divelab/Sys2Bench huggingface dataset:
Question: How many such 3's are there in the following number sequence which are immediately Preceded by an odd number and immediately followed by an even number? 5 3 8 9 4 3 7 2 3 8 1 3 8 4 2 3 5 7 3 4 2 3 6
Options:
A)1
B)2
C)3 three
D)4
E)More than four
Rationale: A is followed by B means : A comes first,B comes next
A precede d by B means : B comes first, A comes next
The sets which satisfy the condition is: 5 3 8
1 3 8
7 3 4
ANSWER:C
Answer: C
Question: What sum of money put at C.I amounts in 2 years to Rs.7000 and in 3 years to Rs.9261?
Options:
A)4000
B)8877
C)2877
D)2678
E)1011
Rationale: 7000 ---- 2261
100 ---- ? => 32.3%
x *1323/100 * 1323/100 = 7000
x*1.75=7000
x=7000/1.75 => 3999.25
Answer: A
Answer: A
Question: All of the students of Music High School are in the band, the orchestra, or both. 80 percent of the students are in only one group. There are 136 students in the band. If 60 percent of the students are in the band only, how many students are in the orchestra only?
Options:
A)33
B)39
C)34
D)42
E)48
Rationale: % of students in one group only = 80%
% of students in both groups = 100 - 80 = 20%
% of students in the band only = 60%
Number of students who are in band = 136
20% + 60% = 80% = 136 Students
Finding total students:
x = (136 x 100)/80
x = 170
Students in orchestra only = 170 - 136 = 34
Answer:C
Answer: C
Question: Three dice are thrown together, Find the probability of getting a total of at least 5?
Options:
A)2/7
B)3/5
C)51/52
D)1/2
E)53/54
Rationale: Three different dice are thrown at the same time.
Therefore, total number of possible outcomes will be 63 = (6 × 6 × 6) = 216.
Number of events of getting a total of less than 5 = 4
i.e. (1, 1, 1), (1, 1, 2), (1, 2, 1) and (2, 1, 1).
Therefore, probability of getting a total of less than 5
P(E) = Number of favorable outcomes/Total number of possible outcome
= 4/216
= 1/54
Therefore, probability of getting a total of at least 5 = 1 - P(getting a total of less than 5)
= 1 - 1/54
= (54 - 1)/54
= 53/54
Answer: E
Question: A chair is bought for Rs.120/- and sold at Rs.240/- find gain or loss percentage
Options:
A)115% loss
B)120% gain
C)125% gain
D)100% gain
E)350% gain
Rationale: Formula = (Selling price ~ Cost price)/Cost price * 100
= (240- 120)/120 = 100% gain
D
Answer: D
Question: A, B, C and D enter into partnership. A subscribes 1/3 of the capital B 1/4, C 1/5 and D the rest. How much share did A get in a profit of Rs.2460?
Options:
A)29999
B)26676
C)29986
D)14000
E)29898
Rationale: 25*12: 30*12: 35*8
15:18:14
14/47 * 47000 = 14000
Answer: D
Answer: D
Question: The average (arithmetic mean) of eight numbers is 44.1. If the sum of half of these numbers is 158.4, what is the average of the other half?
Options:
A)12.8
B)24.2
C)48.6
D)72.1
E)96.8
Rationale: arithmetic mean = sum / total numbers
sum = 44.1 * 8 = 352.8
sum of half of these numbers is 158.4. So, 4 numbers sum is 158.4. Rest 4 numbers sum = 352.8-158.4 = 194.4
Arithmetic mean of the 4 nos = 194.4/4 = 48.6
Hence, C is the answer.
Answer: C
Question: The price of the jewel, passing through three hands, rises on the whole by 80%. If the first and the second sellers 20% and 25% profit respectively find the percentage profit earned by the third seller.
Options:
A)20
B)10
C)15
D)25
E)30
Rationale: Let the original price of the jewel be $ p and let the profit earned by the third seller be x% Then, (100+x)% of 125% of 120% of P =180% Of P ((100+X)/100*125/100*120/100*P)=(180/100*P)
==> (100+X)=(180*100*100)/(125*120)=120=>X=20%
Answer A
Answer: A
Question: A man buys Rs. 44 shares paying 9% dividend. The man wants to have an interest of 12% on his money. The market value of each share is:
Options:
A)s. 12
B)s. 15
C)s. 18
D)s. 21
E)s. 33
Rationale: Dividend on Rs. 44 = Rs.	9/100	x 44 =Rs.	3.96	.
Rs. 12 is an income on Rs. 100.
Rs.	3.96	is an income on Rs.100/12 x 3.96= Rs. 33.
Answer: Option E
Answer: E
Question: Which of the following is greatest?
Options:
A)1/2
B)1/4
C)1/3
D)1/6
E)1/7
Rationale: simply we know that 1/2 is greater than all others.
So, Answer : A
Answer: A
Question: Ron walks to a viewpoint and returns to the starting point by his car and thus takes a total time of 6 hours 45 minutes. He would have gained 2 hours by driving both ways. How long R would it have taken for him to walk both ways.
Options:
A)8 h 45 min
B)7 h 45 min
C)6 h 45 min
D)5 h 30 min
E)None of these
Rationale: 1.Walking to to a viewpoint+Driving back=6 hours 45 minutes
2.Driving to a viewpoint+Driving back=6 hours 45 minutes - 2 hours=4 hours 45 minutes, thereforeone way driving=4 hours 45 minutes/2 =2 hours 22.5 minutes.
3. From 1.one way driving=6 hours 45 minutes-2 hours 22.5 minutes=4 hours 22.5 minutes.
4.Walking to to a viewpoint+Walking back R=4 hours 22.5 minutes+4 hours 22.5 minutes=8 hours 45 minutes.
Answer: A.
Answer: A
Question: A work can be finished in 14 days by thirty women. The same work can be finished in fifteen days by forteen men. The ratio between the capacity of a man and a woman is
Options:
A)3:4
B)4:3
C)2:1
D)3:2
E)4:5
Rationale: Work done by 20 women in 1 day = 1/14
Work done by 1 woman in 1 day = 1/(14Ã—30)
Work done by 14 men in 1 day = 1/15
Work done by 1 man in 1 day = 1/(15Ã—14)
Ratio of the capacity of a man and woman =1/(15Ã—14) : 1/(14Ã—30) = 1/15 : 1/30
= 1/3 :1/6 = 1/1=1/2=2:1
Answer is C
Answer: C
Question: A train moves fast a telegraph post and a bridge 264 m long in 8 sec and 20 sec respectively. What is the speed of the train?
Options:
A)5/6 km/hr
B)25 km/hr
C)79.2 km/hr
D)15 km/hr
E)38 km/hr
Rationale: Explanation:
Let the length of the train be x m and its speed be y m/sec.
Then, x/y = 8 => x = 8y
(x + 264)/20 = y
y = 22
Speed = 22 m/sec = 22 * 18/5 = 79.2 km/hr
Answer:C
Answer: C
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 m
B)240 m
C)227 m
D)167 m
E)186 m
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: If Raj shares all of his amount equally among his five friends then each of his friend's amount increased by $10 then Raj had how much?
Options:
A)$10
B)$20
C)$30
D)$40
E)$50
Rationale: Five friends amount increased by $10 and Raj shared equally so amount = 5 * 10 = 50
Answer:E
Answer: E
Question: The public library has exactly 2 floors. It has 3/4 as many shelves on its 2nd floor as it does on its 1st. If the second floor has 5/6 as many books per shelf as the first floor, what fraction of the library's books are on the first floor?
Options:
A)24/39
B)5/14
C)5/9
D)9/14
E)5/6
Rationale: Let x be the no of shelves and y be the no of books per shelf on first floor.
Now no of shelves on 2nd floor = (3/4)*x
no of books per shelf on 2nd floor = (5/6) * y
So total no books on first floor = xy and total no of books on 2nd floor = (3/4)*x*(5/6)*y = (15/24)*xy
fraction of library books on first floor = (xy)/(xy + (15/24)*xy)
=1 / (1+(15/24))
=24/39
So A
Answer: A
Question: If p / q is an integer, which of the following statements must be true?
Options:
A)p = nq where n is an integer
B)both p and q are integers
C)q / p is an integer
D)either p or q is negative
E)p is an integer
Rationale: Let p = 1/4; q = 1/8 --> p/q = 2
p = nq where n is an integer --> 1/4 = 2*(1/8) --> Correct
Answer: A
Answer: A
Question: The population of a bacteria colony doubles every day. If it was started 6 days ago with 2 bacteria and each bacteria lives for 12 days, how large is the colony today?
Options:
A)64
B)128
C)256
D)512
E)1024
Rationale: 2^6(2) = 2^7 = 128
The answer is B.
Answer: B
Question: A bowl contains equal numbers of red, orange, green, blue, and yellow candies. Kaz eats all of the green candies and half of the orange ones. Next, he eats half of the remaining pieces of each color. Finally, he eats red and yellow candies in equal proportions until the total number of remaining candies of all colors equals 25% of the original number. What percent of the red candies remain?
Options:
A)10%
B)15%
C)25%
D)35%
E)40%
Rationale: Let x be the original number of each color.
Kaz eats all of the green candies and half of the orange ones.
There are 0 green candies and 0.5x orange candies remaining.
He eats half of the remaining pieces of each color.
There are 0.25x orange candies, and 0.5x each of red, yellow, and blue candies.
He eats red and yellow candies in equal proportions.
orange+blue+red+yellow = 0.75x + red + yellow = 1.25x
red + yellow = 0.5x
red = 0.25x, since red = yellow.
The answer is C.
Answer: C
Question: A train ride from Two P to Town Q costs $2.35 more than does a bus ride from Town P to Town Q. Together, the cost of one train ride and one bus ride is $9.85. What is the cost of a bus ride from Town P to Town Q?
Options:
A)$1.25
B)$2.50
C)$3.75
D)$4.70
E)$8.20
Rationale: Let x be the cost of a bus ride.
x + (x+235) = 985
2x = 750
x = $3.75
The answer is C.
Answer: C
Question: Square A has an area of 25 square centimeters. Square B has a perimeter of 12 centimeters. If square B is placed within square A and a random point is chosen within square A, what is the probability the point is not within square B?
Options:
A)9/25
B)1/5
C)16/25
D)3/5
E)6/25
Rationale: I guess it's mean that square B is placed within square Aentirely.
Since, the perimeter of B is 12, then its side is 12/4=3 and the area is 3^2=9
Empty space between the squares is 25-9=16 square centimeters, so if a random point is in this area then it won't be within square B: P=favorable/total=16/25.
Answer: C
Answer: C
Question: What are the unit and symbol for current?
Options:
A)WW
B)776
C)26
D)68
E)26
Rationale: Answer: Option D
Answer: D
Question: If 2x + y = 7 and x + 2y = 5, then 4xy/3 =?
Options:
A)A) 1
B)B) 2
C)C) 17/5
D)D) 18/5
E)E) 4
Rationale: 2*(x+2y = 5) equals 2x+4y=10
2x+4y=10
- 2x + y= 7
= 3y=3
Therefore Y = 1
Plug and solve...
2x + 1 = 7
2x=6
x=3
(4*3*1)/3
= 12/3
=4
E
Answer: E
Question: Three taps A, B and C can fill a tank in 12, 15 and 20 hours respectively. If A is open all the time and B and C are open for one hour each alternately, the tank will be full is?
Options:
A)6 hrs
B)8 hrs
C)7 hrs
D)3 hrs
E)12 hrs
Rationale: (A + B)'s 1 hour work = (1/12 + 1/15) = 3/20
(A + C)'s 1 hour work = (1/12 + 1/20) = 2/15
Part filled in 2 hrs = (3/20 + 2/15) = 17/60
Part filled in 6 hrs = 3 * 17/60 = 17/20
Remaining part = 1 - 17/20 = 3/20
Now, it is the turn of A and B and 3/20 part is filled by A and B in 1 hour.
Total time taken to fill the tank = (6 + 1) = 7 hrs.Answer: C
Answer: C
Question: 10 men can complete a piece of work in 15 days and 15 women can complete the same work in 12 days. If all the 10 men and 15 women work together, in how many days will the work get completed?
Options:
A)6
B)6 1⁄3
C)6 2⁄3
D)7 2⁄3
E)None of these
Rationale: 10 men’s 1 day’s work = 1⁄15
15 women’s 1 day’s work = 1⁄12
(10 men + 15 women)’s 1 day’s work
= (1⁄15 + 1⁄12) = 9⁄60 = 3⁄20
∴ 10 men and 15 women will complete the work in 20⁄3 = 62⁄3 days.
Answer C
Answer: C
Question: Rohan spends 40% of his salary on food, 20% on house rent, 10% on entertainment and 10% on conveyance. If his savings at the end of a month are Rs. 1500. then his monthly salary is
Options:
A)Rs. 6000
B)Rs. 7500
C)Rs. 8000
D)Rs. 10,000
E)None
Rationale: Sol.
Saving = [100 - (40 + 20 + 10 + 10]% = 20%.
Let the monthly salary be Rs. x.
Then, 20% of x = 1500
⇔ 20 / 100x = 1500
⇔ x = 1500 × 5 = 7500.
Answer B
Answer: B
Question: (4300631)-?=2535618
Options:
A)1865113
B)1775123
C)1765013
D)1675123
E)None of them
Rationale: Let 4300631-x=2535618
then x=4300631-2535618
=1765013
Answer is C
Answer: C
Question: A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If four marbles are picked at random, what is the probability that none is blue?
Options:
A)33/98
B)33/91
C)33/92
D)33/96
E)33/93
Rationale: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles. When four marbles are picked at random, then the probability that none is blue is = ¹²C₄/¹⁵C₄
= (12 * 11 * 10 * 9)/(15 * 14 * 13 * 12)
= 33/91
Answer:B
Answer: B
Question: Krishna's monthly expenditure was decreased by 50% and subsequently increased by 50%. How much percent does he loss?
Options:
A)25 %
B)50 %
C)75 %
D)85 %
E)None of these
Rationale: Explanation :
Let the original expenditure = Rs. 100.
New final expenditure = 150% of (50% of Rs. 100)
= Rs.(150/10050/100100)
= Rs. 75.
Decrease = 100- 75 = 25 %
Answer : A
Answer: A
Question: In a school with 5 classes, each class has 2 students less then the previous class. How many students are there in the largest class if the total number of students at school is 95?
Options:
A)17
B)19
C)21
D)23
E)25
Rationale: Total classes = 5
Total students = 95.
Average = 19
If the classes had average number of students: 19 19 19 19 19
Given case = 23 21 19 17 15
Hence number of students in the largest class = 23
Correct Option: D
Answer: D
Question: A lent Rs. 5000 to B for 2 years and Rs. 3000 to C for 4 years on simple interest at the same rate of interest and received Rs. 2200 in all from both of them as interest. The rate of interest per annum is?
Options:
A)16%
B)12%
C)74%
D)10%
E)45%
Rationale: Let the rate be R% p.a. Then,
(5000 * R * 2)/100 + (3000 * R * 4)/100 = 2200
100 R + 120 R = 2200
R = 10%
Answer:D
Answer: D
Question: A merchant gains or loses, in a bargain, a certain sum. In a second bargain, he gains 280 dollars, and, in a third, loses 20. In the end he finds he has gained 120 dollars, by the three together. How much did he gain or lose bv the first ?
Options:
A)80
B)-140
C)140
D)120
E)None
Rationale: In this sum, as the profit and loss are opposite in their nature, they must be distinguished by contrary signs. If the profit is marked +, the loss must be -.
Let x = the sum required.
Then according to the statement x + 280 - 20 = 120
And x = -140.
Answer B
Answer: B
Question: Five bells begin to toll together and toll respectively at intervals of 6, 5, 7, 10 and 12 seconds. How many times will they toll together in one hour excluding the one at the start ?
Options:
A)7 times
B)8 times
C)9 times
D)11 times
E)12 times
Rationale: Explanation:
L.C.M. of 6, 5, 7, 10 and 12 is 420.
So, the bells will toll together after every 420 seconds i.e. 7 minutes.
Now, 7 x 8 = 56 and 7 x 9 = 63.
Thus, in 1-hour (or 60 minutes), the bells will toll together 8 times, excluding the one at the start.
Answer: B
Answer: B
Question: Find the sum lend at C.I. at 5 p.c per annum will amount to Rs.441 in 2 years?
Options:
A)198
B)400
C)268
D)267
E)256
Rationale: 441
= P(21/20)2
P = 400
Answer:B
Answer: B
Question: Set J consists of the terms {a, b, c, d, e}, where e > d > c > b > a > 3. Which of the following operations would decrease the standard deviation of Set J?
Options:
A)Multiply each term by e/d
B)Divide each term by b/c
C)Multiply each term by −1/2
D)Divide each term by d/e
E)Multiply each term by c/e
Rationale: CONCEPT: Standard Deviation is Defined as Average Deviation of Terms in the set from the Mean value of the set. i.e.
1) It depends on the separation between the successive terms of the set
2) If a Constant Value is Added/Subtracted in every terms of set then the Separation between successive terms does NOT change Hence S.D. remains Constant
3) If a Constant Value is Multiplied in every terms then the Separation between succesive terms gets multiplied by the constant Hence S.D. remains gets multiplied by same Number
C
Answer: C
Question: The population of a town is 7900. It decreases annually at the rate of 10% p.a. What was its population 2 years ago?
Options:
A)9750
B)8000
C)8500
D)9500
E)10000
Rationale: Formula :
( After =100 denominator
Ago = 100 numerator)
7900 Ã— 100/90 Ã— 100/90 = 9753
A)
Answer: A
Question: Two trains are running at 40 km/hr and 20 km/hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 9 sec. What is the length of the fast train?
Options:
A)27 7/6
B)27
C)27 7/2
D)50
E)27 7/1
Rationale: Relative speed = (40 - 20) = 20 km/hr.
= 20 * 5/ 18 = 50/9 m/sec.
Length of faster train = 50/9 * 9 = 50 m
Answer:D
Answer: D
Question: When 0.252525...........is converted into a fraction, then find the result.
Options:
A)25/99
B)25/90
C)25/999
D)25/9999
E)None
Rationale: Answer
0.252525 ..... = 0.25= 25/99
Correct Option: A
Answer: A
Question: To apply for the position of photographer at a local magazine, a photographer needs to include three or four photos in an envelope accompanying the application. If the photographer has pre-selected seven photos representative of her work, how many choices does she have to provide the photos for the magazine?
Options:
A)54
B)60
C)64
D)70
E)75
Rationale: 7C3 + 7C4 = 35 + 35 = 70
The answer is D.
Answer: D
Question: A can do a work in 7 days and B in 12 days. If they work on it together then in how many days required to complete the work?
Options:
A)83/19
B)84/19
C)81/19
D)77/19
E)87/19
Rationale: Person ( A ) ( B ) ( A+B )
Time - ( 7 ) ( 12 ) (84/19)
Rate - ( 12 ) ( 7 ) ( 19 )
Work - (84) ( 84 ) ( 84 )
therefore A+B requires (84/19) days to complete entire work
= 84/19
Answer is B
Answer: B
Question: Pat will walk from intersection A to intersection B along a route that is confined to the square grid of four streets and three avenues shown in the map above. How many routes from A to B can Pat take that have the minimum possible length?
Options:
A)6
B)8
C)10
D)14
E)16
Rationale: Consider this a as coordinate plane with A as origin and B as (2,3).
The shortest possible way is when you go take either right or up. (lefts and downs make repetitions and thus non shortest paths)
now, to get to (2,3) form (0,0) you need min 5 steps.
so you have to choose all the paths such that you have 2 steps out of 5 along x axis and getting to 3 of y axis.
The number of ways = 5C2 =10
(or alternately all paths that have 3 steps along y and takes you to 2 of x. .. 5C3 = 10)
Can you explicate your combinatorial method a bit more. For example, If I add another Avenue, eg, Avenue D, and another street, Street 5, I will have to go 3 steps right and 4 steps up to get to point C.
In order the length to be minimum Pat should only go UP and RIGHT: namely thrice UP and twice RIGHT.
So combination of UUURR: # of permutations of 5 letters out of which there are 3 identical U's and 2 identical R's is 5!/3!2!=10.
Answer: C.
Answer: C
Question: A person can row upstream 2 kmph and downstream 8 kmph. Find the rate of the stream and person rate in still water.
Options:
A)1,5
B)2,5
C)5,5
D)3,5
E)5,1
Rationale: Explanation:
Please remember,
If a is rate downstream and b is rate upstream
Rate of current = 1/2(a-b)
Rate in still water = 1/2(a+b)
=> Rate of current = 1/2(8-2) = 3 kmph
=> Rate in still water = 1/2(8+2) = 5 kmph
Option D
Answer: D
Question: Which of the following points is symmetric with y=x at (4,5)?
Options:
A)(-2,-1)
B)(-2,1)
C)(2,1)
D)(-1,-2)
E)(5,4)
Rationale: We can think of line y = x as a mirror. Any point (x,y) becomes (y,x) when it isreflectedover the mirror. Reverse the coordinate and keep the same sign. These two points will be symmetric to the line y = x.
(4,5) would become (5,4).
Answer (E).
Answer: E
Question: In a certain game, each player scores either 2 or 5 points. If n players score 2 points and m players score 5 points and the total number of points scored is 55, what is the least possible difference between n and m.
Options:
A)a.1
B)b.3
C)c.4
D)d.7
E)e.9
Rationale: 2n+5m=55
try with n=5 and m=8 the equation will be satisfied
2(5)+5(9)=55
so difference between M and N is 4,
Answer C
Answer: C
Question: Hendrix works 20 days a month at d dollars per day for m months out of the year. Which of the following represents his 5 year pay?
Options:
A)m/(20d*5)
B)100md
C)50md/6
D)20d/5m
E)20d/5
Rationale: Total income of Amber in a year = d*20*m dollars. Now 5 year income = Total*5= d*20*m *5 = 100md Answer is B
Answer: B
Question: On January 1, 2010, Dave invests 70% of his retirement savings in Antarctic largecap stocks, 20% in Antarctic midcaps, and 10% in Antarctic smallcaps. In 2010, largecaps rise 5%, midcaps rise 10%, and smallcaps rise 15% in the Antarctic stock market; however, in 2011, largecaps fall 10% and midcaps fall 20%, while smallcaps rise x% in Antarctica. If, on January 1, 2012, Dave has the same total amount of retirement savings as he did two years before, then x is between
Options:
A)10 and 20
B)20 and 30
C)30 and 40
D)40 and 50
E)50 and 60
Rationale: Here are the starting values:
L = $7,000
M = $2,000
S = $1,000
Apply the first year’s changes, so that you have these numbers on 1/1/2011:
Newer L = $7,000 + 5% = $7,350
Newer M = $2,000 + 10% = $2,200
Newer S = $1,000 + 15% = $1,150
Now apply the second year’s changes to L and M:
Newest L = $7,350 – 10% = $7,350 – $735 = $6,615
Newest M = $2,200 – 20% = $2,200 – $440 = $1,760
Add these to get $8,375. So the newest S must be $10,000 (the target final total of Dave’s retirement savings) minus $8,375, or $1,625.
The dollar change in S from 1/1/11 to 1/1/12 is $1,625 – $1,150 = $475. So the question is this: what percent change does $475 represent, from a starting point of $1,150? Since $1,150 is a nasty divisor, switch to benchmarks:
10% of $1,150 = $115.
So 20% is just double that, or $230.
And 40% is double that, or $460.
Since $475 is just slightly larger than $460 (but not enough to get you to 50%, which would be $460 + $115), x must be between 40 and 50.
Intuitively, it should make sense that you’d need a much bigger positive percent change in the smallest investment (S) to make up for even a moderate downturn in the larger investments (L and M), so if you were completely stuck for time and needed to guess in a hurry, you should favor C/D/E over A or B.
The correct answer is D.
Answer: D
Question: A plane was originally flying at an altitude of x feet when it ascended 2,000 feet and then descended 5,000 feet. If the plane's altitude after these two changes was 1/2 its original altitude, then the solution of which of the following equations gives the plane's original altitude, in feet ?
Options:
A)x + 2000 = 1/3*(x - 3000)
B)1/3*(x - 3000) = x
C)x - 3000 = 1/2*x
D)x - 7000 = 1/3*x
E)x - 3000 = 1/3*x
Rationale: Plane's original altitude = x
Plane's new altitude after ascending 2000 ft = x+2000
Plane's new altitude after descending 5000 ft from previous altitude = x+2000-5000 = x-3000
So, after two changes plane is at 1/2 its original altitude => x-3000 = x/2
Answer (C)
Answer: C
Question: If a light flashes every 6 seconds, how many times will it flash in 2/5 of an hour?
Options:
A)181
B)211
C)241
D)271
E)301
Rationale: In 2/5 of an hour there are 24*60 = 1440 seconds
The number of 6-second intervals = 1440/6 = 240
After the first flash, there will be 240 more flashes for a total of 241.
The answer is C.
Answer: C
Question: Find a if (ax3 + 3x2 - 3) and (2x3 - 5x + a) when divided by (x-4) leave same rmainder?
Options:
A)1
B)3
C)4
D)5
E)6
Rationale: remainders are,
R1 = f(4) = a(4)3+ 3(4)2-3= 64a+45
R2 = f(4) = 2(4)3- 5(4) + a= a +108
Since R1= R2
64a +45= a+108 => 63a = 63 => a =1
A
Answer: A
Question: A student can select one of 9 different math book, one of 3 different chemistry book & one of 4 different science book.In how many different ways students can select book of math, chemistry & science.
Options:
A)22
B)72
C)99
D)37
E)108
Rationale: 9C1×3C1×4C1= 9x3x4=108 ways
Answer:E
Answer: E
Question: Find the percentage gain if a shop owner sells 18 mtr of fabric and gains Cost Price of 3 meters?
Options:
A)17.67%
B)19.67%
C)11.67%
D)16.67%
E)15.67%
Rationale: Let cost of each metre be Rs. 100.
Therefore, cost price of 3m cloth = 3*100 =300
cost price of 18m cloth = 18*100 = 1800
Since the trader made the CP of 3m from the sale of 18m therefore
Profit on sale of 18m = cost price of 3 m cloth = 300
Selling price of 18m = 1800+300 = 2100
Profit % = 16.67%
D
Answer: D
Question: By selling a book for 260, 20% profit was earned. What is the cost price of the book?
Options:
A)A)215
B)B)216
C)C)230
D)D)235
E)E)240
Rationale: SP = 120% of CP; :. CP = 260 × 100/120 = 216
Option 'B'
Answer: B