mathewhe/aqua_rat huggingface dataset:
Question: The ratio of men to women in the Snyder community choir is 4 to 5. The ratio of men to women in the Leigh community choir is 5 to 6. If the two choirs merged, the ratio of men to women in the combined choir would be 22 to 27. If Snyder has 4 more men and 6 more women than Leigh, how many men's are in the Snyder choir?
(A) 20
(B) 25
(C) 30
(D) 33
(E) 34
Rationale: This question has a number of patterns in it that we can take advantage of. We can also TEST THE ANSWERS (but we can actually eliminate most of the answer choices rather quickly.
We're told that the ratio of the Men to Women in the Snyder choir is 4 to 5, so the number of men MUST be a multiple of 4 and the number of women MUST be a multiple of 4 The question asks how many MEN are in the SNYDER choir, so the answer MUST be a multiple of 4. We can eliminate Answers B,C, D and E (since they're NOT multiples of 4.
Answer A
Answer: (A) 20
Question: From the beginning to the end of 2007, the price of a stock rose 20 percent. In 2008, it dropped 25 percent. In 2009, it rose 25 percent. What percent of the stockâ€™s 2007 starting price was the price of the stock at the end of 2009?
(A) 80
(B) 90
(C) 95
(D) 100
(E) 112.5
Rationale: Assume a value at the beginning of 2007. As this is a % question, assume P=100.
At the end of 2007 it becmae = 1.2*100=120
At the end of 2008 it decreased by 25% = 120*.75 = 90
At the end of 2009 it increased by 25% = 90*1.25 = 112.5
Thus ratio = 112.5/100 = 1.125 (in % terms = 12.5%). Thus E is the correct answer.
Answer: (E) 112.5
Question: Joey is planning to throw a small party and for that he needs to do the following tasks:
I. Decide guest list
II. Send invites
III. Arrange catering
IV. Decide the venue
V. Rent a music system
The tasks can be done in any order as long as the invites are sent after the guest list is decided. In how many ways can Joey do the five tasks listed above?
(A) 24
(B) 48
(C) 60
(D) 120
(E) 240
Rationale: These 5 tasks can be arranged in 5! = 120 ways. In half of them invites are sentafterthe guest list is decided and in half of them before. So, there are total of 120/2 = 60 ways to arrange the task so that the invites are sent after the guest list is decided.
Answer: C.
Answer: (C) 60
Question: Operation # is defined as: a # b = 4a^2 + 4b^2 + 8ab for all non-negative integers. What is the value of (a + b) + 6, when a # b = 100?
(A) 5
(B) 8
(C) 10
(D) 11
(E) 17
Rationale: OFFICIAL SOLUTION:
(B) We know that a # b = 100 and a # b = 4a² + 4b² + 8ab. So
4a² + 4b² + 8ab = 100
We can see that 4a² + 4b² + 8ab is a well-known formula for (2a + 2b)². Therefore
(2a + 2b)² = 100.
(2a + 2b) is non-negative number, since both a and b are non-negative numbers. So we can conclude that 2(a + b) = 10. (a + b) + 6 = 10/2 + 6 = 11.
The correct answer is D.
Answer: (D) 11
Question: In a two-digit, if it is known that its unit’s digit exceeds its ten’s digit by 2 and that the product of the given number and the sum of its digits is equal to 144, then the number is:
(A) 24
(B) 26
(C) 42
(D) 46
(E) None
Rationale: EXPLANATION
Let the ten’s digit be x.
Then, unit’s digit = x + 2.
Number = 10x + (x + 2) = 11x + 2.
Sum of digits = x + (x + 2) = 2x + 2.
(11x + 2)(2x + 2) = 144
22x2 + 26x – 140 = 0
11x2 + 13x – 70 = 0
(x – 2)(11x + 35) = 0
x = 2.
Hence, required number = 11x + 2 = 24.
Answer A
Answer: (A) 24
Question: If a pipe can fill a tank in 6 hours, find the part of tank it fills in one hour.
(A) 1/6
(B) 2/3
(C) 1/2
(D) None of these
(E) Cannot be determined
Rationale: Explanation:
Let the capacity of the tank be C litres.
Time to fill the tank = 6 hours
Hence, in 1 hour C/6 litres gets filled.
Therefore, 1/6th part of the tank gets filled in one hour.
ANSWER A
Answer: (A) 1/6
Question: On the xy co-ordinate plane, point C is (5,-2) and point D is (-1,2). The point on line segment CD that is twice as far from C as from D is:
(A) (1,-1)
(B) (1,1)
(C) (2,0.25)
(D) (3,0.5)
(E) (3,1)
Rationale: We want the point on the line that is twice as far from C as it is from D. We can examine the x and y coordinates separately since they are independent.
*It should be noted that there are two solutions to this problem, one point between C and D, and another point with D in the middle of C and the point. We can quickly look at the answer choices and see that all the points are between C and D, therefore we can search for that point using the following method:
Taking the x-coordinate first, the distance between C and D is |(x-coordinate of C) - (x-coordinate of D)|= |5 - (-1)| = 6
The x-coordinate that is twice as far from C as it is from D (and in between C and D) will be 4 units from C and 2 units from D. So the x coordinate of the point we're looking for is 5-4 = 1, or (-1)+2 = 1.
Now looking at the y-coordinate, we do the same thing. The distance between C and D is |(-2) - 2.5| = 4.5
The y-coordinate that is twice as far from C as it is from D (and in between C and D) will be 3 units from C and 1.5 units from D. So the y coordinate of the point we're looking for is (-2)+3 = 1, or 2.5-1.5 = 1.
So now we have our coordinates of the point on the line that is twice as far from C as it is from D: (3,1)
Answer: D
Answer: (D) (3,0.5)
Question: The table below shows the enrollment in various classes at a certain college.
Class | Number of Students
Biology | 80
Physics | 35
Calculus | 40
Although no student is enrolled in all three classes, 15 are enrolled in both Biology and Physics, 10 are enrolled in both Biology and Calculus, and 12 are enrolled in both Physics and Calculus. How many different students are in the three classes?
(A) 118
(B) 88
(C) 90
(D) 125
(E) 162
Rationale: No. of total students = no of students of biology + no of students of physics but not biology + no of students of calculus but not biology and physics
No. of total students = 80 + (35-15) + (40-10-12) = 80+20+18 = 118
Hence, Answer will be A.
Answer: (A) 118
Question: If the integer n has exactly five positive divisors, including 1 and n, how many positive divisors does n^2 have?
(A) 5
(B) 7
(C) 9
(D) 10
(E) 11
Rationale: take the example of 16...
it has 5 positive divisors (1,2,4,8,16)
Now, take the example of 256...
it has only 9 divisors..
so C is the ans
Answer: (C) 9
Question: A man sitting in a train which is traveling at 56 kmph observes that a goods train, traveling in opposite direction, takes 15 seconds to pass him. If the goods train is 410 m long, find its speed
(A) 52 kmph
(B) 56 kmph
(C) 58 kmph
(D) 42 kmph
(E) 72 kmph
Rationale: Explanation:
Relative speed = 410/15 m / sec = ((410/15)×(18/5)) kmph = 98 kmph.
Speed of goods train = (98 - 56) kmph = 42 kmph
Answer: Option D
Answer: (D) 42 kmph
Question: The bus that travels from St. Louis to Chicago and back comes to St. Louis every 3 hours while the bus that travels from St. Louis to Springfield and back comes to St. Louis every 7 hours. If at 01:00 o'clock both bused arrived at St. Louis, at what time will they meet in St. Louis again?
(A) 16:00.
(B) 18:00.
(C) 20:00.
(D) 22:00.
(E) 24:00.
Rationale: Time taken by bus to travel from St. Louis to Chicago and back comes to St. Louis = 3 hours
Time taken by bus to travel from St. Louis to Springfield and back comes to St. Louis = 7 hours
Time taken by both buses to meet again in St. Louis will be LCM of 3 and 7 = 21
If the buses start at 01:00 o'clock from St. Louis , they will meet again in St. Louis at 22:00 hours
Answer D
Answer: (D) 22:00.
Question: The average marks in mathematics scored by the pupils of a school at the public examination were 39. If four of these pupils who actually scored 25, 12, 15 and 19 marks at the examination had not been sent up, the average marks for the school would have been 44. Find the number of pupils sent up for examination from the school?
(A) 20
(B) 21
(C) 22
(D) 23
(E) 24
Rationale: 39x = 25 + 12 + 15 + 19 + (x – 4)44
39x = 71+44X-176
5X=105
X=21
ANSWER:B
Answer: (B) 21
Question: A shop stores x kg of rice. The first customer buys half this amount plus half a kg of rice. The second customer buys half the remaining amount plus half a kg of rice. Then the third customer also buys half the remaining amount plus half a kg of rice. Thereafter, no rice is left in the shop. Which of the following best describes the value of x?
(A) 2 ≤ x ≤ 6
(B) 5 ≤ x ≤ 8
(C) 9 ≤ x ≤ 12
(D) 11 ≤ x ≤ 14
(E) 13 ≤ x ≤ 18
Rationale: Explanation :
Initial quantity of the rice = x.
The first customer buys half the total rice and another half kg.
Rice purchased by first customer = (x/2) + (1/2)
So, rice left after the first customer =x - (x+1)/2 = (x-1)/2.
Now the second customer buys half the left rice and another half kg.
Rice purchased by second customer = (x-1)/4 + (1/2) = (x+1) / 4.
So, rice left after the second customer = (x-1)/2 - (x+1)/4 = (x-3)/4.
Now the third customer buys half the left rice and another half kg.
Rice purchased by third customer = (x-3)/8 + (1/2) = (x+1)/8.
So, rice left after the second customer= (x-3)/4 -(x+1)/8 = (x-7)/8
Given that (x-7) / 8 = 0 => x=7.
Answer : B
Answer: (B) 5 ≤ x ≤ 8
Question: If a - b = 3 and a(power 2) + b(power 2) = 23, find the value of ab.
(A) 5
(B) 8
(C) 7
(D) 10
(E) 3
Rationale: 2ab = (a(power 2) + b(power 2) - (a - b)(power 2)
= 23 - 9 = 14
ab = 7.
Answer is C.
Answer: (C) 7
Question: A soft drink company had 6000 small and 10000 big bottles in storage. If 12% of small15% of big bottles have been sold, then the total bottles remaining in storage is
(A) 15360
(B) 13780
(C) 15060
(D) 14930
(E) 16075
Rationale: 6000 + 10000 - (0.12*6000 + 0.15*10000) = 13780.
Answer: B.
Answer: (B) 13780
Question: 1,2,3,4,5,6,7 are arranged in order of sum of consecutive numbers is prime number,how many ways we can arrange
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: 1+2 = 3 (Prime no)
2+3 =5 (Prime no)
3+4 =7 (Prime no)
5+6 =11 (Prime no)
6+7 =13 (Prime no)
ANSWER:E
Answer: (E) 5
Question: The length of a train and that of a platform are equal. If with a speed of 54 k/hr, the train crosses the platform in one minute, then the length of the train (in meters) is?
(A) 299
(B) 266
(C) 450
(D) 750
(E) 261
Rationale: Speed = [54 * 5/18] m/sec = 15 m/sec; Time = 1 min. = 60 sec.
Let the length of the train and that of the platform be x meters.
Then, 2x/60 = 15 => x = 15 * 60 / 2 = 450
Answer: C
Answer: (C) 450
Question: There are 4 boys and 3 girls seated in a row.Find the probability that all girls are together?
(A) 1/6
(B) 1/7
(C) 2/7
(D) 3/7
(E) 4/7
Rationale: Total No. of ways boys and girls can be seated = (4 + 3)! = 7! = 5040
No. of ways that girls seated together =>
consider 3 girls as a unit nd remaining 4 boys can be seated in any order...
So (1 + 4)! = 5! = 120
And those 3 girls can be seated among themselves in 3! ways => 6
[(ie) Let g1,g2,g3 be the girls... in 6 ways they can be seated together...
g1g2g3, g1g3g2, g2g1g3, g2g3g1, g3g1g2, g3g2g1]
So prob. that all girls are together => (120 * 6)/5040 => 1/7
ANSWER:B
Answer: (B) 1/7
Question: Tom opened a shop investing Rs.30000. Jose joined him 2 months later, investing Rs.45000. They earned a profit of Rs.54000 after completion of one year. What will be Jose's share of profit?
(A) 10000
(B) 12000
(C) 13000
(D) 14000
(E) 30000
Rationale: SoL = ~s- So Anju’s share = [5/9] x 54000 = 30000
E
Answer: (E) 30000
Question: A trailer carries 3, 4 and 5 crates on a trip. Each crate weighs no less than 1250 kg. What is the maximum weight of the crates on a single trip?
(A) 1250
(B) 6250
(C) 600
(D) 7500
(E) 375
Rationale: Max No. of crates=5.
Max Weight=1250Kg
Max. weight carried = 5*1250=6250Kg=B
Answer: (B) 6250
Question: 61,52,63,94,46,.......
(A) 15
(B) 16
(C) 17
(D) 18
(E) 19
Rationale: Reverse the given numbers like,... 61 16 , 52 25 ...
16,25,36,49,64 these numbers are squares of 4,5,6,7,8 so next number is 9 and square of 9 is 81.
reverse of 81 is 18 so answer is 18 (61,52,63,94,46, 18 ) .
ANSWER:D
Answer: (D) 18
Question: John takes 10 hours to complete a certain job, while Bill takes only 5 hours to complete the same job. If Steve is faster than John but slower than Bill at completing the same job, then which of the following could be the time it takes the three men together, working at their constant, individual rates, to complete the job?
(A) 2 hours, 20 minutes
(B) 2 hours, 45 minutes
(C) 3 hours, 20 minutes
(D) 3 hours, 45 minutes
(E) 4 hours, 10 minutes
Rationale: The rate of John plus Bill is 1/10 + 1/5 = 3/10 of the job completed per hour.
If Steve worked at the same rate as John, the rate would be 3/10 + 1/10 = 2/5
The slowest possible time would be 2.5 hours.
If Steve worked at the same rate as Bill, the rate would be 3/10 + 1/5 = 1/2
The fastest possible time would be 2 hours.
The actual time is somewhere between these two extreme points.
The answer is A.
Answer: (A) 2 hours, 20 minutes
Question: What is the value of âˆš36% ?
(A) 10%
(B) 20%
(C) 30%
(D) 60%
(E) 40%
Rationale: Explanation: br>âˆš16%
=âˆš36/âˆš100
=6/10
=60/100=60%
correct answer is D)60%
Answer: (D) 60%
Question: A car covers a distance of 200km in 2 hours 40 minutes, whereas a jeep covers the same distance in 2 hours. What is the ratio of t
(A) 3:4
(B) 4:3
(C) 4:5
(D) 5:4
(E) 8:7
Rationale: A 3:4
Answer: (A) 3:4
Question: The average age of a group of persons going for picnic is years. Eighteen new persons with an average age of 15 years join the group on the spot due to which their average age becomes 15.5 years. The number of persons initially going for picnic is
(A) 5
(B) 10
(C) 18
(D) 32
(E) 50
Rationale: Solution
Let the initial number of persons be x. Then
16x + 18 x 15 = 15.5(x+20)
= 0.5x = 9
x =18.
Answer C
Answer: (C) 18
Question: In case L is the only individual sewing on committee B, which among the following shouldserve on committee A?
(A) V and U
(B) V and T
(C) U and S
(D) M and N
(E) T and U
Rationale: M and N should serve on A
ANSWER:D
Answer: (D) M and N
Question: There are 8 magazines lying on a table; 4 are fashion magazines and the other 4 are sports magazines. If 2 magazines are to be selected at random from the 8 magazines, what is the probability that at least one of the fashion magazines will be selected?
(A) 1/2
(B) 2/3
(C) 32/35
(D) 11/12
(E) 13/14
Rationale: answer is E
Total probability=8C3=56
4C3 +4C2*4C1+4C1*4C2=4+24+24=52
therefore the probability that at least one of the fashion magazines will be selected= 52/56=13/14
E
Answer: (E) 13/14
Question: At what rate percent on simple interest will Rs.1750 amount to Rs.2000 in 2 years?
(A) 4 %
(B) 7.14 %
(C) 2 6/7 %
(D) 5 %
(E) 6 %
Rationale: Explanation:
250 = (1750x2xR)/100
R = 7.14 %
Answer: Option B
Answer: (B) 7.14 %
Question: Pencils, Pens and Exercise books in a shop are in the ratio of 10: 2 : 3. If there are 120 pencils, the number of exercise books in the shop is:
(A) 26
(B) 36
(C) 46
(D) 56
(E) 66
Rationale: Explanation:
Let Pencils = 10x, Pens = 2x & Exercise books = 3x. Now, 10x = 120 hence x = 12.
Number of exercise books = 3x = 36.
Answer: B
Answer: (B) 36
Question: In Town P, 70 percent of the population are employed, and 21 percent of the population are employed males. What percent of the employed people in Town P are females?
(A) 46%
(B) 52%
(C) 58%
(D) 64%
(E) 70%
Rationale: The percent of the population who are employed females is 70-21 = 49%
The percent of employed people who are female is 49% / 70% = 70%.
The answer is E.
Answer: (E) 70%
Question: What is the diffference between the place value and face value of 8 in the numeral 8635?
(A) 7992
(B) 7892
(C) 7792
(D) 7692
(E) 7982
Rationale: place value of 8 = 8 * 1000 = 8000
face value of 8 = 8
8000 - 8 = 7992
A
Answer: (A) 7992
Question: A meeting has to be conducted with 3 managers. Find the number of ways in which the managers be selected from among 6 managers, if 2 managers will not attend the meeting together?
(A) 18
(B) 20
(C) 16
(D) 22
(E) 24
Rationale: we can either choose all 3 people from 4 manager who have no problems or choose 2 from the 4 and 1 from the 2 managers who have a problem sitting together
so 4C3 + (4C2 * 2C1)
this is 4 + 12=16
Answer : C
Answer: (C) 16
Question: If the letters of the word CHASM are rearranged to form 5 letter words such that none of the word repeat and the results arranged in ascending order as in a dictionary what is the rank of the word CHASM?
(A) 32
(B) 45
(C) 36
(D) 64
(E) 48
Rationale: Explanation :
The 5 letter word can be rearranged in 5!=120 Ways without any of the letters repeating.The first 24 of these words will start with A.Then the 25th word will start will CA _ _ _.The remaining 3 letters can be rearranged in 3!=6 Ways. i.e. 6 words exist that start with CA.The next word starts with CH and then A, i.e., CHA _ _.The first of the words will be CHAMS. The next word will be CHASM.Therefore, the rank of CHASM will be 24+6+2= 32
Answer : A
Answer: (A) 32
Question: The bankers discount of a certain sum of money is Rs. 36 and the true discount on the same sum for the same time is Rs. 30. The sum due is:
(A) 140
(B) 150
(C) 160
(D) 170
(E) 180
Rationale: Sum = (B.D*T.D)/(B.D-T.D)
(36*30)/36-30;
180
ANSWER:E
Answer: (E) 180
Question: Two pipes can fill a tank in 20 and 12 hours, while third pipe will make the tank empty in 20 hours. If all three pipes operate simultaneously. In how many hours the tank will be filled ?
(A) 5 Hours
(B) 7 Hours
(C) 8 Hours
(D) 9 Hours
(E) 12 Hours
Rationale: In 1 hour it fill 1/20 + 1/12 - 1/20 = 1/12
So fill tank fill up in 12 Hours
ANSWER:E
Answer: (E) 12 Hours
Question: The volumes of two cones are in the ratio 1 : 30 and the radii of the cones are in the ratio of 1 : 2. What is the length of the wire?
(A) 6:5
(B) 6:9
(C) 6:2
(D) 2:2
(E) 2:8
Rationale: The volume of the cone = (1/3)πr2h
Only radius (r) and height (h) are varying.
Hence, (1/3)π may be ignored.
V1/V2 = r1^2 . h1/r2^2. h2 => 1/30
= (1)^2h1/(2)^2h2
=> h1/h2 = 6/5
i.e. h1 : h2 = 6:5
Answer: A
Answer: (A) 6:5
Question: A construction company wants to number new houses using digit plates only. If the company puts an order for 1512 plates, how many houses are to be given numbers? (The numbers of houses are consecutive and the number of the first house is 1).
(A) 140
(B) 240
(C) 340
(D) 440
(E) 540
Rationale: You know that the answer is going to be three digits, and it's easy to figure out how many 1 and 2 digit numbers (9 and 90), so the real question is how many 3 digit number are there?
99+(1512-9-90*2)/3=540
Answer : E
Answer: (E) 540
Question: Andrew travelling to 7 cities. Gasoline prices varied from city to city. What is the median gasoline price?
(A) $1
(B) $1.84
(C) $1.96
(D) $2
(E) $2.5
Rationale: Ordering the data from least to greatest, we get:
$1.61, $1.75, $1.79, $1.84, $1.96, $2.09, $2.11
The median gasoline price is $1.84. (There were 3 states with higher gasoline prices and 3 with lower prices.)
B
Answer: (B) $1.84
Question: How many total numbers of not more than 20 digits that can be formed by using the digits 0, 1, 2, 3, and 4 is
(A) 5 20
(B) 5 20 – 1
(C) 5 20 + 1
(D) 6 20
(E) None of these
Rationale: Number of single digit numbers = 5
Number of two digits numbers = 4 × 5
∵ [0 cannot occur at first place and repetition is allowed]
Number of three digits numbers
= 4 × 5 × 5 = 4 × 5(2)
.... .... .... ....
.... .... .... ....
Number of 20 digits numbers = 4 × 5(19)
∴ Total number of numbers
= 5 + 4.5 + 4.5(2) + 4.5(3)........4.5(19)
= 5 + 4⋅5(519−1)5−14⋅5(5[19]−1)5−1 = 5 + 5(20) - 5 = 5(20)
Answer A
Answer: (A) 5 20
Question: A box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that all the four bulbs are defective?
(A) 1/126
(B) 1/129
(C) 1/122
(D) 1/124
(E) 1/123
Rationale: Out of nine, five are good and four are defective. Required probability
= ⁴C₄/⁹C₄
= 1/126
Answer:A
Answer: (A) 1/126
Question: In a particular 100 meter race, 9 athletes are participating that are numbered 1-9. In how many ways can athlete #4 finish ahead of #2 provided there's no tie among the athletes?
(A) 102,330
(B) 115,990
(C) 132,220
(D) 152,770
(E) 181,440
Rationale: The total number of ways for the athletes to finish is 9! = 362,880.
#4 will be ahead of #2 in exactly half of these possibilities.
362,880/2 = 181,440
The answer is E.
Answer: (E) 181,440
Question: In an exam, Gibi scored 59 percent, Jigi scored 55 percent , Mike scored 99 percent and Lizzy 67 percent. The maximum score awarded in the exam is 700. Find the average mark scored by all the four students?
(A) 471
(B) 490
(C) 480
(D) 453
(E) 456
Rationale: Average mark scored by all the three boys =
[59/100 (700) + 55/100 (700) + 99/100 (700)+ 67/100 (700)] / 4
(413+385+693+469)/4= 490
Answer: B
Answer: (B) 490
Question: If S is the sum of the reciprocals of the consecutive integers from 61 to 70, inclusive, which of the following is less than S?
I. 1/6
II. 1/7
III. 1/8
IV .1/6>S >1/7
(A) I
(B) II
(C) IV
(D) III
(E) I&II
Rationale: Since we summarize the reciprocals from 70 to 61, we can say also that we add ten numbers who are all (with one exception 1/70) greater than 1/70, so that the sum must be greater than 1/6.
On the other side we can say that we add the reciprocals from 61 to 70, so that the sum has to be less than the sum of ten times 1/61.
sum has to be greater than 1/7 and less than 1/6
C
Answer: (C) IV
Question: A rectangular plot 15 m × 10 m, has a path of grass outside it. If the area of grassy pathway is 54 m2, find the width of the path.
(A) 4 m
(B) 3 m
(C) 2 m
(D) 1 m
(E) None of these
Rationale: Let the width of the path = W m
then, length of plot with path = (15 + 2W) m
and breadth of plot with path = (10 + 2W) m
Therefore, Area of rectangular plot (without path)
= 15 × 10 = 150 m2
and Area of rectangular plot (with path)
= 150 + 54 = 204 m2
Hence, (15 + 2W) × (10 + 2W) = 204
⇒ 4W2 + 50W – 54 = 0
⇒ 2W2 + 25W – 27 = 0
⇒ (W – 2)(W + 27) = 0
Thus W = 2 or –27
∴ with of the path = 2 m
Answer C
Answer: (C) 2 m
Question: Two trains of length 120 m and 200 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 54 kmph and 72 kmph. In how much time will the trains cross each other?
(A) 100/7 sec
(B) 80/7 sec
(C) 57/7 sec
(D) 120/7 sec
(E) 104/7 sec
Rationale: Relative speed = (54 + 72)* 5/18 = 7 * 5 = 35 mps.
The time required = d/s = (120 + 100 + 300)/35
= 520/35 = 104/7 sec.
ANSWER:E
Answer: (E) 104/7 sec
Question: If six persons sit around a table, the probability that some specified three of them are always together is
(A) 1/20
(B) 3/10
(C) 1/5
(D) 4/5
(E) 3/5
Rationale: There are six persons and three of them are grouped together. Since it is a circle, this can be done in 3! 3! ways.
Therefore, P = 3!3!/5 = 3/10
ANSWER:B
Answer: (B) 3/10
Question: What is the least number which when divided by 5, 6, 7 and 8 leaves a remainder 3, but when divided by 9 leaves no remainder?
(A) 1108
(B) 1683
(C) 2007
(D) 3363
(E) 3567
Rationale: LCM of 5, 6, 7 and 8 = 840
Hence the number can be written in the form (840k + 3) which is divisible by 9.
If k = 1, number = (840 × 1) + 3 = 843 which is not divisible by 9.
If k = 2, number = (840 × 2) + 3 = 1683 which is divisible by 9.
Hence 1683 is the least number which when divided by 5, 6, 7 and 8 leaves a remainder 3, but when divided by 9 leaves no remainder.
Answer: Option B
Answer: (B) 1683
Question: (3x + 2) (2x - 7) = ax^2 + kx + n . What is the value of a - n + k ?
(A) 3
(B) 8
(C) 9
(D) 10
(E) 11
Rationale: Expanding we have 6x^2 - 21x + 4x -14
6x^2 - 17x - 14
Taking coefficients, a = 6, k= -17, n = -14
Therefore a - n + k = 6 - (-14) - 17 = 20 - 17 = 3
The answer is A.
Answer: (A) 3
Question: Pradip spends 40 per cent of his monthly income on food items, and 50 per cent of the remaining on clothes and conveyance. He saves one-third of the remaining amount after spending on food, clothes and conveyance. If he saves 19,200 every year,what is his monthly income?
(A) 24,000
(B) 12,000
(C) 16,000
(D) 20,000
(E) None of these
Rationale: Food items = 40%
Clothes + conveyance = 1⁄2 of 60% = 30%
1⁄3 of 30% = 19,200⁄12 ⇒ 10% = 1600
∴ 100% = 16,000
Answer C
Answer: (C) 16,000