divelab/Sys2Bench huggingface dataset:
Question: TheOG 13thed page 193 #77 says
If n = 90! + 87, then n is divisible by which of the
following?
I. 15
II. 17
III. 19
Options:
A) None
B) I only
C) II only
D) I and II
E) II and III
Rationale: The example you have taken
n = 4! + 4 = 4(3!+1)
The equation gets further simplified to deviate the expected results
Try some other examples
7! + 4
9! + 5
4! + 3
Answer:B
Answer: B
Question: A1B, D4F, H9K,then find next term ?
Options:
A)M16Q
B)L25P
C)N36P
D)N25S
E)M9K
Rationale: By giving the number to alphabets, we get
A - B = 1-2 = -1 --> -1^2 = 1
D - F = 4-6 = -2 --> -2^2 = 4
H - K = 8-11= -3 -->-3^2 = 9
: :
: :
M - Q = 13-17=-4 --->-4^2 = 16
ANSWER:A
Answer: A
Question: A water tank is two-fifth full. Pipe A can fill a tank in 10 minutes and pipe B can empty it in 8 minutes. If both the pipes are open, how long will it take to empty or fill the tank completely?
Options:
A)16 min. to empty
B)6 min. to full
C)9 min. to empty
D)9 min. to full
E)8 min. to full
Rationale: Clearly, pipe B is faster than pipe A and so, the tank will be emptied.
Part to be emptied = 2/5
Part emptied by (A + B) in 1 minute = (1/8 - 1/10) = 1/40
1/40 : 2/5 :: 1 : x
x = (2/5 * 1 * 40) = 16 min.
So, the tank will be emptied in 16 min.
ANSWER:A
Answer: A
Question: My brother is 3 years elder to me. My father was 28 years of age when my sister was born while my mother was 26 years of age when I was born. If my sister was 6 years of age of when my brother was born, then, what was the age of my father and mother respectively when my brother was born?
Options:
A)34 yrs, 23 yrs
B)32 yrs, 29 yrs
C)35 yrs, 29 yrs
D)35 yrs, 33 yrs
E)none
Rationale: Sol.
Clearly, my brother was born 3 years before I was born and 6 years after my sister was born.
So, father's age when brother was born = (28 + 6) = 34 years.
mother's age when was born = (26 - 3) years = 23 years.
Answer A
Answer: A
Question: A, B, C are three consecutive positive integers (A>B>C). What is the value of the expression 2A +2B +3C?
Options:
A)6A+7.
B)5A+1.
C)5A-1.
D)7A-8.
E)6A-7.
Rationale: B = A-1
C= A-2
Putting these values in 2A +2B +3C we get 7A-8
D is the answer
Answer: D
Question: At a restaurant, glasses are stored in two different-sized boxes. One box contains 12 glasses, and the other contains 16 glasses. If the average number of glasses per box is 15, and there are 16 more of the larger boxes, what is the total number of glasses Q at the restaurant? (Assume that all boxes are filled to capacity.)
Options:
A)96
B)240
C)Q=256
D)Q=384
E)Q=480
Rationale: Most Test Takers would recognize the system of equations in this prompt and just do algebra to get to the solution (and that's fine). The wording of the prompt and the 'spread' of the answer choices actually provide an interesting 'brute force' shortcut that you can take advantage of to eliminate the 4 wrong answers....
We're told that there are 2 types of boxes: those that hold 12 glasses and those that hold 16 glasses. Since the AVERAGE number of boxes is 15, we know that there MUST be at least some of each. We're also told that that there are 16 MORE of the larger boxes.
This means, at the minimum, we have...
1 small box and 17 large boxes = 1(12) + 17(16) = 12 + 272 = 284 glasses at the MINIMUM
Since the question asks for the total number of glasses, we can now eliminate Answers A, B and C....
The difference in the number of boxes MUST be 16 though, so we could have....
2 small boxes and 18 large boxes
3 small boxes and 19 large boxes
etc.
With every additional small box + large box that we add, we add 12+16= 28 MORE glasses. Thus, we can justadd 28suntil we hit the correct answer....
284+28 = 312
312+28 = 340
340+28 = 368
368+28 = 396
At this point, we've 'gone past' Answer D, so the correct answer MUST be Answer E.....But here's the proof....
396+28 = 424
424+28 = 452
452+28 = 480
Final Answer:
E
Answer: E
Question: The average of five results is 46 and that of the first four is 45. The fifth result is?
Options:
A)29
B)27
C)29
D)50
E)81
Rationale: 5 * 46 – 4 * 45 = 50
Answer: D
Answer: D
Question: If 3x+y=40, 2x-y=20, for integers of x and y, 4y^2=?
Options:
A)2
B)4
C)0
D)10
E)64
Rationale: 3x+y = 40
2x-y = 20
5x = 60
x = 12
y = 4
4y^2 = 4*16=64
Answer is E
Answer: E
Question: Three candidates contested an election and received 1136, 7636 and 11628 votes respectively. What percentage of the total votes did the winning candidate get?
Options:
A)57%
B)60%
C)65%
D)90%
E)80%
Rationale: total votes are 20400 ( sum of votes obtained by 3 candidates)
percentage of the total votes recd by the winning candidate = 100*11628/20400 = 57%
ANSWER:A
Answer: A
Question: A bag contains 4red, 5blue and 3green balls. If 3 ballsare picked at random, what is the probability that both are red?
Options:
A)1/33
B)1/22
C)1/12
D)1/44
E)1/55
Rationale: P(Both are red),
=4C3/12C3=1/55
E
Answer: E
Question: Jade has 4 flavors of ice cream in his parlor. How many options are there for James to pick a one-flavor, two-flavor, three-flavor or four-flavor order?
Options:
A)15
B)13
C)14
D)17
E)18
Rationale: 4C1 + 4C2+ 4C3+4C4 = 15.
Answer: A
Answer: A
Question: At a special sale, 8 tickets can be purchased for the price of 6 tickets. If 8 tickets are purchased at the sale, the amount saved will be What percent of the original price of the 8 tickets?
Options:
A)25%
B)33.3%
C)40%
D)60%
E)66.6%
Rationale: let the price of a ticket be Rs.100, so 6 tickets cost 600 & 8 tickets cost 800
8 tickets purchased at price of 6 tickets ie., for 600, so amount saved s Rs.200,
% of 6 tickets = (200 /800)*100 =25 %
ANSWER:A
Answer: A
Question: Ten years ago, the age of Anand was one-third the age of Bala at that time. The present age of Bala is 8 years more than the present age of Anand. Find the present age of Anand?
Options:
A)12
B)13
C)14
D)15
E)16
Rationale: Let the present ages of Anand and Bala be 'a' and 'b' respectively.
a - 10 = 1/3 (b - 10) --- (1)
b = a + 8
Substituting b = a + 12 in first equation,
a - 10 = 1/3 (a - 2) => 3a - 30 = a - 2
=> 2a = 28 => a = 14.
ANSWER:C
Answer: C
Question: How long does a train 110metres long running at the speed of 72 km/hr take to cross a bridge 132metres in length?
Options:
A)10
B)11.1
C)12.1
D)31.2
E)21.5
Rationale: speed = 72*5/18 = 20m/s
total distance covered = 110+132 = 242m
required time = 242/20 = 12.1 sec
Answer is C
Answer: C
Question: Joe drives 420 miles at 60 miles per hour, and then he drives the next 120 miles at 40 miles per hour. What is his average speed for the entire trip in miles per hour?
Options:
A)42
B)54
C)50
D)54
E)56
Rationale: t1= 420/60=7 hours
t2=120/40=3 hours
T=t1+t2=10 hours
Avg speed = Total Distance/T
= 540/10 = 54mph=B
Answer: B
Question: A works twice as fast as B. if both of them can together finish a piece of work in 12 days, then B alone can do it in
Options:
A)24 days
B)27 days
C)36 days
D)48 days
E)50 days
Rationale: Explanation:
B = 2A
2A × A/3A = 12
2A/3 = 12
A = 18 days
B = 2 × 18 = 36 days
Therefore, B alone can finish the work in 36 days.
Answer: Option C
Answer: C
Question: There are 50 employees in the office of ABC Company. Of these, 22 have taken an accounting course, 15 have taken a course in finance and 14 have taken a marketing course. Nine of the employees have taken exactly two of the courses and 2 employee has taken all three of the courses. How many of the 50 employees have taken none of the courses?
Options:
A)12
B)8
C)5
D)4
E)9
Rationale: 50 Employees. Counting every different attendand to the courses we have:
Accounting: 22
Finance: 15
Marketing: 14
Which would add up to 51 different attendands, which is not possible.
Now 9 have taken exactly 2 courses, which means that there are 9 less different attendands. Say that 9 of the Finance attentands also attended Accounting.
51-9= 42
2 Person has taken all three courses. As above, we subtract him from the number of different attendands. Since this time the person took all three courses, we have to substract him two times.
42-4= 38.
Answer : A
Answer: A
Question: Jackson invested $200,000, dividing it all unequally between Account P and Account Q. At the end of the year, it turned out that Account P had earned 12% interest and Account Q had earned 25% interest. If Jackson earned a total of $60,000 in interest between the two accounts, which of the following is approximately the amount he put in account P?
Options:
A)$115,384
B)$120,000
C)$121,072
D)$124,129
E)$130,000
Rationale: x be the amount invested in account P
0.12*x +(200000-x)*0.25=60,000
15000/.13=x
x=1500000/13=11...=$105,384
hence answer is A
Answer: A
Question: In a class there are 20 boys and 20 girls. In how many ways can a boy and a girl be selected?
Options:
A)508
B)400
C)800
D)570
E)503
Rationale: We can select one boy from 20 boys in 20 ways.
We select one girl from 20 girls in 20 ways
We select a boy and girl in 20 * 20 ways i.e., = 400 ways.
Answer:B
Answer: B
Question: Ravi can do a piece of work in 30 days while Prakash can do it in 40 days. In how many days will they finish it together?
Options:
A)17 1/7
B)2/7
C)8/5
D)4/9
E)3/8
Rationale: Explanation:
1/30 + 1/40 = 7/120
120/7 = 17 1/7 days
So, both together will finish the work in 17 1/ 7 days.
Answer:A
Answer: A
Question: A cab driver 5days income was $45, $50, $60, $65 , $70. Then his average income is?
Options:
A)$58
B)$42
C)$65
D)$48
E)$62
Rationale: avg = sum of observations/number of observations
avg income=(45+50+60+65+70)/5 = 58
Answer is A
Answer: A
Question: An isosceles triangle has angles with ratios 1:2:2. What is the measurement of the angle within the triangle with ratio 2?
Options:
A)36Â°
B)46Â°
C)72Â°
D)92Â°
E)100Â°
Rationale: Given that the ratio is 1:2:2 and that the total angle measurement within a triangle is 180Â°, the equation is
1x + 2x + 2x = 180Â°
5x = 180Â°
x = 36Â°
But since we want to find the angle measurement with ratio 2, we multiple x by 2
2x = 2(36Â°) = 72Â°
Therefore, the answer is 72Â° or C.
Answer: C
Question: A candidate got 40% of the votes polled and he lost to his rival by 5000 votes. How many votes were cast?
Options:
A)25000
B)2028
C)2775
D)5496
E)6851
Rationale: 40%-----------L
60%-----------W
------------------
20%----------5000
100%---------? => 25000
Answer:A
Answer: A
Question: If f(f(n)) + f(n) = 2n+3, f(0) = 1 then f(2012) = ?
Options:
A)2013
B)2088
C)270
D)1881
E)1781
Rationale: f (f(0)) + f(0) = 2(0) + 3 ⇒⇒ f(1) = 3-1 = 2, f(1) = 2
f(f(1)) + f(1) = 2(1) + 3 ⇒⇒ f(2) = 5-2 = 3, f(2) = 3
f(f(2)) + f(2) = 2(2) + 3 ⇒⇒ f(3) = 7-3 = 4, f(3) = 4
..............
f(2012) = 2013
Ans: A
Answer: A
Question: The first three terms of a proportion are 3, 9 and 12. The fourth term is?
Options:
A)6
B)36
C)5
D)25
E)30
Rationale: Explanation:
(9*12)/3 = 36
ANSWER B
Answer: B
Question: Find the middle one when The sum of five consecutive even numbers is 65?
Options:
A)9
B)13
C)15
D)17
E)11
Rationale: Let the first number be n
Let the second number be n + 2
Let the third number be n + 4
Let the third number be n + 6
Let the third number be n + 8
n + n + 2 + n + 4 + n + 6 + n + 8= 65
Combine like terms:
5n + 20 = 65
5n = 65 - 20
5n = 45
5n = 45
n = 9
n + 2 = 11
n + 4 = 13
n + 6 = 15
n + 8 = 17
The middle number is 13
Answer: B
Answer: B
Question: A, B and C enter into a partnership. They invest Rs. 70,000, Rs. 80,000 and Rs. 1,20,000 respectively. At the end of the first year, B withdraws Rs. 40,000, while at the end of the second year, C withdraws Rs. 80,000. In what ratio will the profit be shared at the end of 3 years?
Options:
A)21 : 32 : 4
B)21 : 26 : 4
C)21: 12 : 1
D)21: 16 : 28
E)none
Rationale: Sol.
A : B : C = (40000 * 36) : (80000 * 12 + 40000 * 24)
: (120000 * 24 + 40000 * 12) =252 : 192 : 336 = 21: 16 : 28
Answer D
Answer: D
Question: Three fill pipes A, B and C can fill separately a cistern in 3, 4 and 6 minutes respectively. A was opened first. After 1 minute, B was opened and after 2 minutes from the start of A, C was also opened. Find the time when the cistern will be full ?
Options:
A)2 1⁄9 min.
B)4 1⁄2 min.
C)3 3⁄4 min.
D)3 min.
E)None of these
Rationale: Let cistern will be full in x min. Then,
part filled by A in x min + part filled by B in (x – 1) min + part filled by C in (x – 2)min = 1
⇒ x/3+x−1/4+x−2/6=1
⇒ 9x = 19 ⇒ x = 19⁄9 = 21⁄9 min.
Answer A
Answer: A
Question: The forth proportional to 20,8,15 is?
Options:
A)15
B)6
C)18
D)20
E)24
Rationale: Let the fourth proportional to 20,8,15 be x
then 20:8::15:x
20x = 8*15
x = 6
Answer is B
Answer: B
Question: A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
Options:
A)228
B)240
C)188
D)266
E)281
Rationale: Speed = (54 * 5/18) m/sec = 15 m/sec. Length of the train = (15 x 20)m = 300 m. Let the length of the platform be x meters. Then, (x + 300)/36 = 15 ==> x + 300 = 540 ==> x = 240 m.
Answer: B
Answer: B
Question: Marge has 3 pumps for filling her swimming pool. When all 3 pumps work at their maximum rates, the swimming pool is filled in 60 minutes. Pump 1's maximum rate is twice the maximum rate of pump 2 and four times the maximum rate of pump 3. How long would it take Marge to fill the pool if she used only pump 3 at its maximum rate ?
Options:
A)2hrs, 48mins
B)7hrs,
C)7hrs, 12mins
D)13hrs, 4mins
E)14hrs, 24mins
Rationale: The rate of pump 1 = 4x job/minute.
The rate of pump 2 = 2x job/minute.
The rate of pump 3 = x job/minute.
Given that x+2x+4x=1/60 --> x=1/420--> (time) = (reciprocal of rate) = 392 minutes = 7 hours
Answer: B.
Answer: B
Question: A machine puts c caps on bottles in m minutes. How many R hours will it take to put caps on b bottles?
Options:
A)60bm/c
B)R=bm/60c
C)bc/60m
D)60b/cm
E)b/60cm
Rationale: The machine puts c caps in m minutes or c caps in m/60 hours.
Rate = c/m/60 = 60c/m.
To put b caps the machine will take:-
Time = Work/Rate
T = b/60c/m = bm/60c
Answer is B.
Answer: B
Question: At the beginning of a year ,the owner of a jewel shop raised the price of all the jewels in his shop by x% and lowered them by x%. The price of one jewel after this up and down cycle reduced by Rs.100.The owner carried out the same procedure after a month.After this second up-down cycle,the price of that jewel was Rs.2304.Find the original price of that jewel(in Rs.)
Options:
A)2500
B)550
C)2600
D)2650
E)None of these
Rationale: Solution: Let the original price = y,
After first change, It becomes,
y * (1+(x/100))
After second change, It becomes
y *(1+(x/100))(1-(x/100)) = y(1-(x/100)^2 )
Thus,
x2*y = 106 ------- (1)
x2 = 106/y
Now,
y(1-(106/10000y))2 = 2304(similar to above)
y(1-100/y)2 = 2304
y = 2500.
Answer: Option A
Answer: A
Question: By approximately what percent is x greater than 1/2 if (1/2)(x) = 1?
Options:
A)732%
B)560%
C)641%
D)370%
E)300%
Rationale: what percent is x greater than 1/2 if (1/2)(x) = 1?
=> x = 2
% change =[(2 -1/2) /(1/2) ] * 100
= (4 - 1) *100
= 300% approx
Ans ,E
Answer: E
Question: Mirun travels the first 3 hours of her journey at 20 mph speed and the remaining 2 hours at 40 mph speed. What is the average speed of Mirun 's travel in mph?
Options:
A)26mph
B)27mph
C)22mph
D)28mph
E)23mph
Rationale: Explanation :
Average speed=Total Distance/Time.
Total distance travelled by Mirun = Distance covered in the first 3 hours + Distance covered in the next 2 hours.
Distance covered in the first 3 hours = 3Ã—20=60 miles
Distance covered in the next 2 hours= 2Ã—40=80 miles
Therefore, total distance travelled = 60+80=140 miles.
The total time taken = 3+2=5hours.
Hence, the average speed =140/5= 28mph.
Answer : D
Answer: D
Question: Three fifth of the roads from A to B are at least 5 miles long, and 5/6 of the roads from B to C are at least 5 miles long. If you randomly pick a road from A to B and then randomly pick a road from B to C, what is the probability that at least one of the roads you pick is at least 5 miles long?
Options:
A)1/6
B)1/4
C)2/3
D)3/4
E)11/12
Rationale: So please:
Find the probability of the event thatnoneof the roads you pick will be at least 5 miles long and subtract from 1 to get the probability thatat least oneof the roads you pick will be at least 5 miles long: P=1-2/5*5/6=2/3.
Answer: C.
Answer: C
Question: Each side of a rectangle is increased by 100% .By what percentage does the area increase?
Options:
A)300%
B)400%
C)500%
D)200%
E)600%
Rationale: original area=a*b where a and b are sides
after increase in side increase in area will be=(((2a*2b)-(a*b))*100)/(a*b)=300%
ANSWER:A
Answer: A
Question: If the number of boys in a class are 8 times the number of girls, which value can never be the total number of students?
Options:
A)27
B)45
C)81
D)42
E)56
Rationale: Explanation :
Let the number of girls = x and the number of boys = 8x
Then, total number of students = x + 8x = 9x
i.e., the total number of students must be a multiple of 9
From the given choices, 42 cannot be a multiple of 9.
Hence, 42 cannot be the total number of students.
Answer : D
Answer: D
Question: The cost price of a radio is Rs.1500 and it was sold for Rs.1230, find the loss %?
Options:
A)18%
B)28%
C)34%
D)39%
E)93%
Rationale: 1500 ---- 270
100 ---- ? => 18%
Answer: A
Answer: A
Question: If four coins are tossed, the probability of getting two heads and two tails is
Options:
A)3/8
B)3/5
C)3/9
D)3/1
E)3/3
Rationale: Since four coins are tossed, sample space = 24
Getting two heads and two tails can happen in six ways.
n(E) = six ways
p(E) = 6/24 = 3/8
Answer:A
Answer: A
Question: In how many different ways can 5 boys and 2 girls sit on a bench such that the girls always sit together?
Options:
A)360
B)720
C)1440
D)1800
E)2160
Rationale: We can think of the girls as one unit.
The number of ways to arrange 6 units in order is 6!
The girls can have different arrangements, so we multiply this by 2!
The number of ways to sit is 6!*2!=1440
The answer is C.
Answer: C
Question: In how many different ways can the letters of the word ‘CAN’ be arranged?
Options:
A)6
B)12
C)8
D)2
E)4
Rationale: A
6
The word SMART has 3 distinct letters.
Number of arrangements = 3!
= 3 × 2 × 1 = 6
Answer: A
Question: How long does a truck of 200 m long traveling at 60 kmph takes to cross a bridge of 180 m in length?
Options:
A)36.7
B)26.8
C)22.8
D)21.1
E)16.2
Rationale: D = 200 + 180 = 380 m
S = 60 * 5/18 = 50/3
T = 380 * 3/50 = 22.8 sec
Answer:C
Answer: C
Question: The principal that amounts to Rs. 4913 in 3 years at 6 1/4 % per annum C.I. compounded annually, is?
Options:
A)2368
B)2768
C)1121
D)4096
E)2687
Rationale: Explanation:
Principal = [4913 / (1 + 25/(4 * 100))3]
= 4913 * 16/17 * 16/17 * 16/17 = Rs. 4096.
Answer:D
Answer: D
Question: A person can row at 10 kmph in still water. If the velocity of the current is 2 kmph and it takes him 25 hour to row to a place and come back, how far is the place?
Options:
A)24km
B)30km
C)48km
D)120km
E)15km
Rationale: Speed of down stream = 10+2 = 12kmph
speed of upstream = 10-2 = 8kmph
Let the required distance be xkm
x/12 + x/8 = 25
2x+3x = 600
x = 120 km
Answer is D
Answer: D
Question: In the rectangular coordinate system, what is the area of triangle CDE with points
C=(3,3)
D=(4,1)
E=(0,8)
Options:
A)0.75
B)1
C)0.5
D)0.25
E)1.5
Rationale: Use the formula of the distance formula
square root (x2-x1)^2+(y2-y1)^2
Do this for each of the sides and then the value is given as C.
Answer: C
Question: A basket has 5 apples and 4 oranges. Three fruits are picked at random. The probability that at least 2 apples are picked is?
Options:
A)25/42
B)25/47
C)25/48
D)25/21
E)25/41
Rationale: Total fruits = 9
Since there must be at least two apples,
(⁵C₂ * ⁴C₁)/⁹C₃ + ⁵C₃/⁹C₃ = 25/42
Answer:A
Answer: A
Question: Two-third of two-fifth of three-fourth of a number is 36. What is the square root of four-fifth of that number?
Options:
A)9
B)12
C)14
D)16
E)18
Rationale: Explanation:
We have, 2/3 * 2/5 * 3/4 * X = 36
X = 180
Now, 4/5 * X ===> 4/5 * 180 = 144
√144 = 12
ANSWER: B
Answer: B
Question: If x dollars is invested at 10 percent for one year and y dollars is invested at 8 percent for one year, the annual income from the 10 percent investment will exceed the annual income from the 8 percent investment by $56. If $2,000 is the total amount invested, how much is invested at 10 percent?
Options:
A)a. $280
B)b. $800
C)c. $892
D)d. $1108
E)e. $1200
Rationale: 2 equations with 2 unknowns
10x / 100 - 8y / 100 = 56
and
x + y = 2000
Solving these 2 equations, x = 1200 and y = 800
Answer E.
Answer: E
Question: The dimensions of a room are 25 feet * 15 feet * 12 feet. What is the cost of white washing the four walls of the room at Rs. 8 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each?
Options:
A)s.7248
B)s.4518
C)s.4518
D)s.4530
E)s.4517
Rationale: Area of the four walls = 2h(l + b)
Since there are doors and windows, area of the walls = 2 * 12 (15 + 25) - (6 * 3) - 3(4 * 3) = 906 sq.ft.
Total cost = 906 * 5 = Rs.7248
Answer: A
Answer: A
Question: The first doughnut is priced at $1 and then if you purchase additional doughnuts as dozens then the price is $6/dozen. What is the total number of doughnuts purchased if you paid $21?
Options:
A)33
B)35
C)37
D)39
E)41
Rationale: $21 = 3 * $6 + $3
The number of doughnuts is 3*12 + 3 = 39
The answer is D.
Answer: D
Question: If Rs.7500 are borrowed at C.I at the rate of 4% per annum, then after 2 years the amount to be paid is?
Options:
A)Rs.544
B)Rs. 8112
C)Rs.820
D)Rs.639
E)Rs.897
Rationale: Explanation:
Explanation:
A = 7500(26/25)2 =Rs. 8112
Answer:B
Answer: B
Question: If k > 0, x + 2k = y, and y + 5k = z, what is the ratio between z - x and y - x ?
Options:
A)3 to 1
B)3 to 2
C)4 to 3
D)7 to 2
E)5 to 3
Rationale: y-x = 2k
z-y = 5k
Let's add the two equations together:
z-x = 7k
The ratio of z-x to y-x is 7:2.
The answer is D.
Answer: D
Question: Nine men went to a hotel. Eight of them spent Rs.3 each over their meals and the ninth spent Rs.2 more than the average expenditure of all the nine. Determine the total money spent by them?
Options:
A)29.25
B)29.28
C)39.25
D)29.21
E)29.22
Rationale: Average of 9 = x
9x = 8 * 3 + x * 2 x = 3.25
Total = 9 * 3.25 = 29.25.A
Answer: A
Question: Two pipes P and Q can fill a tank in 15 min and 20 min respectively. Both the pipes are opened together but after 4 min, pipe P is turned off. What is the total time required to fill the tank?
Options:
A)10 min
B)12 min
C)14 min 40 sec
D)15 min 30 sec
E)18 min
Rationale: filled in 4 min = 4(1/15 + 1/20) = 7/15
part = 1-7/15==>8/15
filled by Q in 1 min = 1/20
x=8/15*1*20==> 10 2/3 min==>10 min 40 sec
so tank will be full in (4 min +10 min 40 sec) = 14min 40 sec
ANSWER C
Answer: C
Question: If f(2, 3) = 17 and f(2, 4) = 24, what is the value of f(2, 5)?
Options:
A)107
B)127
C)147
D)33
E)Cannot be determined
Rationale: Solution:
The function f(a, b) = a3 + b2
f(2, 3) therefore is = 17 and
f(2, 4) = 24
Therefore, f(2, 5) = 33
Answer D
Answer: D
Question: Two trains are moving in opposite directions at 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.4 km respectively. The time taken by the slower train to cross the faster train in seconds is?
Options:
A)12
B)77
C)48
D)99
E)36
Rationale: Relative speed = 60 + 90 = 150 km/hr.
= 150 * 5/18 = 125/3 m/sec.
Distance covered = 1.10 + 0.4 = 1.5 km = 1500 m.
Required time = 1500 * 3/125 = 36 sec.
Answer: E
Answer: E
Question: A boat covers a certain distance downstream in I hour, while it comes back in 1½ hours. If the speed of the stream be 3 kmph. what is the speed of the boat in still Water?
Options:
A)12kmph
B)13kmph
C)15kmph
D)16kmph
E)None
Rationale: Solution
Let the speed of the boat in still water be x kmph. Then,
Speed downsteram	= (x + 3) kmph.
Speed upsteram	= (x - 3) kmph.
= (x+3)x1
= (x - 3)x3/2 kmph.
= 2x+6 = 3x-9
x= 15 kmph.
Answer C
Answer: C