divelab/Sys2Bench huggingface dataset:
Question: A train crosses a platform of 160 m in 15 sec, same train crosses another platform of length 250 m in 20 sec. then find the length of the train?
Options:
A)110
B)887
C)167
D)197
E)161
Rationale: Length of the train be ‘X’
X + 160/15 = X + 250/20
20X + 3200 = 15X + 3750
5x=550
X = 110m
Answer: A
Answer: A
Question: Mahesh marks an article 15% above the cost price of Rs. 540. What must be his discount percentage if he sells it at Rs. 496.80?
Options:
A)22
B)88
C)20
D)88
E)62
Rationale: CP = Rs. 540, MP = 540 + 15% of 540 = Rs. 621
SP = Rs. 496.80, Discount = 621 - 496.80 = 124.20
Discount % = 124.2/621 * 100 = 20%
Answer:C
Answer: C
Question: A man can swim in still water at 15 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is?
Options:
A)3.9
B)5
C)5.3
D)1.5
E)5.2
Rationale: M = 15
S = x
DS = 15 + x
US = 15 - x
15 + x = (15 - x)2
15 + x = 30 -2x
3x = 15
x = 5
Answer:B
Answer: B
Question: The total of company C's assets in 1994 was 200% greater than the total in 1993, which in turn was 400% greater than the total in 1992. If the total of company C's assets in in 1992 was N dollars, which one of the following represents company C's assets in 1994:
Options:
A)7N
B)8N
C)9N
D)15
E)20
Rationale: Let's use actual numbers. Starting in 1992, let's say company C had $100 in assets.
In 1993, the total assets were 400% GREATER, which means 1992 PLUS 400% of 1992:
$100 + 4x$100 = $100 + $400 =$500
In 1994, the total assets were 200% GREATER than they were in 1993, which means 1993 PLUS 200% of 1993:
$500 + 2x$500 = $500 + $1000 =$1500
This is 15 times the 1992 number, so the correct answer is 15N.
D
Answer: D
Question: Four car rental agencies A, B, C and D rented a plot for parking their cars during the night. A parked 15 cars for 12 days, B parked 12 cars for 20 days, C parked 18 cars for 18 days and D parked 16 cars for 15 days. If A paid Rs. 1215 as rent for parking his cars, what is the total rent paid by all the four agencies?
Options:
A)Rs. 4500
B)Rs. 4800
C)Rs. 5250
D)Rs. 6642
E)None of these
Rationale: The ratio in which the four agencies will be paying the rents = 15 * 12 : 12 * 20 : 18 * 18 : 16 * 15
= 180 : 240 : 324 : 240 = 45 : 60 : 81 : 60
Let us consider the four amounts to be 45k, 60k, 81k and 60k respectively.
The total rent paid by the four agencies = 45k + 60k + 81k + 60k= 246k
It is given that A paid Rs. 1215
45k = 1215 => k = 27
246k = 246(27) = Rs. 6642
Thus the total rent paid by all the four agencies is Rs. 6642.
ANSWER:D
Answer: D
Question: How many 5 digit nos are there if the 2 leftmost digits are odd and the digit 4 can't appear more than once in the number ?
Could someone please provide a solution using a approach other than ( 1-x(none)) approach?
Options:
A)24300
B)25700
C)26500
D)24400
E)26300
Rationale: A. 4 is used once: OO**4 --> (5*5*9*9)*3: 5 choices for the first digit as there are 5 odd numbers, 5 choices for the second digit for the same reason, 9 choices for one of the two * (not-4 digit), 9 choices for another * (not-4 digit), multiplied by 3 as 4 can take the place of any of the three last digits (OO**4, OO*4*, OO4**);
B. 4 is not used: OO*** --> 5*5*9*9*9: the same logic as above.
5*5*9*9*3+5*5*9*9*9=24,300.
ANSWER:A
Answer: A
Question: 40!^40! will end in how many zeroes?
Options:
A)40!
B)8 x 40!
C)9 x 40!
D)8^40!
E)9^40!
Rationale: 40/5^1 + 40/5^2 = 8+1 = 9
Ans : 9^40!
ANSWER:E
Answer: E
Question: At a particular pizza shop, a pizza can be created from any combination of 6 different types of spice, 7 different types of meat, among which are pepperoni and anchovies, and 4 different types of cheese. If a customer at the shop decides to order a pizza with 1 type of spice, 2 types of cheese, and 4 types of meat but without pepperoni and anchovies together, how many possible ways to garnish the pizza are available to the customer?
Options:
A)6
B)35
C)120
D)450
E)900
Rationale: Number of possible ways to select 1 type of spice = 6c1 = 6
Number of possible ways to select 2 types of cheese = 4c2 = 6
Number of possible ways to select 4 types of meat but without pepperoni and anchovies together
= Total number of ways without any restriction - Total number of ways in which pepperoni and anchovies together
= 7c4 - 5c2
=35 - 10
=25
Possible ways to garnish the pizza are available to the customer = 6*6 * 25
=900
Answer E
Answer: E
Question: You collect baseball cards. Suppose you start out with 19. Maria takes half of one more than the number of baseball cards you have. Since you're nice, you give Peter 1 baseball card. Since his father makes baseball cards, Paul decides to triple your baseball cards. How many baseball cards do you have at the end?
Options:
A)17
B)18
C)19
D)20
E)24
Rationale: Solution
Start with 19 baseball cards.
Maria takes half of one more than the number of baseball cards you have. So Maria takes half of 19 + 1 which is 10,
so you're left with 19 - 10 = 9.
Peter takes 1 baseball card from you: 9 - 1 = 8 baseball cards.
Paul triples the number of baseball cards you have: 8 Ã— 3 = 24 baseball cards.
So you have 24 at the end.
Correct answer : E
Answer: E
Question: A baseball team won 35 percent of the first 80 games it played. How many of the remaining 82 games will the team have to win in order to have won exactly 50 percent of all the games it played?
Options:
A)36
B)45
C)53
D)55
E)81
Rationale: Games won out of first 80 questions = (35/100)*80 = 28
Total Games = 80+82 = 162
Games to be won = (50/100)*162 = 81
Remaining games to be won = 81-28 = 53
Answer: Option C
Answer: C
Question: What is the probability that a 4 person committee chosen at random from a group consisting of 6 men, 7 women, and 2 children contains exactly 1 woman?
Options:
A)77/204
B)56/195
C)11/77
D)308/1411
E)22/832
Rationale: Total possible selections = 4 out of 15 group members = 15C4
Favorable selections = 1 out of 7 women and 3 out of 8 (= 6 men + 2 children) = 7C1 * 8C3
Thus the required probability = 7C1*8C3 / 15C4 = 56/195. Thus B is the correct answer.
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 40%?
Options:
A)s.429
B)s.480
C)s.429
D)s.128
E)s.384
Rationale: SP = 800
Profit = 25%
CP = (SP)*[100/(100+P)]
= 800 * [100/125]
= 640
Loss = 40% = 40% of 640 = Rs.256
SP = CP - Loss = 640 - 256
= Rs.384
Answer:E
Answer: E
Question: A wooden cube whose edge length is 9 inches is composed of smaller cubes with edge lengths of one inch. The outside surface of the large cube is painted red and then it is split up into its smaller cubes. If one cube is randomly selected from the small cubes, what is the probability that the cube will have at least one red face?
Options:
A)52.9%
B)55.4%
C)58.3%
D)61.7%
E)64.5%
Rationale: There are a total of 9*9*9 = 729 cubes.
All the exterior cubes will have at least one face painted red.
The interior is formed by 7*7*7 = 343 cubes.
The number of cubes with at least one side painted red is 729 - 343 = 386 cubes
The probability that a cube has at least one side painted red is 386/729 which is about 52.9%
The answer is A.
Answer: A
Question: If two of the four expressions a+b, 3a+b, a-b, and a-3b are chosen at random, what is the probability that their product will be of the form of a^2 + kb^2, where k is a positive integer?
Options:
A)1/2
B)1/6
C)1/4
D)1/3
E)1/2
Rationale: *3=12 --> total number of outcomes
but only two of the expressions will result in desired form -->so the probability of choosing the right pair is 2/12=1/6
ANS:B
Answer: B
Question: The perimeter of a triangle is 44 cm and the in radius of the triangle is 2.5 cm. What is the area of the triangle?
Options:
A)76
B)88
C)66
D)55
E)35
Rationale: Area of a triangle = r * s
Where r is the in radius and s is the semi perimeter of the triangle.
Area of triangle = 2.5 * 44/2 = 55 cm2
Answer:D
Answer: D
Question: If a and b are Positive Integers and a<b, b is not equal to zero, which of the following can give NEGATIVE answer?
Options:
A)a+b
B)ab
C)a/2+b/2
D)a-b
E)a^2+b^2
Rationale: (A)a+b
This cannot be answer. Because a and b are positive integers
All the following options (Except D) should not be an answer.
(D) a-b
If a>0,a-b gives a negative answer.
So the option D is answer
Answer: D
Question: John was thrice as old as Tom 6 yrs back. He will be 5/3 times as old as Tom 6 years hence. How old is Tom today?
Options:
A)10
B)11
C)12
D)15
E)16
Rationale: Sol. RMBflSk -6 = 3 (Ravi - 6) ...(j)
and Rupesh + 6 = | (Ravi + 6) ...(ii)
Solving both the equations we get,
Ravi = 12 years.
C
Answer: C
Question: A single discount equivalent to the discount series of 20%, 12% and 5% is?
Options:
A)31.6
B)31.0
C)31.6
D)33.12
E)31.5
Rationale: 100*(80/100)*(88/100)*(95/100)
= 68.4
100 - 66.88 = 33.12
Answer: D
Answer: D
Question: Calculate how long it will take a swimmer to swim a distance of 3km against the current of a river which flows at 1.7km/hr, given that he can swim in still water at 3km/h
Options:
A)2.31
B)9.31
C)1.31
D)4.31
E)3.31
Rationale: swim in still water at = 3
speed of river= 1.7
US = 3 - 1.7= 1.3
Distance = 3
T = 3/1.3 = 2.31
Answer: A
Answer: A
Question: Find the odd man out. 3, 5, 15, 75, 1120, 84375
Options:
A)84375
B)1120
C)15
D)3
E)75
Rationale: Explanation :
Pattern : 1st * 2nd = 3rd, 2nd * 3rd = 4th, etc.
3
5
3 × 5 = 15
5 × 15 = 75
15 × 75 = 1125
75 × 1125 = 84375
Hence, 1120 is wrong. 1125 should have come in place of 1120
Answer : Option B
Answer: B
Question: A company, Chauncy Co., has an annual travel budget of $53,000. The accounting department estimates that transportation expenses will increase 5 percent in the coming year, and nontransportation travel expenses will increase by 15 percent in the coming year. Last year, Chauncy Co. spent $19,500 on transportation-related expenses, and $35,000 on nontransportation travel expenses. If the annual travel budget does not increase this year, and if the accounting department’s estimates are correct, how far over the annual travel budget will expenses be this year?
Options:
A)Expenses will not go over the budget.
B)$500
C)$4,225
D)$7,725
E)$60,725
Rationale: annual travel budget of $53,000
Let, Transportation expenses = T = 19500
and Non-Transportation expenses = N=35000
i.e. Increased Transportation expenses = 1.05T = 20475
and Increased Non-Transportation expenses = 1.15N = 40250
Total Expense = 20475+40250 = 60725
Expense over Budget = Budget - expense = 53000-60725 = 7725
Answer: Option D
Answer: D
Question: The forth proportional to 10,20,30 is?
Options:
A)20
B)60
C)45
D)75
E)100
Rationale: Let the fourth proportional to 10,20,30 be x
then 10:20::30:x
10x = 20*30
x = 60
Answer is B
Answer: B
Question: If â€œ*â€ is called â€œ+â€, â€œ/â€ is called â€œ*â€, â€œ-â€ is called â€œ/â€, â€œ+â€ is called â€œ-â€. 120/40 â€“ 30 * 20 - 5 = ?
Options:
A)178.5
B)156.6
C)160.4
D)163.6
E)164.1
Rationale: Explanation:
Given : 120/40 â€“ 30 * 20 - 5 = ?
Substituting the coded symbols for mathematical operations, we get,
120 * 40/30 +20 / 5 = ?
120 * 1.33 + 4 = ?
159.6 + 4 = 163.6
ANSWER : D
Answer: D
Question: Two trains are running in opposite directions with the same speed. If the length of each train is 120 m and they cross each other in 12 sec, then the speed of each train is?
Options:
A)10
B)18
C)36
D)72
E)64
Rationale: Explanation:
Let the speed of each train be x m/sec.
Then, relative speed of the two trains = 2x m/sec.
So, 2x = (120 + 120)/12 => x = 10
Speed of each train = 10 m/sec.
= 10 * 18/5 =- 36 km/hr.
ANSWER IS C
Answer: C
Question: .003/?= .01
Options:
A).3
B).09
C).009
D).0009
E)None of them
Rationale: Let .003/x = .01;
Then x = .003/.01
= .3/1
= .3
Answer is A
Answer: A
Question: Find the fourth proportion to 2,4,6
Options:
A)18
B)12
C)9
D)6
E)8
Rationale: Explanation:
2:4 :: 6:x
=> 2/4= 6/x
=> x = 24/2
=> x = 12
Answer:B
Answer: B
Question: A man takes 6 hours 15 minutes in walking a distance and riding back to the starting place. He could walk both ways in 7 hours 45 minutes. The time taken by him to ride both ways, is
Options:
A)4 hours
B)4 hours 30 minutes
C)4 hours 45 minutes
D)5 hours
E)6 hours
Rationale: Explanation:
Time taken in walking both ways = 7 hours 45 minutes --------(i)
Time taken in walking one way and riding back= 6 hours 15 minutes-------(ii)
By equation (ii)*2 -(i), we have
Time taken to man ride both ways, = 12 hours 30 minutes - 7 hours 45 minutes
= 4 hours 45 minutes
ANSWER IS C
Answer: C
Question: In a psychology school the grade of the students is determined by the following method: At the end of the first year the grade equals to twice the age of the student. From then on, the grade is determined by twice the age of the student plus half of his grade from the previous year. If Joey's grade at the end of the first year is 40, what will be his grade at the end of the third year?
Options:
A)74
B)75
C)76
D)77
E)78
Rationale: let the age is 'x' so after 1st yr 2x=40 and x=20
after 2nd year (now age become 21)
2*21+ 20=62 grades
after 3rd year(now age becomes 22)
2*22+31=75
ANSWER:B
Answer: B
Question: Find smallest prime number is:
Options:
A)13
B)21
C)14
D)18
E)42
Rationale: A
13
Answer: A
Question: The radius of a cylindrical vessel is 7cm and height is 2cm. Find the whole surface of the cylinder?
Options:
A)281
B)396
C)440
D)767
E)1981
Rationale: r = 7 h = 2
2πr(h + r) = 2 * 22/7 * 7(9) = 396
Answer:B
Answer: B
Question: What is the median from the below series 90, 92, 93, 88, 95, 88, 97, 87, and 98
Options:
A)76
B)79
C)92
D)94
E)95
Rationale: Ordering the data from least to greatest, we get:
87, 88, 88, 90, 92, 93, 95, 96, 98
The median quiz score was 92. (Four quiz scores were higher than 92 and four were lower.)
C
Answer: C
Question: A rectangle having length 140 cm and width 40 cm. If the length of the rectangle is increased by thirty percent then how much percent the breadth should be decreased so as to maintain the same area.
Options:
A)17.64%
B)33.33%
C)40%
D)75%
E)None of these
Rationale: Explanation :
Solution: (30/(140+30) * 100)% = 17.64%
Answer : A
Answer: A
Question: A number increased by 30% gives 650. The number is?
Options:
A)200
B)300
C)400
D)500
E)600
Rationale: Formula = TOTAL=100% ,INCREASE = "+" DECREASE= "-"
A number means = 100 %
That same number increased by 30 % = 130 %
130 % -------> 650 (130 Ã— 5 = 650)
100 % -------> 400 (100 Ã— 5 = 500)
Option 'D'
Answer: D
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 5 sec. What is the length of the fast train?
Options:
A)23 m
B)23 2/9 m
C)27 m
D)27 7/9 m
E)28 m
Rationale: Relative speed = (40 - 20) = 20 km/hr.
= 20 * 5/ 18 = 50/9 m/sec.
Length of faster train = 50/9 * 5 = 250/9 = 27 7/9 m.
ANSWER:D
Answer: D
Question: In covering a distance of 30 km, Abhay takes 2 hours more than Sameer. If Abhay doubles his speed, then he would take 1 hour less than Sameer. Abhay's speed is:
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: Abhay speed =x
sameer speed=y
(30/x)- (30/y)= 2 ....1
-(30/2x)+(30/y)= 1 ...-2
Solving 1 and 2 we get
6x=30
x=5
ANSWER E
Answer: E
Question: There are two inlets and one outlet to a cistern. One of the inlets takes 5/2hours to fill up the cistern and the other inlet takes twice as much time to fill up the same cistern. Both of the inlets are turned on at 9:00 AM with the cistern completely empty, and at 10:30AM, the outlet is turned on and it takes 1 more hour to fill the cistern completely. How much time does the outlet working alone takes to empty the cistern when the cistern is full?
Options:
A)2 hours
B)2.5 hours
C)3 hours
D)3.5 hours
E)4 hours
Rationale: The combined inflow rate of the two inlets is 2/5 + 1/5 = 3/5 cistern/hour. Thus, working together, it takes 5/3 hours (time is reciprocal of rate) to fill the cistern.
From 9:00 AM to 10:30 AM, so in 1.5=3/2 hours, the inlet pipes will fill (time)*(rate) = 3/2*3/5 = 9/10 th of the cistern .
Then the outlet is turned on and the remaining 1/10 th of the cistern is filled in 1 hour.
Letting x to be the rate of the outlet, we would have: 3/5 - x = 1/10 --> x = 1/2 cistern/hour, which means that it takes 2 hours the outlet working alone to empty the cistern.
Answer: A.
Answer: A
Question: What is the next number: 3, 27, 627, __
Options:
A)8847
B)9837
C)11,497
D)15,627
E)19,307
Rationale: 5^0 + 2 = 3
5^2 + 2 = 27
5^4 + 2 = 627
5^6 + 2 = 15,627
The answer is D.
Answer: D
Question: There are 6561 balls out of them 1 is heavy.Find the min. no. of times the balls have to be
weighed for finding out the haevy ball.
Options:
A)7
B)8
C)9
D)10
E)11
Rationale: 1))6561/3=2187->2187,2187,2187
2)2187/3=729->729,729,729
3)729/3=243->243,243,243
4)243/3=81->81,81,81
5)81/3=27->27,27,27
6)27/3=9->9,9,9
7)9/3=3->3,3,3
8)3/3=1->1,1,1
8 times required
ANSWER:B
Answer: B
Question: A rectangular ground is to be filled with square tiles of unit area. The border of the ground should be of red coloured tiles and inside white. If the number of red and white tiles are the same, find the minimum dimensions of the ground.
Options:
A)44
B)45
C)46
D)47
E)48
Rationale: Let us consider R for RED & W for WHITE
[R01][R02][R03][R04][R05][R06][R07][R08]
[R24][W01][W02][W03][W04][W05][W06][R09]
[R23][W07][W08][W09][W10][W11][W12][R10]
[R22][W13][W14][W15][W16][W17][W18][R11]
[R21][W19][W20][W21][W22][W23][W24][R12]
[R20][R19][R18][R17][R16][R15][R14][R13]
In this rectangle there are 24 RED & 24 WHITE.
So the dimension is (6*8) or (8*6).
Total number of tiles is 48.
ANSWER:E
Answer: E
Question: A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If three marbles are picked at random, what is the probability that they are all blue?
Options:
A)1/455
B)1/458
C)1/457
D)1/454
E)1/451
Rationale: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles.
Probability that all the three marbles picked at random are blue
= ³C₃/¹⁵C₃
= (1 * 3 * 2 * 1)/(15 * 14 * 13)
= 1/455
Answer: A
Answer: A
Question: Carmen made a sculpture from small pieces of wood. The sculpture is 2 feet 6 inches tall.Carmen places her sculpture on a base that is 12 inches tall. How tall are the sculpture andbase together?
Options:
A)3.1 feet
B)3.2 feet
C)3.3 feet
D)3.4 feet
E)3.83 feet
Rationale: we know 1 feet =12 inch then
2 feet =24 inch
24+10=34 then
34+12=44
46/12=3.83 feet
ANSWER:E
Answer: E
Question: One train is travelling 45 kmph and other is at 10 meters a second. Ratio of the speed of the two trains is?
Options:
A)3:3
B)5:7
C)5:4
D)7:2
E)8:5
Rationale: C
5:4
45 * 5/18 = 10
25:20 => 5:4
Answer: C
Question: A person walking 5/6 of his usual rate is 40 minutes late. What is
his usual time?
Options:
A)3 hrs 20 min
B)4 hrs 20 min
C)5 hrs 20 min
D)6 hrs 20 min
E)3 hrs 30 min
Rationale: Let t be the usual time. If the usual rate is 1 unit, then the unusual rate is 5/6.
Balance by the distance,
1*t = (5/6)(t+40)
6t = 5(t+40)
Solve for t,
t = 200 minutes = 3 hrs 20 min
ANSWER:A
Answer: A
Question: The ratio between the perimeter and the breadth of a rectangle is 5 : 1. If the area of the rectangle is 216 sq. cm, what is the length of the rectangle?
Options:
A)12 cm
B)14 cm
C)18 cm
D)20 cm
E)15 cm
Rationale: 2(l+b)/b=5/1
2l+2b=5b
3b=2l
b=2/3l
Then, Area = 216 cm2
lx b=216
lx 2/3l=216
l2=324
l=18 cm
ANSWER:C
Answer: C
Question: 217 * 217 + 183 * 183
Options:
A)70578
B)82578
C)80578
D)80568
E)89045
Rationale: Explanation:
1/2×2(a2+b2)=1/2×[(a+b)2+(a−b)2]
=1/2×[(217+183)2+(217−183)2]=80578
Option C
Answer: C
Question: In how many ways Chief Minister and Minister be elected from a team of 13 members?
Options:
A)124
B)131
C)132
D)145
E)156
Rationale: To do this, if captain is elected first, then we have 13 ways of doing this.
For election of vice-captain, we have only 12 ways left, coz 1 way is already consumed. (Situations like this is called dependent situation. One selection depends upon other selection.)
So, the ans is 13*12 = 156 ways.
E
Answer: E
Question: Which of the following is closest in value to (9^11)-(9^2)?
Options:
A)9^9
B)9^8
C)9^7
D)9^6
E)9^11
Rationale: 9^11 is much larger number than 9^2 and as we need approximate value then it's pretty much negligible in this case, so: (9^11)-(9^2) = ~9^11.
Answer: E.
Similar questions to practice:
Hope it helps.
Answer: E
Question: Six bells commence tolling together and toll at intervals of 2, 4, 6, 8 10 and 12 seconds respectively. In 30 minutes, how many times do they toll together ?
Options:
A)4
B)10
C)15
D)16
E)17
Rationale: Explanation:
L.C.M. of 2, 4, 6, 8, 10, 12 is 120.
So, the bells will toll together after every 120 seconds(2 minutes).
In 30 minutes, they will toll together	30/2+ 1 = 16 times.
ANSWER IS D
Answer: D
Question: Income and expenditure of a person are in the ratio 10 : 7. If the income of the person is Rs. 10000, then find his savings?
Options:
A)3005
B)3098
C)3300
D)3010
E)3000
Rationale: Let the income and the expenditure of the person be Rs. 10x and Rs. 7x respectively.
Income, 10x = 10000 => x = 1000
Savings = Income - expenditure = 10x - 7x = 3x = 3(1000)
So, savings = Rs. 3000.
Answer:E
Answer: E
Question: Q is as much younger than R as he is older than T. If the sum of the ages of R and T is 50 years. What is definitely the difference between R and Q's age?
Options:
A)16
B)17
C)13
D)50
E)27
Rationale: R - Q = R - T
Q = T.
Also R + T = 50; R + Q
= 50
So, (R - Q) cannot be determined.
Answer: D
Answer: D
Question: What is the lowest possible common multiple of 2 distinct integers, each greater than 130?
Options:
A)131
B)131*132
C)131*131
D)262
E)132
Rationale: The least common multiple of two numbers greater than 130 is 2(131) = 262, where the two distinct integers are 131 and 262.
The answer is D.
Answer: D
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 22 cm2. Find the lengths of all sides.
Options:
A)10 and 3
B)7 and 10
C)10 and 7
D)3 and 10
E)12 and 9
Rationale: Let x be the length of the longer side x>3, then the other side's length is x−3 cm. Then the area is S1 = x(x - 3) cm2. After we increase the lengths of the sides they will become (x+1) and (x−3+1)=(x−2) cm long. Hence the area of the new rectangle will be A2=(x+1)⋅(x−2) cm2, which is 22 cm2 more than the first area. Therefore
A1+22=A2
x(x−3)+22=(x+1)(x−2)
x2−3x+22=x2+x−2x−2
2x=24
x=12. So, the sides of the rectangle are 12 cm and (12−3)=9 cm long.
So answer is E.
Answer: E
Question: A man covered a certain distance at some speed. Had he moved 3 kmph faster, he would have taken 40 minutes less. If he had moved 2 kmph slower, he would have taken 40 minutes more. The distance (in km) is:
Options:
A)35
B)36 2/3
C)37 1/2
D)40
E)45
Rationale: Explanation:
Let distance = x km and usual rate = y kmph.
Then,	x/y-x/y + 3=40/60 =>2y(y + 3) = 9x ....(i)
And, x/y -2-x/y =40/60 =>y(y - 2) = 3x ....(ii)
On dividing (i) by (ii), we get: x = 40.
ANSWER IS D
Answer: D
Question: The average of seven numbers is 15. The average of first three numbers is 14 and the average of last three numbers is 19. What is the middle number?
Options:
A)6
B)29
C)31
D)34
E)35
Rationale: The total of seven numbers = 7X15 = 105
The total of first 3 and last 3 numbers is = 3 X 14+3 X 19 = 99
So, the middle number is (105 - 99 ) = 6
A
Answer: A
Question: A fast food company plans to build 5 new restaurants. If there are 14 sites that satisfy the company's criteria for location of new restaurant, in how many different ways can company select the 5 sites needed for the new restaurant if the order of selection doesn't matter.
Options:
A)1001
B)2002
C)495
D)1532
E)395
Rationale: The number of ways of choosing 5 sites out of 14 are counted by = 14C5 ways = 2002
Answer: Option B
Answer: B
Question: The ratio of the cost price and the selling price is 4:5. The profit percent is:
Options:
A)33
B)77
C)25
D)66
E)711
Rationale: Let C.P. = Rs. 4x. Then, S.P. = Rs. 5x
Gain = (5x - 4x) = Rs. x
Gain % = (x * 100)/ 4x = 25%.
Answer: C
Answer: C