divelab/Sys2Bench huggingface dataset:
Question: An airline passenger is planning a trip that involves three connecting flights that leave from airports A, B and C, respectively. The First flight leaves Airport A every Hour, beginning at 8:00 a.m., and arrives at Airport B 2nd a half hours later. The second flight leaves Airport B every 20minutes, beginning at 8:00a.m, and arrives at Airport C 1h 10 minutes later. The third flight leaves Airport C every hour, beginning at 8.45 a.m. What is the least total amount of time the passenger must spend between flights if all flights keep to their schedules?
Options:
A)25min
B)1hr 5min
C)1hr 15min
D)2hr 20min
E)3hr 40min
Rationale: Following way may not be a pure mathematical approach to solve it but it got me the result within a minute.
A: Flight leaves every hour; 8,9,10,11,12,1,2,3
B: Flight leaves every 20min; 8:20,8:40,9,9:20,9:40,10,10:20,10:40,11
C: Flight leaves every hour: 8:45,9:45,10:45,11:45,12:45
Passenger leaves at 8:00AM from A; reaches B@ 10:30am - he will catch 10:40am flight from B{10 minutes spent at airport B}; reaches c after 1hour10minutes @11:50AM;his next flight at C is at 12:45 - he waits another 55minutes;
Total wait = 10+55= 65 minutes = 1hour 5 mins
Ans:B
Answer: B
Question: Divide Rs.118000 among three persons A, B and C such that the ratio of the shares of A and B is 3:4 and that of B:C is 5:6?
Options:
A)A = 30000 B = 40000 C = 48000
B)A = 30000 B = 40000 C = 48030
C)A = 30000 B = 40070 C = 48000
D)A = 30000 B = 40000 C = 48300
E)A = 30200 B = 40000 C = 48000
Rationale: Compound ratio of A:B:C
A:B = 3:4
B:C = 5:6
----------
A:B:C = 15:20:24
We can divide Rs.118000 in this ratio.
Share of A = 15/59 * 118000 = 30000
Share of B = 20/59 * 118000 = 40000
Share of C = 24/59 * 118000 = 48000
Answer: A
Answer: A
Question: If 0 < x ≤ 2, then which one of the following is the maximum value of (x – 1)^2 + x ?
Options:
A)–2
B)–1
C)0
D)2
E)3
Rationale: If you cannot spot that the maximum value of (x – 1)^2 + x for 0 < x ≤ 2 is when x=2 --> (x – 1)^2 + x = 2 you can do the following:
Since 0 < x ≤ 2, then (x – 1)^2 + x is positive --> discard A, B and C.
For the same reason: (x – 1)^2 is a non-negative fraction less than 1.
Thus (x – 1)^2 + x = (non-negative fraction less than 1) + (0 < x ≤ 2) < 3. Discard E.
Only D is left.
Answer: D.
Answer: D
Question: Find the odd man out
2, 5, 14, 41, 122, 365, 1125
Options:
A)2
B)14
C)41
D)365
E)1125
Rationale: 1*3-1 = 2
2*3-1 = 5
5*3-1 = 14
14*3-1 = 41
41*3-1 = 122
122*3-1= 365
365*3-1= 1094
ANSWER:E
Answer: E
Question: A and B started business in partnership investing Rs. 20,000 and Rs. 15,000 respectively. After six months, C joined them with Rs. 20,000. What will be B's share in the total profit of Rs. 25,000 earned at the end of 2 years from the starting of the business?
Options:
A)Rs.7500
B)Rs.7502
C)Rs.7529
D)Rs.7596
E)Rs.7506
Rationale: A:B:C = (20000 * 24) : (15000 * 24) : (20000 * 18)
= 4:3:3
B's share = 25000 * 3/10
= Rs.7500.
Answer:A
Answer: A
Question: How much time will it take for an amount of Rs. 450 to yield Rs. 81 as interest at 4.5% per annum of simple interest?
Options:
A)8 years
B)4 years
C)7 years
D)6 years
E)2 years
Rationale: Explanation:
Time = (100 x 81)/(450 x 4.5) years
= 4 years.
Answer: B
Answer: B
Question: You add x ml of a 25% alcohol solution to a 200 ml of a 10% alcohol solution to obtain another solution. Find the amount of alcohol in the final solution in terms of x. Find the ratio, in terms of x, of the alcohol in the final solution to the total amount of the solution. What do you think will happen if x is very large? Find x so that the final solution has a percentage of 15%.
Options:
A)100 ml
B)200 ml
C)300 ml
D)400 ml
E)500 ml
Rationale: Let us first find the amount of alcohol in the 10% solution of 200 ml.
200 * 10% = 20 ml
The amount of alcohol in the x ml of 25% solution is given by
25% x = 0.25 x
The total amount of alcohol in the final solution is given by
20 + 0.25 x
The ratio of alcohol in the final solution to the total amount of the solution is given by
[ ( 20 + 0.25 x ) / (x + 200)]
If x becomes very large in the above formula for the ratio, then the ratio becomes close to 0.25 or 25% (The above function is a rational function and 0.25 is its horizontal asymptote). This means that if you increase the amount x of the 25% solution, this will dominate and the final solution will be very close to a 25% solution.
To have a percentage of 15%, we need to have
[ ( 20 + 0.25 x ) / (x + 200)] = 15% = 0.15
Solve the above equation for x
20 + 0.25 x = 0.15 * (x + 200)
x = 100 ml
Answer A
Answer: A
Question: Find the third proportional to 2 and 10?
Options:
A)10
B)12
C)16
D)19
E)50
Rationale: Formula = Third proportional = (b × b)/a
A = 2 and B = 10
(10 × 10)/ 2 = 100/2 = 50
E
Answer: E
Question: John has 10 pairs of matched socks. If he loses 3 individual socks, what is the greatest number of pairs of matched socks he can have left?
Options:
A) 7
B) 8
C) 5
D) 4
E) 3
Rationale: Because we have to maximize the pair of matched socks, we will remove 1 pairs(2 socks) out of 10 pairs 1 sock from the 2th pair.
Thus the no of matching socks pair remaining = 10 - 2 = 8
Answer B
Answer: B
Question: 16384, 8192, 2048, 256, 16, ?
Options:
A)0.3
B)9.0
C)0.5
D)1.0
E)2.0
Rationale: 16384
16384 ÷ 2 = 8192
8192 ÷ 4 = 2048
2048 ÷ 8 = 256
256 ÷ 16 = 16
16 ÷ 32 = 0.5
Answer is C
Answer: C
Question: An advertising agency finds that, of its 170 clients, 115 use Television, 110 use Radio and 130 use Magazines. Also, 85 use Television and Magazines, 75 use Television and Radio, 95 use Radio and Magazines. How many use all the three?
Options:
A)56
B)70
C)90
D)98
E)95
Rationale: Total=170
Television=115
Radio=110
Magazine=130
All the three =170-115-110-130+85+75+95=70
ANSWER B
Answer: B
Question: The average height of 50 pupils in a class is 150 cm. Five of them whose height is 146 cm, leave the class and five others whose average height is 156 cm, join. The new average height of the pupils of the class (in cm) is?
Options:
A)718 cm
B)151 cm
C)627 cm
D)282 cm
E)636 cm
Rationale: Total height = 150 * 50 = 7500 cm.
New average
= [7500 - 5 * 146 + 5 * 156 ] / 50 = 151 cm.
Answer:B
Answer: B
Question: A jogger running at 9 km/hr along side a railway track is 240 m ahead of the engine of a 120 m long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger?
Options:
A)76 sec
B)67 sec
C)98 sec
D)36 sec
E)23 sec
Rationale: Speed of train relative to jogger = 45 - 9 = 36 km/hr.
= 36 * 5/18 = 10 m/sec.
Distance to be covered = 240 + 120 = 360 m.
Time taken = 360/10 =36 sec.
Answer:C
Answer: C
Question: If p is an odd integer and q is an even integer, which of the following must be an odd integer?
Options:
A)2q+2p
B)3(2p-q)
C)p^2+q^2
D)p+q+3
E)5p-2q+1
Rationale: p is odd; for this assume p=1
q is even; for this assume q = 2
(2*1)+(2*2) = 6 Even
3((2*1)-2) = 0 Even
1^2+2^2 = 5 Odd
1+2+3 = 6 Even
(5*1)-(2*2)+1 = 2 Even
Answer:C
Answer: C
Question: Suresh borrowed some money at the rate of 6% p.a. for the first three years, 9% p.a. for the next five years and 13% p.a. for the period beyond eight years. If the total interest paid by him at the end of 11 years is Rs.8160, how much money did he borrow?
Options:
A)Rs.8500
B)Rs.6000
C)Rs.8000
D)Rs.9000
E)Rs.7000
Rationale: using the formula S.I=P*T*R/100
(x*6*3/100)+(x*9*5/100)+(x*13*3/100)=8160
x=8000
i.e money borrowed is Rs.8000
ANSWER:C
Answer: C
Question: If xy not equal 0 and x^2*y^2 -xy = 12, which of the following could be y in terms of x?
I. 1/2x
II. -4/x
III. 3/x
Options:
A)II and III
B)II
C)III
D)IV
E)I &II
Rationale: x2y2 - xy = 12
x2y2-xy-12 = 0
(xy-3)(xy+4)=0
xy = 3 or xy=-4
y = 3/x or y = -4/x
II and III only
A
Answer: A
Question: A reduction of 20% in the price of salt enables a lady to obtain 10kgs more for Rs.300, find the original price per kg?
Options:
A)s.7.7
B)s.7.4
C)s.7.5
D)s.7.1
E)s.7.9
Rationale: 100*(20/100) = 20 --- 10
? --- 1 => Rs.2
300 --- 80
? --- 2 => Rs.7.5
Answer:C
Answer: C
Question: One side of a rectangle is 3 cm shorter than the other side. If we increase the length of each side by 1 cm, then the area of the rectangle will increase by 18 cm2. Find the lengths of all sides.
Options:
A)4
B)56
C)6
D)7
E)9
Rationale: Let xx be the length of the longer side x>3x>3, then the other side's length is x−3x−3 cm. Then the area is S1 = x(x - 3) cm2. After we increase the lengths of the sides they will become (x+1)(x+1) and (x−3+1)=(x−2)(x−3+1)=(x−2) cm long. Hence the area of the new rectangle will be A2=(x+1)⋅(x−2)A2=(x+1)⋅(x−2) cm2, which is 18 cm2 more than the first area. Therefore
A1+18=A2A1+18=A2
x(x−3)+18=(x+1)(x−2)x(x−3)+18=(x+1)(x−2)
x2−3x+18=x2+x−2x−2x2−3x+18=x2+x−2x−2
2x=202x=20
x=10x=10. So, the sides of the rectangle are 1010 cm and (10−3)=7(10−3)=7 cm long.
Answer:	E
Answer: E
Question: A bottle is 80% full. The liquid in the bottle consists of 60% guava juice and 40% pineapple juice. The remainder of the bottle is then filled with 70 lm of rum. How much guava is in the bottle?
Options:
A)155 ml
B)158 ml
C)165 ml
D)168 ml
E)175 ml
Rationale: if the Bottle is 100ml:
we have 48% Guava, 32% Pineapple, and 20% Rum.
Now, is the bottle 20% of rum is represented by 70 ml. So, we have to find for the same bottle 48% guava is what ml?
therefore, Guava= (70*48)/20= 168 ml
ANSWER:C
Answer: C
Question: The cost of 16 pens and 8 pencils is Rs.352 and the cost of 4 pens and 4 pencils is Rs.96. Find the cost of each pen?
Options:
A)33
B)88
C)66
D)88
E)20
Rationale: Let the cost of each pen and pencil be 'p' and 'q' respectively.
16p + 8q = 352 --- (1)
4p + 4q = 96
8p + 8q = 192 --- (2)
(1) - (2) => 8p = 160
=> p = 20
Answer: E
Answer: E
Question: Which of the following will divide evenly into 607,406,520?
Options:
A)13
B)21
C)11
D)3
E)none of these
Rationale: Rule:
3: Sum of the digits should be divisible by 3
Given number : 6+7+4+6+5+2 = 30
Answer : D
Answer: D
Question: Find the mode of the given set of number
2, 2, 3, 5, 4, 3, 2, 3, 3, 5
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: Arranging the number with same values together, we get
2, 2, 2, 3, 3, 3, 3, 4, 5, 5
We observe that 3 occurs maximum number of times, i.e., four.
Therefore, mode of this data is 3. ANSWER :C
Answer: C
Question: The cash difference between the selling prices of an article at a profit of 4% and 8% is Rs. 3. The ratio of the two selling prices is?
Options:
A)52:56
B)52:53
C)52:54
D)22:56
E)52:51
Rationale: Let C.P. of the article be Rs. x.
Then, required ratio = 104% of x / 108% of x
= 104/108 = 52/54 = 52:54
Answer: C
Answer: C
Question: What is the unit’s digit of 7^7
Options:
A)9
B)5
C)3
D)7
E)1
Rationale: 7^1=7
7^2=49
7^3=343
7^4=1(last digit)
7^5=7(last digit) and the cycle repeats after every 4 powers
Therefore, last digit of 7^7=3
Answer C
Answer: C
Question: Ravi and sunil are partners in a business. Ravi invests Rs.15,000 for 8 months and Sunil invested Rs.8000 for 10 months then after one year ratio of their profits will be
Options:
A)1:3
B)2:3
C)3:2
D)3:1
E)3:4
Rationale: =(15000*8):(8000*10)
=120000:80000
=3:2
ANSWER:C
Answer: C
Question: Three walls have wallpaper covering a combined area of 280 square meters. By overlapping the wallpaper to cover a wall with an area of 180 square meters, the area that is covered by exactly two layers of wallpaper is 36 square meters. What is the area that is covered with three layers of wallpaper?
Options:
A)5 Square Meters
B)32 Square Meters
C)42 Square Meters
D)83.3 Square Meters
E)120 Square Meters
Rationale: 280 - 180 = 100 sq m of the wallpaper overlaps (in either two layers or three layers)
If 36 sq m has two layers, 100 - 36 = 64 sq m of the wallpaper overlaps in three layers. 64 sq m makes two extra layers hence the area over which it makes two extra layers is 32 sq m.
Answer (B).
Answer: B
Question: Which number should replace both the asterisks in (* /20) x (*/180) = 1 ?
Options:
A)20
B)40
C)60
D)90
E)120
Rationale: Let (y/20) x (y/180) = 1
y^2 = 20 x 180 = 20 x 20 x 9
y = (20 x 3) = 60
The answer is C.
Answer: C
Question: A rectangular field has to be fenced on three sides leaving a side of 20 feet uncovered. If the area of the field is 680 sq. feet, how many feet of fencing will be required?
Options:
A)88 Feet
B)66 Feet
C)77 Feet
D)99 Feet
E)55 Feet
Rationale: A
88 Feet
Area of the field =680 sq. feet.
Length of the adjacent sides are
20 feet and 680/20=34 feet.
Required length of the fencing
=20+34+34=88 feet
Answer: A
Question: Which of the following equations represents a line that is perpendicular to y=1/2*x+1?
Options:
A)y−2x=8
B)2x+4y=10
C)3y+6x=12
D)4y−8x=16
E)5x−10y=20
Rationale: For two lines to be perpendicular, the product of slopes should be equal to -1.
Slope of line 1 = 1/2
Slope of the line perpendicular to line 1 must be -2. Option C can be rewritten as y = -2x + 4 --> Slope = -2
Answer: A
Answer: A
Question: Find the circumference and area of radius 6 cm.
Options:
A)113 cm²
B)144 cm²
C)154 cm²
D)184 cm²
E)194 cm²
Rationale: Area of circle = πr²
= 22/7 × 6 × 6 cm²
= 113 cm²
ANSWER:A
Answer: A
Question: How many cubes of 4 cm edge can be put in a cubical box of 1 m edge.
Options:
A)17725 cm
B)15625 cm
C)12786 cm
D)12617 cm
E)12187 cm
Rationale: Number of cubes =100âˆ—100âˆ—100/4*4*4=15625
Note: 1 m = 100 cm
Answer:B
Answer: B
Question: Rita and Sam play the following game with n sticks on a table. Each must remove 1,2,3,4, or 5 sticks at a time on alternate turns, and no stick that is removed is put back on the table. Tha one who removes the last stick (or sticks) from the table wins. If Rita goes first, which of the following is a value of n such that Sam can always win no matter how Rita plays?
Options:
A)7
B)10
C)11
D)12
E)16
Rationale: If the number of sticks on a table is a multiple of 6, then the second player will win in any case (well if the player is smart enough).
Consider n=6, no matter how many sticks will be removed by the first player (1, 2, 3 ,4 or 5), the rest (5, 4, 3, 2, or 1) can be removed by the second one.
The same for n=12: no matter how many sticks will be removed by the first player 1, 2, 3 ,4 or 5, the second one can remove 5, 4, 3, 2, or 1 so that to leave 6 sticks on the table and we are back to the case we discussed above.
Answer: D.
Answer: D
Question: Aparna cuts a cake into two halves and cuts one-half into smaller pieces of equal size. Each of the small pieces is twenty grams in weight. If she has seven pieces of the cake in all with her, how heavy was the original cake?
Options:
A)140 grams
B)280 grams
C)240 grams
D)120 grams
E)None of these
Rationale: one cake =1/2 + 1/2
1/2------6 pieces
total pieces = (1/2)cake +(6 pieces of 1/2) = 7 pieces
then 6 small picese weight = half piece cake
So 2*(6*20) =240
ANSWER:C
Answer: C
Question: How many Books each of Volume 200 meter cube can be packed into a crate of volume 4000 meter cube?
Options:
A)20
B)40
C)60
D)80
E)cannot be determined
Rationale: Gud question with a simple concept.
In geo if we want to insert one shape into another we need to know the dimensions of the two shapes.
In above with volume given , we can come up with different shapes, so we cant know the answer
For ex :4000 m3 can be 400*10 or 40*100 or just 4000*1 we don't know , so we cant calculate
Answer : E
Answer: E
Question: Steve traveled the first 2 hours of his journey at 50 mph and the last 3 hours of his journey at 80 mph. What is his average speed of travel for the entire journey?
Options:
A)60 mph
B)68 mph
C)53.33 mph
D)64 mph
E)66.67 mph
Rationale: Answer
Average speed of travel = Total distance travelled/Total time taken
Total distance traveled by Steve = Distance covered in the first 2 hours + distance covered in the next 3 hours.
Distance covered in the first 2 hours = speed * time = 50 * 2 = 100 miles.
Distance covered in the next 3 hours = speed * time = 80 * 3 = 240 miles.
Therefore, total distance covered = 100 + 240 = 340 miles.
Total time taken = 2 + 3 = 5 hours.
Hence, average speed = Total distance travelled/Total time taken=340/5 = 68 miles per hour.
Choice B
Answer: B
Question: In a rectangular coordinate system, what is the area of a rhombus whose vertices have the coordinates (0, 3.5), (10, 0), (0, -3.5), (-10, 0)?
Options:
A)56
B)88
C)70
D)116
E)120
Rationale: Area of rhombus= 1/2* D1 *D2
Length of 1st diagonal = 10+10= 20
Length of 2nd diagonal= 3.5+3.5= 7
Area= 1/2*20*7= 70
C is the answer
Answer: C
Question: Two painters 'P1' & 'P2' paint the bungalow in 3 days. If P1 alone can paint the bungalow in 12 days, in how many days can 'P2'' alone complete the same paint work?
Options:
A)4 days
B)6 days
C)9 days
D)12 days
E)15 days
Rationale: EXPLANATION:
Hint:
If a person can do a part of work in 'n' days, then person's work in 1 day =	1/n
As painters P1 & P2 paint the bungalows in 3 days, then work done by both painters =	1/3
As P1 paint it alone in 12 days, then work done by painter P1 =	1/12
Work done by painter P2 =	1/3	–	1/12	=	4 – 1/12	=	3/12	=	1/4
Therefore, same work will be completed by painter P2 in 4 days.
ANSWER IS A
Answer: A
Question: Let q represent the integer length of a side of a triangle. If r represents the number of distinct values for q such that we can create a triangle with lengths q, 12, and 16, what is the value of r?
Options:
A)18
B)20
C)22
D)23
E)24
Rationale: From the triangle inequality rule, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. So, the three inequalities are:
1. q + 12 > 16
2. 12 + 16 > q
3. q + 16 > 12
Equation 3 is true for any positive value of q.
From equation 1, q > 4
From equation 2, 28 > q
Then 28 > q > 4 so q can be any value from 5 to 27 inclusive.
The number of possible values is 23.
The answer is D.
Answer: D
Question: A number when successively divided by 3,5 and 8 leaves remainders 1,4 and 7 respectively. Find the respective remainders Q when the order of the divisors is reversed.
Options:
A)8,5,3
B)4,2,1
C)Q=3,2,1
D)Q=6,4,2
E)None of above
Rationale: My approach would be
Three Divisors: 3, 5, 8
Three Remain: 1, 4, 7
Start from the bottom of the last column i.e. from the third remainder:
Go up diagonally and multiply by the second divisor: 5*7 = 35
Go down and add the second remainder: 35 + 4 = 39
Go up diagonally and multiply by the first divisor: 39* 3 = 117
Go down and add the first remainder: 117 + 1 = 118
Divide 118 by 8, 5, 3
118/8 gives quotient = 14 and remainder = 6
14/5 gives quotient = 2 and remainder = 4
2/3 gives quotient = 0 and remainder = 2
Ans is D i.e. 6,4,2
Answer: D
Question: If the numerator of a fraction is increased by 50% and denominator by 20%, the fraction become 9/15. What was the original fraction ?
Options:
A)12/25
B)13/25
C)3/5
D)6/7
E)7/8
Rationale: Explanation :
Let the fraction be x/y
We have 150x/120y = 9/15
= x/y = 12/25
Answer : Option A
Answer: A
Question: A 300 meter long train crosses a platform in 27 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform?
Options:
A)150m
B)278m
C)350m
D)228m
E)282m
Rationale: Speed = [300 / 18] m/sec = 50/3 m/sec.
Let the length of the platform be x meters.
Then, x + 300 / 27
= 50/3
3(x + 300)
= 1350 è x
= 150m.
Answer:A
Answer: A
Question: On June 1 a bicycle dealer noted that the number of bicycles in stock had decreased by 3 for each of the past 5 months. If the stock continues to decrease at the same rate for the rest of the year, how many fewer bicycles will be in stock on September 1 than were in stock on January 1?
Options:
A) 8
B) 12
C) 24
D) 32
E) 36
Rationale: Jan 1 = C
Feb 1 = C - 3
March 1 = C - 6
April 1 = C - 9
May 1 = C - 12
June 1 = C - 15
July 1 = C - 18
Aug 1 = C - 21
Sept 1 = C - 24
Difference between stock on September 1 than were in stock on January 1 will be -
C - ( C - 24 )= 24
Hence answer will be (C)
Answer: C
Question: A rectangular-shaped carpet remnant that measures x feet by y feet is priced at $40. What is the cost of the carpet, in dollars per square yard? (9 square feet = 1 square yard)
Options:
A)50xy
B)450xy
C)xy/9
D)xy/50
E)360/(xy)
Rationale: xy sq ft = $40
1 sq ft = $40/xy
multiplying by 9 on both side
9 sq ft = $360/xy
or 1 sq yard = $360/xy
Hence E.
Answer: E
Question: If the cost price of 20 articles is equal to the selling price of 25 articles, what is the % profit or loss made by the merchant?
Options:
A)25% loss
B)20% loss
C)25% Profit
D)20% Profit
E)5% profit
Rationale: Let the cost price of 1 article be Rs. 1.
Therefore, cost price of 20 articles = 20 * 1 = Rs. 20
The selling price of 25 articles = cost price of 20 articles = Rs. 20.
Let us find the cost price of 25 articles.
Cost price of 25 articles = 25 * 1 = Rs. 25.
Therefore, profit made on sale of 25 articles = Selling price of 25 articles - cost price of 25 articles
= 20 - 25 = -Rs. 5.
Because the profit is in the negative, the merchant has made a loss of Rs.5.
Therefore, % loss = Loss /Cost Price∗100
% loss = 5/25∗100 =20% loss.
Answer : B
Answer: B
Question: By selling an article at Rs.800, a shopkeeper makes a profit of 25%. At what price should he sell the article so as to make a loss of 15%?
Options:
A)228
B)480
C)267
D)288
E)544
Rationale: SP = 800
Profit = 25%
CP = (SP)*[100/(100+P)]
= 800 * [100/125]
= 640
Loss = 25% = 25% of 640 = Rs.96
SP = CP - Loss = 640 - 96 = Rs.544
Answer: E
Answer: E
Question: 0---:-|---:--|-:--:-|--:---|-:----1
On the number line above, the segment from 0 to 1 has been divided into fifths, as indicated by the large tick marks, and also into sevenths, as indicated by the small tick marks. What is the LEAST possible distance W between any two of the tick marks?
Options:
A)1/70
B)1/35
C)2/35
D)1/12
E)1/7
Rationale: divisions are 0 1/7 2/7 3/7 4/7 5/7 6/7 1
1/5 2/5 3/5 4/5 5/5
expressing the same in terms of the lcm of 5,7 ,i.e 35
0 7/35 14/35 21/35 28/35 35/35
5/35 10/35 15/35 20/35 25/35 30/35
by comparing the divisions with each other we can see 1/35 is the shortest possible distance between any two selected divisions.
W=1/35
Answer is B.
Answer: B
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 5, 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?
Options:
A)28
B)30
C)38
D)38
E)38
Rationale: 39x = 5 + 12 + 15 + 19 + (x – 4)44
x = 25
Answer:B
Answer: B
Question: 7^1+7^2+7^3+.......+7^205. Find out how many numbers present which unit place contain 3?
Options:
A)78
B)51
C)11
D)27
E)99
Rationale: Units digits of first 4 terms are 7, 9, 3, 1. and this pattern repeats. So for every 4 terms we get one term with 3 in its unit digit. So there are total of 205/4 = 51 sets and each set contains one terms with 3 in its unit digit.
Ans is 51.
Answer:B
Answer: B
Question: In a bag, there are coins of 25 p, 10 p and 5 p in the ratio of 1 : 2 : 3. If there is Rs. 30 in all, how many 5 p coins are there?
Options:
A)50
B)200
C)100
D)250
E)150
Rationale: Let the number of 25 p, 10 p and 5 p coins be x, 2x, 3x respectively.
Then, sum of their values = Rs. ((25x/100) + (10 x 2x/100)+(5 x 3x)/100= Rs. 60x/100
Therefore, 60x/100 = 30
x = 30 x 100/60 = 50.
Hence, the number of 5 p coins = (3 x 50) = 150.
Answer is E.
Answer: E
Question: You roll two six sided dices together.
Can you calculate the probability that the first dice gives the number 2 while the second dice gives the number 5?
Options:
A)1/23
B)3/52
C)1/53
D)4/24
E)1/36
Rationale: E
1/36
Explanation:
The number of possibilities for the first as well as the second dice are 6 and 6 respectively. Therefore the total possibilities or outcome are 6 * 6 = 36.
Out of 36 outcomes, we need only one case i.e. the first gives 2 and the second gives 5.
Therefore, the probability will be 1 on 36 or 1/36.
Answer: E
Question: A jogger running at 9 km/hr along side a railway track is 240 m ahead of the engine of a 120 m long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger?
Options:
A)19 sec
B)87 sec
C)36 sec
D)16 sec
E)11 sec
Rationale: Speed of train relative to jogger = 45 - 9 = 36 km/hr.
= 36 * 5/18 = 10 m/sec.
Distance to be covered = 240 + 120 = 360 m.
Time taken = 360/10 = 36 sec.
Answer: C
Answer: C