possible palindromes is 4^3=64.
The answer is B.
Answer: (B) 64
Question: Three pipes of same capacity can fill a tank in 8 hours. If there are only two pipes of same capacity, the tank can be filled in.
(A) 17
(B) 13
(C) 15
(D) 16
(E) 12
Rationale: he part of the tank filled by three pipes in one hour = 1/8
=> The part of the tank filled by two pipes in 1 hour = 2/3 * 1/8 = 1/12.
The tank can be filled in 12 hours.
ANSWER E
Answer: (E) 12
Question: f the LCM of two integers a, b (where b> a and a>1) is a*b, then which of the following can not be true?
(A) Both a and b can be Prime Numbers.
(B) Both a and b can be consecutive integers.
(C) All Prime factors of a must be Prime factors of b.
(D) a and b do not share any Prime factors.
(E) a and b do not have a common factor
Rationale: Say a = 2; b = 3; only option C contradicts
All Prime factors of a must be Prime factors of b
Answer = C
Answer: (C) All Prime factors of a must be Prime factors of b.
Question: A rectangular grass field is 75 m * 55 m, it has a path of 2.5 m wide all round it on the outside. Find the area of the path and the cost of constructing it at Rs.2 per sq m?
(A) 1350
(B) 1357
(C) 1328
(D) 1329
(E) 1829
Rationale: Area = (l + b +2d) 2d
= (75 + 55 +2.5 * 2) 2*2.5 => 675
675 * 2 = Rs.1350
Answer:A
Answer: (A) 1350
Question: A cistern can be filled by a tap in 4 hours while it can be emptied by another tap in 8 hours. If both the taps are opened simultaneously, then after how much time will the cistern get filled?
(A) 2.9 hrs
(B) 8.9 hrs
(C) 2.9 hrs
(D) 7.2 hrs
(E) 8 hrs
Rationale: Net part filled in 1 hour = (1/4 - 1/8)
= 1/8
The cistern will be filled in 8 hrs i.e., 8 hrs.
Answer:E
Answer: (E) 8 hrs
Question: Which of the following numbers doesn't belong to the group?
(A) 14
(B) 16
(C) 20
(D) 28
(E) 36
Rationale: All of the numbers are multiples of 2. But only one is not a multiple of 4: 14.
Answer: 14
Answer: (A) 14
Question: In a certain game, a large container is filled with red, yellow, green, and blue beads worth, respectively, 7, 5, 3, and 2 points each. A number of beads are then removed from the container. If the product of the point values of the removed beads is 10,290,000, how many red beads were removed?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: 10,290,000
= 2^4 * 5^4 * 1029
= 2^4 * 3 * 5^4 * 343
= 2^4 * 3 * 5^4 * 7^3
The answer is B.
Answer: (B) 3
Question: By selling an article at Rs.700, a shopkeeper makes a profit of 25%. At what price should he sell the article so as to make a loss of 25%?
(A) s.600
(B) s.480
(C) s.500
(D) s.450
(E) s.420
Rationale: SP = 700
Profit = 25%
CP = (SP)*[100/(100+P)]
= 700 * [100/125]
= 560
Loss = 25% = 25% of 560 = Rs.140
SP = CP - Loss = 560 - 140 = Rs.420
ANSWER:E
Answer: (E) s.420
Question: If the area of circle is 706 sq cm then its circumference?
(A) 21
(B) 88
(C) 66
(D) 94
(E) 90
Rationale: 22/7 r2 = 706 => r = 15
2 * 22/7 * 15 = 94
Answer: D
Answer: (D) 94
Question: Two trains of equal length are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. The faster train catches and completely passes the slower train in 54 seconds. What is the length of each train (in meters)?
(A) 45
(B) 55
(C) 65
(D) 75
(E) 85
Rationale: The relative speed = 46 - 36 = 10 km/hr = 10 * 5/18 = 25/9 m/s
In 54 seconds, the relative difference in distance traveled is 54 * 25/9 = 150 meters
This distance is twice the length of each train.
The length of each train is 150/2 = 75 meters
The answer is D.
Answer: (D) 75
Question: Which of the following fractions is greater than 3/4 and less than 5/6?
1. 3/4 2. 5/6 3. 1/2 4. 2/3 5. 4/5 6. 9/10
(A) 4/5
(B) 1/2
(C) 9/10
(D) 5/6
(E) 2/3
Rationale: 3/4 = 0.75, 5/6 = 0.833, 1/2= 0.5, 2/3= 0.66, 4/5= 0.8, 9/10= 0.9.
Clearly, 0.8 lies between 0.75 and 0.833.
Therefore, 4/5 lies between 3/4 and 5/6.
Answer is A.
Answer: (A) 4/5
Question: Find the sum of prime numbers lying between 58 and 72?
(A) 198
(B) 258
(C) 252
(D) 272
(E) None
Rationale: Solution
Required sum	= 59 + 61 + 67 + 71)
= 258.
Answer B
Answer: (B) 258
Question: If a and b are different positive integers and a + b = ab(a + b), then which of the following must be true?
I. a = 1
II. b = 1
III. a < b
(A) I only
(B) II only
(C) III only
(D) I and II
(E) I and III
Rationale: Number picking might not be the best way to solve MUST BE TRUE questions.
The question asks which of the followingMUSTbe true, or which of the following isALWAYStrue no matter what set of numbers you choose. For such kind of questionsif you can prove that a statement is NOT truefor one particular set of numbers, it will mean that this statement is not always true and hence not a correct answer.
So the set you chose just proves that II is not always true and hence it's not a part of a correct choice. As for I and III: they might be true for this particular set of numbers but not true for another set, so you can not say that I and III are always true just based on one set of numbers (it just happens to be that I and III are always true).
As forCOULD BE TRUEquestions:
The questions asking which of the followingCOULDbe true are different:if you can prove that a statement is truefor one particular set of numbers, it will mean that this statement could be true and hence is a correct answer.
A
Answer: (A) I only
Question: A car travels uphill at 30 km/hr and downhill at 50 km/hr. It goes 100 km uphill and 50 km downhill. Find the average speed of the car?
(A) 32kmph
(B) 33kmph
(C) 34kmph
(D) 35kmph
(E) 36kmph
Rationale: avg speed=total distance/total time.
total distance traveled=100+50=150km;
time taken for uphill journey=100/30=10/3;
time taken for down hill journey=50/50=5/5;
avg speed=150/(10/3+5/5)=35kmph
ANSWER:D
Answer: (D) 35kmph
Question: A circle passes through two adjacent vertices of a square and is tangent to one side of the
square. If the side length of the square is 2, what is the radius of the circle?
(A) 3/2
(B) 4 /3
(C) 5 /4
(D) 6 /5
(E) None of these
Rationale: Let A and B be the vertices through which the circle passes. LetM be the midpoint
of the line segment AB. The center C of the circle is on the line joining M to the midpoint of
the opposite side, which is also on the circle (see diagram below). Let r be the radius of the
circle. The length of the line segment joiningM to C is r-(2r-2) = 2-r as shown below.
Then 12+(2-r)2 = r2 by the Pythagorean Theorem. This gives 1+4-4r+r2 = r2, which
simplifies to 5- r = 0, so r = 5/4
correct answer C
Answer: (C) 5 /4
Question: n is a positive integer and k is the product of all integers from 1 to n inclusive. If k is a multiple of 1800, then what is the smallest possible value of n?
(A) 8
(B) 10
(C) 12
(D) 15
(E) 18
Rationale: 1800=2^3*3^2*5^2
5^2 means that n must be at least 10. That is, We need 5 and 10.
The answer is B.
Answer: (B) 10