divelab/Sys2Bench huggingface dataset:
Question: The length of a rectangualr hll is 5m more than its breadth. The area of the hall is 750 m. The length of the hall is
Options:
A)15 m
B)22.5 m
C)25 m
D)30 m
E)None
Rationale: Solution
Let the length = xmetres.
Then length = (x +5)metres.
Then,x(x +5)= 750
= x² + 5x - 750= 0
(x+30)(x-25)= 0
x=25.
Answer C
Answer: C
Question: Find the L.C.M of 12, 8, 24 and 16.
Options:
A)48
B)96
C)80
D)44
E)140
Rationale: Explanation:
2x3x2x2x2 = 48
Answer: Option A
Answer: A
Question: The Banker’s gain on a bill due 1 year hence at 12% per annum is Rs. 6. The true discount is:
Options:
A)30
B)40
C)50
D)60
E)None
Rationale: Sol.
T.D. = B.G. * 100 / R * T = Rs.[6 * 100 / 12 * 1] = Rs.50
Answer C
Answer: C
Question: A train covers a distance in 1 h 40 min, if it runs at a speed of 96 km/h on an average. Find the speed at which the train must run reduce the time of journey to 1 h 20 min.
Options:
A)120 km/h
B)90 km/h
C)144 km/h
D)150 km/h
E)160 km/h
Rationale: Distance= Speed x Time = 96 x (100/60) = 160 km
New time = 80/60 h = 4/3 h
New speed = 160 x 3/4 = 40 x 3 =120 km/h
Answer :A
Answer: A
Question: A tortoise is making its way to eat a piece of lettuce at a constant speed. On its way to the lettuce, it takes 10 seconds to walk past a grain of sand. It then passes a piece of wood 20 cm long in 30 seconds to get to the lettuce. What is the length of the tortoise?
Options:
A)4 cm
B)5 cm
C)7.5 cm
D)9 cm
E)10 cm
Rationale: Sol.Let the length of the tortoise be x centimetres and its speed be y cm/sec. Then, x / y = 10 ⇒ y = x / 10∴ (x + 20) / 30 = x / 10 ⇔ x = 10 cm. Answer E
Answer: E
Question: Stephanie, Regine, and Brian ran a 20 mile race. Stephanie and Regine's combined times exceeded Brian's time by exactly 2 hours. If nobody ran faster than 8 miles per hour, who could have won the race?
I. Stephanie
II. Regine,Brian
III.Regine
Options:
A)I only
B)II only
C)III only
D)I or II only
E)I, or III only
Rationale: Given that S+R=B+2, where S, R, and B are times in which Stephanie, Regine, and Brian completed the race.
Min time one could complete the race is 20/8=2.5 hours. Let's see if Brian could have won the race: if he ran at the fastest rate, he would complete the race in 2.5 hours, so combined time needed for Stephanie and Regine would be S+R=B+2=4.5 hours, which is not possible as sum of two must be more than or equal the twice the least time: 2*2.5=5. So Brian could not have won the race.
There is no reason to distinguish Stephanie and Regine so if one could have won the race, another also could. So both could have won the race.
Answer: E.
Answer: E
Question: Graph G has a line of symmetry of x = –1. Graph G passes through the point (3, 3). What is the x-coordinate of another point that must have a y-coordinate of 3?
Options:
A) –8
B) –7
C) –5
D) –4
E) 2
Rationale: Line of symmetry is X=-1; one point is (3,3)
Right side distance =1+3(distance from origin) = 4; therefore Left side distance should be same from line of symmetry =4;
therefore left side co-ordinate=4+ 1(distance from origin) = 5; as the X coordinate is in 2nd quadrant hence -5
Therefore answer is C
Answer: C
Question: A certain tax rate is $.32 per $100.00. What is the rate, expressed as a percent?
Options:
A)32%
B)3.2%
C)0.82%
D)0.032%
E)0.32%
Rationale: Here in question it is asking $.32 is what percent of $ 100.Suppose $ .32 is x% of 100 means
100* (x/100) = .32
Hence x = .32 %
So answer is E
Answer: E
Question: If a is an integer greater than 2 but less than 11 and b is an integer greater than 11 but less than 21, what is the range of a/b?
Options:
A)52/45
B)23/47
C)60/41
D)51/42
E)41/60
Rationale: The way to approach this problem is 2<a<11 and 11<b<21
Minimum possible value of a is 3 and maximum is 10
Minimum possible value of b is 12 and maximum is 20
Range = max a/min b - min a/max b
(Highest - lowest)
10/12 - 3/20 = 41/60
Hence E
Answer: E
Question: A man swims downstream 48 km and upstream 18 km taking 3 hours each time, what is the speed of the man in still water?
Options:
A)2
B)8
C)9
D)11
E)14
Rationale: 48 --- 3 DS = 16
? ---- 1
18 ---- 3 US = 6
? ---- 1 M = ?
M = (16 + 6)/2 = 11
Answer: D
Answer: D
Question: A shopkeeper sold some articles @ 35 per article and earned a profit of 40%. At what price each article should have been sold so that 60% profit was earned?
Options:
A)25
B)29
C)30
D)40
E)45
Rationale: SP = 140% of CP; :. CP = 35 × 100/140 = 25
Then, 60% of CP = 2.5 × 6 = 15
To set a profit of 60% the SP = 25 + 15 = 40.
Option 'D'
Answer: D
Question: The five sides of a pentagon have lengths of 2, 3, 4, 5 and 7 inches. Two pentagons are considered different only when the positions of the side lengths are different relative to each others. What is the total number of different possible pentagons that could be drawn using these five side lengths ?
Options:
A) 5
B) 15
C) 24
D) 32
E) 120
Rationale: CONCEPT: The number of ways to arrange n elements around a circular Manner is (n-1)!.
But the number of ways to arrange n elements in circular manner where the arrangement can be flipped around (e.g. Necklace, Garland, Bracelet) = (n-1)!/2.
The pentagon in the problem above can be flipped over (Clockwise Arrangement of Sides = Counter-clockwise arrangement), the number of distinct ways to arrange the 5 sides = (5-1)!/2 = 15.
Answer: option B
Answer: B
Question: The average of temperatures at noontime from Monday to Friday is 50; the lowest one is 42, what is the possible maximum range of the temperatures?
Options:
A)20
B)25
C)40
D)45
E)86
Rationale: there are 5 days so the sum of temperature can be 50*5=250
lowest is 42. to find the maximum range we can say the temperature was the lowest for 4 of the 5 days
so 4*42=168.
on the fifth day it is 250-168=281
range is therefore 128-42=86
answer E
Answer: E
Question: What is the place value of 7 in the numeral 55468?
Options:
A)5
B)50
C)5000
D)55
E)500
Rationale: place value of 5 = 5* 1000 = 5000
Answer is C
Answer: C
Question: The temperatures in degrees Celsius recorded at a certain specific point in the evening in various parts of a country were 10°, 5°, -2°, -1°, -5°, 15°. What is the median of these temperatures?
Options:
A)-2°C
B)-1°C
C)2°C
D)3°C
E)5°C
Rationale: Explanation:
To get the median first we need to sort the temperatures in ascending order:
-5°, -2°, -1°, 5°, 10°, 15°
When the number of values in a list is even, the median is the average of the middle two values in the list in this case -1 and 5, i.e. 2.
Answer: Option C
Answer: C
Question: 10 books are placed at random in a shelf. The probability that a pair of books will always be together is ?
Options:
A)1/8
B)1/2
C)1/5
D)1/5
E)1/3
Rationale: 10 books can be rearranged in 10! ways consider the two books taken as a pair then number of favourable ways of getting these two books together is 9! 2!
Required probability = 1/5
Answer:C
Answer: C
Question: what is the sum of the first 18 odd natural numbers
Options:
A)300
B)400
C)500
D)324
E)700
Rationale: sum of first n odd natural nuber is = n^2
so sum of the first 18 odd natural numbers=(18)^2=324
ans 324
ANSWER:D
Answer: D
Question: A tap can fill a tank in 16 minutes and another can empty it in 8 minutes. If the tank is already 1/2 full and both the taps are opened together, will the tank be filled or emptied? How long will it take before the tank is either filled completely or emptied completely as the case may be? .
Options:
A)Emptied; 16 mins
B)Filled; 8 mins
C)Emptied; 12 mins
D)Filled; 12 mins
E)None of These
Rationale: if A and B open together
since B can empty faster than A so tank will empty not fill.
the whole tank will empty in 16*8/(16-8)
=16 min
since tank is half so it will take only 8 min to empty.
ANSWER:E
Answer: E
Question: A person want to give his money of $4500 to his 3 children A,B,C in the ratio 2:3:4. What is the B's share?
Options:
A)$2000
B)$1500
C)$2500
D)$1800
E)$1600
Rationale: B's share = 4500*3/9 = $1500
Answer is B
Answer: B
Question: Scott's average (arithmetic mean) golf score on his first four rounds was 38.What score does he need on his fifth round to drop his average score by 2 points?
Options:
A)68
B)28
C)78
D)88
E)312
Rationale: Average score for first 4 rounds = 38
Average score after 5 rounds = 36
Score Scott needs on his 5th round to drop average score by 2 points =38 - (2*5) = 28
Answer B
Answer: B
Question: What is the units digit of 18! + 7 ?
Options:
A)1
B)3
C)5
D)7
E)9
Rationale: Any number above 4!, such as 5!, 6!, etc... are always multiples of 10, so their units digit is 0.
The units digit of 18! + 7 is 7.
The answer is D.
Answer: D
Question: Without stoppages a train travels a certain distance with an average speed of 80 km/h and with stoppages with an average speed speed of 60 km/h. How many minutes per hour does the train stops ?
Options:
A)25 min
B)10 min
C)18 min
D)15 min
E)20 min
Rationale: let us assume the distance is x km.
if the train travels 80km/h without stopages then it takes (x/80) hour to rech.
and with stopage it takes (x/60) hour.
let the train stops t min per hour.
then according to the question
(x/80)=(x/60)+(t/60)*(x/60)
then t=15 min.
ANSWER:D
Answer: D
Question: 4,25,121,289,?
Options:
A)345
B)445
C)515
D)529
E)645
Rationale: Prime numbers- 2,3,5,7,11,13,17,19,23.....
Series - 2^2,5^2,11^2,17^2,23^2
Series- 4, 25, 121, 289, 529.
So next term in series is- 529.
ANSWER:D
Answer: D
Question: Half of 7 percent written as decimal is
Options:
A)5
B)0.5
C)0.025
D)0.035
E)None of these
Rationale: Explanation:
It will be 1/2(7%) = 1/2(7/100) = 7/200 = 0.035
Option D
Answer: D
Question: There are 6 red balls and 4 blue balls in a jar. If 3 balls are selected from the jar, what is the probability that all 3 balls selected are blue balls?
Options:
A)1/18
B)1/24
C)1/30
D)1/36
E)1/48
Rationale: The number of ways of choosing 3 balls from the jar is 10C3 = 120.
The number of ways of choosing 3 blue balls is 4C3 = 4.
P(3 blue balls) = 4/120=1/30.
The answer is C.
Answer: C
Question: The sum of money will be double itself in 20years and simple interest find rate of interest?
Options:
A)10%
B)5%
C)15%
D)20%
E)25%
Rationale: T = 20 years
P= principle amount = x
A = total amount = 2x
SI = simple interest = A-P = 2x-x = x
R = 100SI/PT = 100x/20x =5%
Answer is B
Answer: B
Question: A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. How far is the place?
Options:
A)2.98
B)2.88
C)2.82
D)2.86
E)2.81
Rationale: M = 6
S = 1.2
DS = 6 + 1.2 = 7.2
US = 6 - 1.2 = 4.8
x/7.2 + x/4.8 = 1
x = 2.88
Answer: B
Answer: B
Question: P, Q and R have Rs.4000 among themselves. R has two-thirds of the total amount with P and Q. Find the amount with R?
Options:
A)Rs.3000
B)Rs.1600
C)Rs.2400
D)Rs.4000
E)None of these
Rationale: Let the amount with R be Rs.r
r = 2/3 (total amount with P and Q)
r = 2/3(4000 - r) => 3r = 8000 - 2r
=> 5r = 8000 => r = 1600.
ANSWER:B
Answer: B
Question: On Saturday morning, Malachi will begin a camping vacation and he will return home at the end of the first day on which it rains. If on the first three days of the vacation the probability of rain on each day is 0.9, what is the probability that Malachi will return home at the end of the day on the following Monday?
Options:
A)0.009
B)0.128
C)0.488
D)0.512
E)0.64
Rationale: Re-phrasing the question:
What is the probability of: Saturday: No rain, Sunday: No rain, Monday: Rain
Probablity of rain = 0.9
Therefore, probability of no rain = 0.1
0.1*0.1*0.9 = 0.009
Hence A
Answer: A
Question: What is the value of 3x^2 − 1.6x + 0.3 for x = 0.8?
Options:
A)−0.3
B)0
C)0.3
D)0.94
E)2.46
Rationale: 3x^2-1.6x+0.3 for x=0.6
=3(0.8*0.8)-2*0.8*(0.8)+0.3
=0.8*0.8+0.3
=0.94
Correct Option : D
Answer: D
Question: A certain list consists of 21 different numbers. If n is in the list and n is 2 times the average (arithmetic mean) of the other 20 numbers in the list, then n is what fraction of the sum of the 21 numbers in the list?
Options:
A)1/20
B)1/6
C)1/11
D)4/21
E)5/21
Rationale: series : a1, a2....a20,n
sum of a1+a2+...+a20 = 20*x (x = average)
so, n = 2*x
Hence, a1+a2+..+a20+n = 22x
So, the fraction asked = 2x/22x = 1/11
Answer C
Answer: C
Question: A = {2, 3, 5, 7, 19}
B = {2, 4, 6, 13}
Two integers will be randomly selected from sets A and B, one integer from set A and one from set B, and then multiplied together. How many different products can be obtained?
Options:
A)32
B)16
C)19
D)20
E)36
Rationale: Step 1: Find out the number of products you get.
5 distinct numbers in set A and 4 distinct in set B so number of products = 5*4 = 20
Step 2: Remove the products that appear more than once.
Notice that 5, 7, 11 and 13 are primes and none of their multiples are in either set. So ignore them. We just need to focus on 2 and 3 of set A and 2, 4 and 6 of set B.
2, 3
2, 4, 6
The only product repeated when you take a number from each set is 12. (3*4 and 2*6) Rest all are distinct.
Answer = 20 - 1 = 32
Note here that the second step will involve manual calculation since it will depend on the specific numbers you have in the two sets.
A
Answer: A
Question: A person purchased a TV set for Rs. 1600 and a DVD player for Rs. 700 . He sold both the items together for Rs. 3500. What percentage of profit did he make?
Options:
A)20.12%
B)96.21%
C)52.17%
D)75.01%
E)23.00%
Rationale: The total CP = Rs. 1600 + Rs. 700
= Rs. 2300 and SP = Rs. 3500
Profit(%)
= (3500 - 2300)/2300 * 100
= 52.17%
Answer: C
Answer: C
Question: Find three consecutive odd integers so that the sum of twice the first, the second
and three times the third is 152.
Options:
A)20,23,25
B)23,25,27
C)25,28,31
D)30,33,35
E)29,31,35
Rationale: First x Make the first x
Second x+2 Odd numbers sowe add 2(same as even!)
Third x+4 Add 2more (4 total) to get the third
2F +S +3T =152 Twicethefirstgives2F andthree times thethirdgives3T
2(x)+(x+2)+3(x+4)=152 Replace F , S, and T withwhatwe labled them
2x+x+2+3x+12=152 Distirbute through parenthesis
6x+14=152 Combine like terms 2x+x+3x and 2+14
−14 −14 Subtract 14 fromboth sides
6x=138 Variable ismultiplied by 6
6 6 Divide both sides by 6
x=23 Our solution for x
First 23 Replace xwith 23 in the original list
Second (23)+2=25 The numbers are 23, 25, and 27
Third (23)+4=27
correct answer B
Answer: B
Question: A girl borrows 65000 for 5 years at 5% p.a. simple interest. she immediately lends it to another person at 9 % p.a. for 5 years. Find her gain in the transaction per year.
Options:
A)2600
B)2500
C)2550
D)2650
E)3600
Rationale: Gain in 5 years
= [(65000Ã—9Ã—5/100)âˆ’(65000Ã—5Ã—5/100)]
= (29250 â€“ 16250) = 13000.
âˆ´ Gain in 1 year = (13000â„5) = 2600
Answer A
Answer: A
Question: A man walks from B to C, a distance of x miles, at 15 miles per hour and returns at 12 miles per hour. What is his average speed?
Options:
A)10 mph
B)13 mph
C)12 mph
D)13.3 mph
E)14 mph
Rationale: Total distance covered = 2x
Time taken12miles / hour = x/12 hrs
Time taken @ 15 miles / hour = x/10 hrs
Avg speed = 2x / (x/15 + x/12) = 13.3 mph
Ans is D
Answer: D
Question: The speed of a subway train is represented by the equation z=s^2+2s for all situations where 0≤s≤7, where z is the rate of speed in kilometers per hour and s is the time in seconds from the moment the train starts moving. In kilometers per hour, how much faster is the subway train moving after 6 seconds than it was moving after 3 seconds?
Options:
A)4
B)9
C)15
D)48
E)33
Rationale: Given: z=s^2+2s for 0≤s≤7
z(3) = 3^2 + 2*3 = 15
z(6) = 6^2 + 2*6 = 48
Therefore z(7) - z(3) = 48 - 15 = 33 km/hr
Option E
Answer: E
Question: Johnny borrows $30,000 from Tony at 2% daily interest compounded daily. How much does Johnny owe Tony after 8 weeks?
Options:
A)30000*0.02^56
B)30000*1.12
C)30000*2.12
D)30000*1.02^56
E)(30000*1.02)^56
Rationale: A=A= P(1+r100)^n
So, A=30000(1+2/100)^7∗8
So, A=A= 30000(1.02)^56
Hence answer will be (D)
Answer: D
Question: A tree is 12 m tall and casts an an 8 m long shadow. At the same time, a flag pole caste a 100 m long shadow. How long is the flag pole ?
Options:
A)150 m
B)200 m
C)125 m
D)115 m
E)None
Rationale: Answer
∵ 8 m shadow means original height = 12 m
∴ 1 m shadow means original height = 12/8 m
∴ 100 m shadow means original height = (12/8) x 100 m
= (6/4) x 100 = 6 x 25 = 150 m
Correct Option: A
Answer: A
Question: At what rate percent per annum will a sum of money double in 16years?
Options:
A)10.6%
B)3.65%
C)6.25%
D)8.32%
E)11%
Rationale: Let principle = P
S.I. = P
T = 16yrs
Rate = 100*P/P*16 = 25/4% = 6.25%
Answer is C
Answer: C
Question: The organizers of a week-long fair have hired exactly six security guards to patrol the fairgrounds at night for the duration of the event. Exactly two guards are assigned to patrol the grounds every night, with no guard assigned consecutive nights. If the fair begins on a Monday, how many different pairs of guards will be available to patrol the fairgrounds on the following Saturday night?
Options:
A)7
B)6
C)5
D)3
E)2
Rationale: For any given day, only the guards patrolling on the previous day won't be available. So, 2 guards who patrolled on Friday won't be available. We are thus left with 4 guards.
To choose 2 out of 4, we will have 4C2 = 6 different pairs.
The answer is B.
Answer: B
Question: The sum of even numbers between 1 and 31 is:
Options:
A)240
B)789
C)520
D)879
E)456
Rationale: Explanation:
Let Sn = (2 + 4 + 6 + ... + 30). This is an A.P. in which a = 2, d = 2 and l = 30
Let the number of terms be n. Then
a + (n - 1)d = 30
=>2 + (n - 1) x 2 = 30
n = 15.
Sn =	n/2(a + l)=15/2	x(2 + 30) = (15 x 16) = 240.
ANSWER:A
Answer: A
Question: The two lines y = x and x = -4 intersect on the coordinate plane. If z represents the area of the figure formed by the intersecting lines and the x-axis, what is the side length W of a cube whose surface area is equal to 6z?
Options:
A)W=16
B)W=8√2
C)W=8
D)W=2√2
E)(√2)/3
Rationale: 800 score Official Solution:
The first step to solving this problem is to actually graph the two lines. The lines intersect at the point (-4, -4) and form a right triangle whose base length and height are both equal to 4. As you know, the area of a triangle is equal to one half the product of its base length and height: A = (1/2)bh = (1/2)(4 × 4) = 8; so z = 8.
The next step requires us to find the length of a side of a cube that has a face area equal to 8. As you know the 6 faces of a cube are squares. So, we can reduce the problem to finding the length of the side of a square that has an area of 8. Since the area of a square is equal to s², where s is the length of one of its side, we can write and solve the equation s² = 8. Clearly s = √8 = 2√2 , oranswer choice (D).
Answer: D
Question: In a certain corporation, there are 300 male employees and 100 female employees. It is known that 20% of the male employees have advanced degrees and 40% of the females have advanced degrees. If one of the 400 employees is chosen at random, what is the probability this employee has an advanced degree or is female?
Options:
A)1/20
B)1/10
C)1/5
D)2/5
E)3/4
Rationale: In this corporation, there are 400 total employees. There are 100 women. Of the 300 men, 20% have advanced degrees —-10% of 300 must be 30, so 20% of 300 must be 60. Add the women and the men with advanced degrees: 100 + 60 = 160. This is the OR region, full set of individuals that satisfy the condition “has an advanced degree or is female.” Of the 400 employees, what’s the probability of picking one of the 160 in this particular group?
P = 160/400 = 16/40 = 4/10 = 2/5
Answer = D
Answer: D
Question: The ratio between the speeds of two trains is 5: 7. If the second train runs 840 kms in 6 hours, then the speed of the first train is ?
Options:
A)90 km/hr
B)120 km/hr
C)100 km/hr
D)110 km/hr
E)None of these
Rationale: Explanation:
Let the speeds of two trains be 5X and 7X km/hr.
7/X=840/6=>X=20Km/hr
So speed of first train is 20*5 = 100 km/hr
Option C
Answer: C
Question: A gang of 8 boys goes on an tour in 2 cars, of which 1 canseat 5 & the other only 4. In how many ways can they travel?
Options:
A)100
B)114
C)126
D)154
E)157
Rationale: There are 8 students and the maximum capacity of the cars together is 9.
We may divide the 8 students as follows
Case I: 5 students in the first car and 3 in the second
Or Case II: 4 students in the first car and 4 in the second
Hence, in Case I: 8 students are divided into groups of 5 and 3 in8C3 ways.
Similarly, in Case II: 8 students are divided into two groups of 4 and 4 in 8C4ways.
Therefore, the total number of ways in which 8 students can travel is:
\inline {\color{Blue}8C_{3}+8C_{4}}=56 + 70= 126
C
Answer: C
Question: Excluding the stoppages, the speed of a bus is 32 km/hr and including the stoppages the speed of the bus is 16 km/hr. For how many minutes does the bus stop per hour?
Options:
A)15 min
B)10 min
C)12 min
D)30 min
E)18 min
Rationale: Speed of the bus without stoppage=32 km/hr
Speed of the bus with stoppage=16km/hr
Difference in speed=16 km/hr
so,the time taken in the stoppages = time taken to cover 16 km=(16/32)hr = 1/2 hr =30 min
ANSWER:D
Answer: D
Question: From the given equation find the value of c: cÂ²-3c-10
Options:
A)1
B)3
C)5
D)2
E)-5
Rationale: (c - 5)(c + 2)
C = -2 or 5
Answer is C
Answer: C
Question: Walking at 5/6th of its usual speed a cab is 5mnts late. Find its usual time to cover the journey?
Options:
A)25m
B)45m
C)32m
D)50m
E)62m
Rationale: New speed = 5/6th of usual speed
New time = 6/5th of usual time
6/5 UT - UT = 5m
UT/5 = 5m
UT = 25m
Answer is A
Answer: A
Question: A fair coin is tossed repeatedly. If heads appears on first 6 tosses what is the probability that tail appears on the next two tosses?
Options:
A)1/6
B)1/5
C)1/3
D)1/4
E)1/6
Rationale: Explanation :
Like mentioned in the question, the coin is fair. So chance of appearing of head and tail on each toss is same and each toss is independent from the previous one. So the chance of appearing tail on the next two tosses is still 1/2 each.
1/2 * 1/2 = 1/4
Answer : D
Answer: D
Question: A and B go around a circular track of length 600 m on a cycle at speeds of 18 kmph and 48 kmph. After how much time will they meet for the first time at the starting point?
Options:
A)120 sec
B)176 sec
C)360 sec
D)187 sec
E)189 sec
Rationale: Time taken to meet for the first time at the starting point
= LCM { length of the track / speed of A , length of the track / speed of B}
= LCM { 600/ (18 * 5/18) , 600/ (48 * 5 /18) }
= 360 sec.
Answer: C
Answer: C
Question: If 6 and 8 are factors of 60n, what is the minimum value of n?
Options:
A) 2
B) 4
C) 7
D) 14
E) 56
Rationale: 60n/6*8 should be integer => 2*2*3*5*n/2*3*2*2*2 = 5*n/4 must be an integer
for this to be true n must multiple of 4, thus min of n = 4
hence B
Answer: B
Question: How many 3-digit numerals begin with a digit that represents a prime and end with a digit that represents a odd prime number?
Options:
A)16
B)120
C)160
D)180
E)240
Rationale: prime digits 2,3,5 and 7.
three digit numbers _ _ _
1st place can be filled in 4 ways
2nd place can be filled in 10 ways
3rd place can be filled in 3 ways
Total=4*10*3=120
Ans : B
Answer: B
Question: If a - b = 6 and a2 + b2 = 50, find the value of ab.
Options:
A)A)7
B)B)12
C)C)15
D)D)18
E)E)20
Rationale: Explanation:
2ab = (a2 + b2) - (a - b)2
= 50 - 36 = 14
ab = 7.
Answer: A
Answer: A
Question: There are 15 points in a given plane, no three of which are on the same line. If one of the points is represented as 'S', then how many triangles can be determined with the 15 points that contain the point S?
Options:
A)91
B)105
C)182
D)210
E)455
Rationale: Fist point is S which is fixed so can be selected in 1 way
Second point can be selected in 14 ways
Third point can be selected in 13 ways
so total ways = 1x14x13 = 182
but answer is 91 which is 182/2=C
Answer: C
Question: If a:b=5:6 and b:c=2:3 find a:b:c?
Options:
A)6:5:9
B)5:9:3
C)9:5:6
D)5:9:6
E)5:6:9
Rationale: a:b = 5:6, b:c = 2:3
5:6
2:3
(a = a × b, b = b × b and c = b × c)
a:b:c = 5:6:9
E
Answer: E
Question: A train running at the speed of 50 km/hr crosses a post in 4 seconds. What is the length of the train?
Options:
A)90
B)120
C)60
D)95
E)75
Rationale: Speed=(54x5/18)=15 m/sec.
Length of the train=(Speed x Time).
Length of the train=15x4m=60m.
Answer: C
Answer: C