divelab/Sys2Bench huggingface dataset:
Question: The distance between two cities A and B is 330 km. A train starts from A at 8 a.m. and travels towards B at 60 km/hr. Another train starts from B at 9 a.m. and travels towards A at 75 km/hr. At what time do they meet?
Options:
A)10 a.m
B)07 a.m
C)11 a.m
D)03 a.m
E)06 a.m
Rationale: Suppose they meet x hrs after 8 a.m. Then,
(Distance moved by first in x hrs) + [Distance moved by second in (x - 1) hrs] = 330
60x + 75(x - 1) = 330 => x = 3
So, they meet at (8 + 3) i.e., 11 a.m.
Answer: C
Answer: C
Question: Rs.6160 were divided among B, C & D in such a way that B had Rs.320 more than C and D had Rs 240 more than B . How much was Câ€™s share?
Options:
A)Rs.2300
B)Rs.2310
C)Rs.2320
D)Rs.2330
E)Rs.2340
Rationale: Let C gets Rs x. Then We can say B gets Rs (x + 320 ) and D gets Rs ( x + 280) .
x + 320 + x + x + 560 = 6160
3x = 5280
x = 1760 .
Câ€™s share = Rs ( 1760+560 ) = Rs.2320
C
Answer: C
Question: What is the smallest positive integer nn such that √6,480∗n is a perfect cube?
Options:
A)5
B)5^2
C)30
D)30^2
E)30^4
Rationale: Sol: Let's factorize 6480 and we get 6480= 3^4*2^4*5
Now we need to see for what minimum value of n√n*6480= a^3 where a is an Integer
So from 6480 we already have 2^4*3^4*5*n√n = (2^2)^3* (3^2)^3*(5)^3 why cause a is an integer which will need to be have the same factors which are in LHS
solving for n√n = (2^6*3^6*5^3)/ 2^4*3^4*5 and we get
n√n= 2^2*3^2*5^2
Or n = 2^4*3^4*5^4 or 30^4
Answer is E
Answer: E
Question: The H.C.F of 1.75, 5.6 and 7 is?
Options:
A)0.07
B)0.7
C)3.5
D)0.35
E)None of these
Rationale: Given numbers with two decimal place are: 1.75, 5.60 and 7.00. Without decimal places, these numbers are: 175, 560 and 700, whose H.C.F. is 35.
H.C.F. of given numbers = 0.35.
Correct Option : D
Answer: D
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)288
B)151
C)177
D)282
E)277
Rationale: :
Total height = 150 * 50 = 7500 cm.
New average = [7500 - 5 * 146 + 5 * 156 ] / 50 = 151 cm.
Answer: B
Answer: B
Question: A work crew of 5 Men takes 6 days to complete one-half of a job. If 7 men are then added to the crew and the men continue to work at the same rate, how many days will it take the enlarged crew to do the rest of the job?
Options:
A)2 1/2
B)3
C)3 1/3
D)4
E)4 4/5
Rationale: Suppose 1 man can do work in X days..
so 5 men will do in ..
5/X=1/6*1/2 as half job is done
X=60
now 7 more are added then
12/60=1/2*1/d for remaining half job
d=2 1/2 Number of days
A
Answer: A
Question: 20% of a number is more than 30% of 120 by 80. Find the number?
Options:
A)520
B)560
C)580
D)620
E)610
Rationale: (20/100) * X – (30/100) * 120 = 80
1/5 X = 116
X = 580
Answer:C
Answer: C
Question: A bag contains an equal number of one rupee, 50 paise and 25 paise coins respectively. If the total value is 105, how many coins of each type are there?
Options:
A)20 coins
B)30 coins
C)40 coins
D)60 coins
E)None of these
Rationale: Let number of each type of coin = x. Then,
1 × x + .50 × x + .25x = 105
⇒ 1.75x = 105 ⇒ x = 60 coins
Answer D
Answer: D
Question: If the radius of a sphere is increased by 50%, find the increase percent in
volume and the increase percent in the surface area.
Sol.
Options:
A)100%
B)120%
C)90%
D)115%
E)125%
Rationale: Let original radius = R. Then, new radius = (150/100)R=(3R/2)
Original volume = (4/3)R3, New volume = (4/3)(3R/2)3 =(9R3/2)
Increase % in volume=((19/6)R3)*(3/4R3)*100))% = 237.5%
Original surface area =4R2. New surface area = 4(3R/2)2=9R2
Increase % in surface area =(5R2/4R2) * 100) % = 125%.
ANSWER E 125%
Answer: E
Question: Out of a classroom of 6 boys and 4 girls the teacher picks a president for the student board, a vice president and a secretary. What is the probability that only girls will be elected?
Options:
A)8/125.
B)2/5.
C)1/30.
D)1/720.
E)13/48.
Rationale: probability that only girls will be elected = 4C3/10C3 = 1/30
Answer C.
Answer: C
Question: 70 91 120
14 13 24
5 7 ?
What number should replace the question mark?
Options:
A)2
B)5
C)3
D)19
E)68
Rationale: B
5
70 Ã· 14 = 5;
91 Ã· 13 = 7,
120 Ã· 24 = 5;
Answer: B
Question: Mohan's salary was first increased by 20% and then decreased by 20%. If his present salary is Rs. 7200, then what was his original salary?
Options:
A)188
B)7500
C)2788
D)1277
E)2771
Rationale: Let Mohan's salary be Rs.100.
When increased by 20%, Mohan's salary = Rs.120
Again when decreased by 20%, Mohan's salary = 120 - 24 = Rs. 96.
But present salary is Rs. 7200
for, 96 ---> 100 ; 7200 ---> ?
Required salary is 7200/96 * 100 = Rs. 7500
Answer: B
Answer: B
Question: How many times the keys of a typewriter have to be pressed in order to write first 400 counting numbers?
Options:
A)1092
B)1300
C)1500
D)1125
E)1234
Rationale: 1 to 9 = 9 * 1 = 9
10 to 99 = 90 * 2 = 180
100 to 400 = 301 * 3 = 903
=====> 1092
ANSWER A
Answer: A
Question: Increasing the original price of an article by 10 percent and then increasing the new price by 10 percent is equivalent to increasing the original price by
Options:
A)20%
B)20.5%
C)20.8%
D)21%
E)21.8%
Rationale: 1.1*1.1*x = 1.21*x
The answer is D.
Answer: D
Question: How many different sets of positive square integers M, each greater than 1, add up to 75?
Options:
A) 1
B) 4
C) 7
D) 11
E) 13
Rationale: E = 13 is the correct answer.
Answer: E
Question: A jar contains 3 red marbles and 7 green marbles.If a marble is drawn from a jar at random,what is the probability that this marble is green?
Options:
A)3/10
B)7/10
C)1
D)4/10
E)6/10
Rationale: Total number of marbles = 7+3 = 10
no. of green marbles = 7
probability of drawn a green marble= 7/10
Answer is B
Answer: B
Question: The equal amounts of money are deposited in two banks each at 15% per annum for 3.5 years and 5 years respectively. If the difference between their interests is Rs.144, find the each sum?
Options:
A)337
B)640
C)297
D)276
E)912
Rationale: (P*5*15)/100 - (P*3.5*15)/100 = 144
75P/100 – 52.5P/100 = 144
22.5P = 144 * 100
=> P = Rs.640
Answer:B
Answer: B
Question: A batsman in his 12th inning makes a score of 60 and their by increasing his average by 4. What is his average after the 12th inning?
Options:
A)12
B)16
C)20
D)24
E)28
Rationale: 11x + 60 = 12(x + 4)
x = 12 + 4 = 16
Answer:B
Answer: B
Question: If books bought at prices ranging from Rs. 130 to Rs. 320 are sold at prices ranging from Rs. 210 to Rs 310, what is the greatest possible profit that might be made in selling 18 books ?
Options:
A)Rs. 2500
B)Rs. 3000
C)Rs. 3500
D)Rs. 3240
E)Rs. 3600
Rationale: The greatest profit is possible only if the cost price of the books are minimum and selling prices are maximum.
Let lowest cost price of the 18 books = 130*18 = Rs. 2,340
Maximum selling price of 18 books = 310 *18 = Rs. 5,580
So, maximum profit = 5580 - 2340 = Rs. 3,240
ANSWER : OPTION D
Answer: D
Question: In a simultaneous throw of two dice , what is the probability of getting to total of 10 or 11?
Options:
A)15/66
B)4/9
C)7/36
D)3/5
E)5/36
Rationale: n(S)36
n(E)=5
P(E)=5/36
Ans: E
Answer: E
Question: The average of the five numbers is 6.8. If one of the numbers is multiplied by 3, the average of the numbers increases to 9.2. Which of the five numbers is multiplied by 3?
Options:
A)1.5
B)3.0
C)3.9
D)4.0
E)6.0
Rationale: Initial avg is 6.8
So the summation of the nos is 6.8*5 = 34
Now the new avg is 9.2
So summation will be 9.2*5 = 46.
So change in summation is 12.
This comes when a number is multiplied by 3.
In the original sum we already have that number added once. To bring additional 12 increment by multiplying by 3, we get a total increase of 18. Thus, 6 is multiplied by 3.
ANSWER:E
Answer: E
Question: You have found a mutant algae that doubles in size every hour. It takes 18 hours for one algae plant to take up half of a certain lake.
How long would it take for two of these plants to take up half of the same lake?
Options:
A)7
B)17
C)27
D)37
E)47
Rationale: At 17 hours the one plant will take up 1/4 of the lake (1/2 of 1/2). At 17 hours the two plants would be double the size of the one plant and double 1/4 is one half.
Answer: B
Question: The difference of two numbers is 1385. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder. What is the smaller number ?
Options:
A)274
B)270
C)295
D)360
E)252
Rationale: Let the smaller number be x. Then larger number = (x + 1385).
x + 1385 = 6x + 15
5x = 1370
x = 274
Smaller number = 274.
ANSWER A
Answer: A
Question: At what price must an article costing Rs.47.50 be marked in order that after deducting 5% from the list price. It may be sold at a profit of 25% on the cost price?
Options:
A)62.5
B)62.0
C)62.6
D)62.1
E)62.2
Rationale: CP = 47.50
SP = 47.50*(125/100) = 59.375
MP*(95/100) = 59.375
MP = 62.5
Answer: A
Answer: A
Question: A and B together can do a piece of work in 10 days. B alone can finish it in 20 days. In how many days can A alone finish the work ?
Options:
A)20
B)10
C)15
D)5
E)7
Rationale: Time taken by A to finish the work = XY/(Y-X)
= 10 x 20 / (20-10)
= 200/10
= 20 days
Answer: A
Answer: A
Question: A train moves fast a telegraph post and a bridge 264 m long in 8 sec and 40 sec respectively. What is the speed of the train?
Options:
A)89
B)29.7
C)56
D)79.2
E)67
Rationale: Let the length of the train be x m and its speed be y m/sec.
Then, x/y = 8 => x = 8y
(x + 264)/40 = y
y = 8.25 Speed = 8.25 m/sec = 8.25 * 18/5 = 29.7 km/hr.
Answer: Option B
Answer: B
Question: Three numbers are in the ratio 3:4:5 and their L.C.M is 2400. Their H.C.F is:
Options:
A)40
B)80
C)120
D)200
E)220
Rationale: Let the numbers be 3x, 4x and 5x.
Then, their L.C.M = 60x. So, 60x = 2400 or x = 40.
The numbers are (3 * 40), (4 * 40) and (5 * 40).
Hence, required H.C.F = 40.
ANSWER:A
Answer: A
Question: Three students appear at an examination of Mathematics. The probability of their success are 1/2, 1/4, 1/5 respectively. Find the probability of success of at least two.
Options:
A)1/60
B)2/50
C)9/40
D)3/40
E)4/50
Rationale: The probability of success of at least two students will involve the following possibilities.
The first two students are successful, the last two students are successful, the first and third students are successful and all the three students are successful.
Therefore, the required probability = 1/2 x 1/4 x 4/5 + 1/4 x 1/5 x 1/2 + 1/2 x 1/5 x 3/4 + 1/2 x 1/4 x 1/5 = 9/40
ANSWER:C
Answer: C
Question: A shipment of 1500 heads of cabbage, each of which was approximately the same size was purchased for $600.The day the shipment arrived 2/3 of the heads were sold, each at 25% above the cost per head.The following day the rest were sold at a price per head equal to 10% less than the price each head sold for the day before.what was the gross profit V on this shipment?
Options:
A)a) $100
B)b) $115
C)c) $125
D)d) $130
E)e) $135
Rationale: I recommend one should use fractions to solve this one rather than converting it into decimals
Sol:
1500 heads -> $600
1 head -> $600/1500
1 head -> $(2/5)
25% more of (2/5) -> 125/100 * 2/5 = $(1/2)
He sold 2/3*1500 = 1000 heads for $(1/2) per head
Total revenue by selling 1000 heads = 1000 * 1/2 = $500
Heads left: 500
Cost per head: 90% of the previous price: 90/100 * 1/2 = $(9/20)
Total revenue by selling 500 heads = 9/20 * 500 = 225
Total revenue after selling 1500 cabbage heads - 225+500 = $725
Money spent on the purchase: $600
Profit V= 725-600 = $125
Ans:C
Answer: C
Question: How long does a train 110 m long running at the speed of 72 km/hr takes to cross a bridge 132 m length?
Options:
A)11
B)12.1
C)13
D)14
E)15
Rationale: Speed = 72 * 5/18 = 20 m/sec
Total distance covered = 110 + 132 = 242 m.
Required time = 242/20 = 12.1 sec.
Answer: Option B
Answer: B
Question: John purchased a fridge & a mobile for Rs. 15000&Rs. 8000 respectively. He sold the fridgeat a loss of 4% and the mobile phone at a profit of 10%. Overall how much he make a profit.
Options:
A)Rs. 100
B)Rs. 150
C)Rs. 200
D)Rs. 300
E)Rs. 350
Rationale: Let the SP of the refrigerator and the mobile phone be Rs. r and Rs. m respectively.
r = 15000(1 - 4/100) = 15000 - 600
m = 8000(1 + 10/100) = 8000 + 800
Total SP - Total CP = r + m - (15000 + 8000) = -600 + 800 = Rs. 200
As this is positive, an overall profit of Rs. 200 was made.
C
Answer: C
Question: If –1 < x < 1 and x ≠ 0, which of the following inequalities must be true?
I. x^3 < x
II. x^2 < |x|
III. x^4 – x^5 > x^3 – x
Options:
A) I only
B) II only
C) III only
D) II and III only
E) I, II, and III
Rationale: Answer is D. Let's look at the statements one by one
Stmt I. x^3 < x
if 0<x<1 then x^3< x but if -1<x<0 then x^3>x
So this statement is not always true
Stmt II. x^2 < |x|
Because we know that x is a number less than one but not equal to zero then x^2 will always be less than |x|.
Why? think of positive fractions (and you can think in terms of positive fractions because the inequality is in regards to |x|). Lets set x = 1/2, then x^2 = 1/4 and 1/4<1/2
So Stmt II is always true
Stmt III. x^4 – x^5 > x^3 – x^2
This one may seem tricky but lets break it down. x^4 – x^5 > x^3 – x^2 = x^4(1-x)>x^2(x-1).
Because lets concentrate on (1-x) and (x-1). We are given that -1<x<1 which means that (1-x)>0 and (x-1)<0. x^4 will always be positive and x^2 will always be positive so without doing any math we are looking at positive > negative... which is always true.
So Stmt III is always true
A
Answer: A
Question: A woman is 18 years older than her son. In 4 years, her age will be twice the age of her son. The present age of her son is
Options:
A)12
B)14
C)16
D)18
E)20
Rationale: Explanation:
Let the son's present age be x years. Then, woman's present age = (x + 18) years
=> (x + 18) + 4 = 2(x + 4)
=> x + 22 = 2x +8
So, x = 14 Answer: B
Answer: B
Question: Excluding stoppages, the speed of a train is 45 kmph and including stoppages it is 33 kmph. Of how many minutes does the train stop per hour?
Options:
A)E982
B)16
C)12
D)121
E)28
Rationale: Explanation:
T = 12/45 * 60 = 16
Answer: Option B
Answer: B
Question: Find the fourth proportional to 0.5, 1.12 and 1.3?
Options:
A)2.914
B)2.81
C)2.192
D)2.912
E)None of these
Rationale: Explanation:
Formula = Fourth proportional = (b × c)/a
A = 0.5 , B = 1.12 and C = 1.3
(1.12 × 1.3)/0.5
1.456/0.5 = 2.912
Answer: Option D
Answer: D
Question: If number divisible by both 3 and 2 ,then the same number divisible by which number?
Options:
A)4
B)5
C)8
D)6
E)9
Rationale: Obviously,The answer is 6
Option D
Answer: D
Question: John bought 2 shares and sold them for $75 each. If he had a profit of 20% on the sale of one of the shares but a loss of 20% on the sale of the other share, then on the sale of both shares John had
Options:
A)a profit of $10
B)a profit of $6.25
C)a loss of $6.25
D)a loss of $10
E)neither a profit nor a loss
Rationale: Loss% = (%age Profit or loss / 10)^2 = (20/10)^2 = 4% loss
Total Selling Price = 75*2 = $192
Total Cost Price = 150/(0.96) = $156.25
Loss = 156.25 - 150 = $6.25
Answer: Option C
Answer: C
Question: If a is the smallest positive integer such that 5,880 multiplied by a is the square of an integer, then ya must be
Options:
A)30
B)15
C)12
D)23
E)17
Rationale: 5880= 2*2*7*7*5*6, so we need one 5 and one 6 to make it a square of a number. so 5*6= 30
Ans: A
Answer: A
Question: In a division sum, the remainder is 6 and the divisor is 5 times the quotient and is obtained by adding 22 to the thrice of the remainder. The dividend is
Options:
A)74
B)166
C)86
D)92
E)98
Rationale: Divisor = (6 * 3) + 22 = 40
5 * Quotient = 40
Quotient = 8.
Dividend = (Divisor * Quotient) + Remainder
Dividend = (20 * 8) + 6 = 166.
B)
Answer: B
Question: If the sides of a triangle are 26 cm, 22 cm and 10 cm, what is its area?
Options:
A)120
B)110
C)130
D)140
E)150
Rationale: The triangle with sides 26 cm, 22 cm and 10 cm is right angled, where the hypotenuse is 26 cm.
Area of the triangle = 1/2 * 22 * 10 = 110 cm2
Answer: Option B
Answer: B
Question: The original price of a suit is $100. The price increased 20%, and after this increase, the store published a 20% off coupon for a one-day sale. Given that the consumers who used the coupon on sale day were getting 20% off the increased price, how much did these consumers pay for the suit?
Options:
A)$88
B)$96
C)$100
D)$106
E)$110
Rationale: 0.8*(1.2*100) = $96
The answer is B.
Answer: B
Question: If x, y, and z are positive integers and x = 5y = 9z, then the least possible value of x + y - z is
Options:
A)33
B)40
C)49
D)61
E)84
Rationale: x + y - z = x/5 + x - x/9
= (45 + 9 - 5 )x/45 = 49x/45
49 is not divisible by 45, so for least value, x = 45
C
Answer: C
Question: A pump can fill a tank with water in 3 hours. Because of a leak, it took 3 1/3 hours to fill the tank. The leak can drain all the water of the tank in?
Options:
A)17 hr
B)19 hr
C)30 hr
D)14 hr
E)16 hr
Rationale: Work done by the tank in 1 hour
= (1/3 - 3 1/3)
= 1/30 Leak will empty the tank in 30 hrs.
Answer:C
Answer: C
Question: If z is a multiple of 9402, what is the remainder when z^2 is divided by 9?
Options:
A)0
B)2
C)4
D)6
E)8
Rationale: The sum of the digits is 9+4+2=15.
Thus 3 is a factor of 9402, so 3 is a factor of z.
Then 3^3 = 9 is a factor of z^2.
Then the remainder when z^2 is divided by 9 is 0.
The answer is A.
Answer: A
Question: Two trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 16 hours respectively. The ratio of their speeds is?
Options:
A)2:3
B)4:3
C)6:7
D)9:16
E)10:8
Rationale: Explanation:
Let us name the trains A and B.
Then, (A's speed) : (B's speed)
= √b : √a = √16 : √9 = 4:3
ANSWER IS B
Answer: B
Question: What amount does Kiran get if he invests Rs.8000 at 10% p.a. compound interest for four years, compounding done annually?
Options:
A)9688
B)9687
C)9685
D)9682
E)11713
Rationale: A= P{1 + R/100}n
=> 8000{1 + 10/100}4 = Rs.11713
Answer:E
Answer: E
Question: The area of a square is equal to three times the area of a rectangle of dimensions 25 cm * 27 cm. What is the perimeter of the square?
Options:
A)180 cm
B)190 cm
C)170 cm
D)150 cm
E)160 cm
Rationale: Area of the square = s * s = 3(25 * 27)
=> s = 3 * 5 * 3 = 45 cm
Perimeter of the square = 4 * 45 = 180 cm.
Answer: A
Answer: A
Question: Two numbers are respectively 20% and 25% more than a third number. The percentage that is first of the second is?
Options:
A)98%
B)56%
C)96%
D)964%
E)16%
Rationale: I II III
120 125 100
125----------120
100-----------? => 96%
Answer:C
Answer: C
Question: If n > 0 , which of the following must be true?
I 2n - 1 > 0
II n - n^2 < 0
III n^2 > 1
Options:
A)I only
B)II only
C)none
D)I and II only
E)III only
Rationale: I. True for all values of n except 1
When n = 1 ; n^2 = 1
II. True for all values of n except 1
When n = 1 ; n - n^2 = 1 - 1 =>0
III	True for all values of n
Hence the correct answer will be (C)
Answer: C
Question: Ranjani can buy watches at a price of X dollars per watch, which she marks up by a certain percentage before selling. If she makes a total profit of T by selling N watches, then in terms of X and T and N, what is the percent of the markup from her buy price to her sell price?
Options:
A)100T-X
B)100T/NX
C)100TX/N
D)100TX
E)100N/TX
Rationale: Algebraic Solution:If she makes a total profit of T for N watches, then that must be a profit of T/N for each watch. That must be the markup above cost on each watch, the amount of the increase. Well, percent increase = (amount of increase)/(starting amount) x 100% = (T/N)/X *100 = 100T/(NX)
Answer : B
Answer: B
Question: The ratio of buses to cars on River Road is 1 to 17. If there are 80 fewer buses than cars on River Road, how many cars are on River Road?
Options:
A)40
B)85
C)60
D)30
E)20
Rationale: B/C=1/17
C-B=80.........> B=C-80
(C-80)/C=1/17
Testing answers. Clearly Eliminate ACDE
Put C=85.........> (85-80)/85=5/85=1/17
Answer: B
Answer: B
Question: David paid $7,000 for 100 shares of stock X and $5,000 for 100 shares of stock Y. He later sold the same shares of both stocks, gaining 3/4 the amount he paid for stock Y. If the prices he had paid for the stocks had been reversed and everything else remained the same, then the net result would have been:
Options:
A)A Gain of 1.67 times as much
B)A Gain of 1.4 times as much
C)A Gain of 2 times as much
D)A Gain of 1.6 times as much
E)A Gain of 1.7 times as much
Rationale: A = 7000; B = 5000; Profit = (3/4)*5000 = 3750
After prices are reversed:
A = 5000; B =7000; Profit = (3/4)*7000 =5250
5250 --> Gain of 1.4 times 3750
Answer: B
Answer: B
Question: In a manufacturing plant, it takes 36 machines 4 hours of continuous work to fill 6 standard orders. At this rate, how many hours of continuous work by 72 machines are required to fill 12 standard orders?
Options:
A)4
B)6
C)8
D)9
E)12
Rationale: the choices give away the answer..
36 machines take 4 hours to fill 8 standard orders..
in next eq we aredoubling the machines from 36 to 72, but thework is not doubling(only 1 1/2 times),= 4*48/72*12/6 = 4
Ans A
Answer: A
Question: One hour after Yolanda started walking from X to Y, a distance of 10 miles, Bob started walking along the same road from Y to X. If Yolanda's walking rate was 3 miles per hour and Bobт's was 4 miles per hour, how many miles had Bob walked when they met?
Options:
A)24
B)23
C)22
D)21
E)4
Rationale: When B started walking Y already has covered 3 miles out of 10, hence the distance at that time between them was 10-3=7 miles.
Combined rate of B and Y was 3+4=7 miles per hour, hence they would meet each other in 7/7=1 hours. In 6 hours B walked 1*4=4 miles.
Answer: E.
Answer: E
Question: The second angle of a triangle is 45° more than the smallest angle. The third angle is three times
the smallest. How many degrees are there in each angle?
Options:
A)L=6/W=18
B)L=18/W=6
C)L=7/W=19
D)L=19/W=7
E)L=10/W=20
Rationale: We are looking for three angles.
! 1 - x
! 2 - x + 45
! 3 - 3x
You would not be able to solve this problem unless you knew that the sum of the interior angles
of a triangle is 180°.
! 1 + ! 2 + ! 3 = 180°
x + x + 45 + 3x = 180°
5x + 45 = 180°
5x = 135°
x = 27°
That means the first angle is 27°, the second angle is 27 + 45 or 72°, and the third angle is 3 times
27 or 81°.
Try this on your own. The length of a rectangle is three times the width and its perimeter is 48 ft.
Find the length and width. The answers are length is 18 and the width is 6 ft.
correct answer B
Answer: B
Question: A basket contains 9 apples, of which 1 is spoiled and the rest are good. If we select 2 apples from the basket simultaneously and at random, what is the probability that the 2 apples selected will include the spoiled apple?
Options:
A)2/3
B)2/5
C)2/7
D)2/9
E)2/11
Rationale: The total number of ways to choose 2 apples is 9C2 = 36
The number of ways that include the spoiled apple is 8C1 = 8
P(the spoiled apple is included) = 8/36 = 2/9
The answer is D.
Answer: D
Question: A jogger running at 10 km/hr along side a railway track is 340 m ahead of the engine of a 120 m long train running at 46 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)46 sec
E)23 sec
Rationale: Speed of train relative to jogger = 46 - 10 = 36 km/hr.
= 36 * 5/18 = 10 m/sec.
Distance to be covered = 340 + 120 = 460 m.
Time taken = 460/10 =46 sec.
Answer:D
Answer: D
Question: Manish, Rahul and Bharti have some stones with each of them. Five times the number of stones with Rahul equals seven times the number of stones with Manish while five times the number of stones with Manish equals seven times the number of stones with Bharti. What is the minimum number of stones that can be there with all three of them put together?
Options:
A)113
B)109
C)93
D)97
E)66
Rationale: Explanation :
Let the stones with Manish, rahul and Bharti be m,r and b respectively.
Given,
=>5r=7m and 5m=7b.
=>25r=35m and 35m=49b.
=>25r=35m=49b=k.
=>r/49=m/35=b/25.
The least possible integral values for r,m,b will be r=49, m=35 and b=25.
=>Total=49+35+25=109.
Answer : B
Answer: B