divelab/Sys2Bench huggingface dataset:
Question: Harold works at a resort from the beginning of March to the end of September. During the month of August this past year, he made 4 times the average (arithmetic mean) of his monthly totals in tips for the other months. His total tips for August were what fraction of his total tips for all of the months he worked?
Options:
A)1/3
B)2/5
C)3/7
D)1/2
E)4/7
Rationale: The time from beginning of March to the end of September is 7 months.
If x is the average monthly tip for all months other than August then his August month tip will be 4*x
His total tip for the 7 months = 6*(average tip for the months other than August) + 4x
=10x
August tips as a fraction of total tips = 4x/10x =2/5. So B
Answer: B
Question: Angela has 11 pairs of matched socks. If she loses 7 individual socks, which of the following is NOT a possible number of matched pairs she has left?
Options:
A)8
B)9
C)10
D)11
E)12
Rationale: I think if Angela loses 7 individual socks,then she is bound to have lost minimum of 3 pairs and 1 individual sock,in this way she is left with only 7 pairs of socks (11-(3+1)).
Hence,8 cannot be the answer as maximum is 7.
Hence, option (A)
Answer: A
Question: Akash will arrange 6 people of 6 different heights for photograph by placing them in two rows of three so that each person in the first row is standing is standing in front of someone in the second row. The heights of the people within each row must increase from left to right, and each person in the second row must be taller than the person standing in front of him or her. How many such arrangements of the 6 people are possible?
Options:
A)5
B)6
C)9
D)24
E)26
Rationale: Akash will arrange 6 people of 6 different heights for photograph by placing them in two rows of three so that each person in the first row is standing is standing in front of someone in the second row. person with max height is in the second row, person with min height is in the first row. We need to select 1 person in the middle of each row... In the middle of the first row we can put only 2, 3 or 4. In the middle of the second row we can put only 3, 4, 5. If we select {3 in the sec. row, 2 in the first}, {4,2}, {5,2}, {4,3}, {5,3}, {5,4}. So, there are 0*1 + 1*1 + 2*1 + 1*1 + 1*1 + 0*1 = 5 cases...A
Answer: A
Question: In covering a distance of 60 km, A takes 2 hours more than B. If A doubles his speed, then he would take 1 hour less than B. A's speed is:
Options:
A)5 km/h
B)8 km/h
C)10 km/h
D)15 km/h
E)20 km/h
Rationale: Let A's speed be X km/hr.
Then, 60/x - 60/2x = 3
30/x = 3
x = 10 km/hr.
Answer : C
Answer: C
Question: What percent is 2 minutes 24 seconds of an hour?
Options:
A)6%
B)2%
C)4%
D)8%
E)9%
Rationale: 2mt 24s =144s
144*100/60*60=4%
ANSWER:C
Answer: C
Question: In how many different ways can the letters A, A, B, B, B, C, D, E be arranged if the letter C must be to the right of the letter D?
Options:
A)1680
B)2160
C)2520
D)3240
E)3360
Rationale: We have 8 letters out of which A appears twice and B appears three time. Total number of permutation of these letters (without restriction) would be: 8!/2!3!=3360
Now, in half of these cases D will be to the right of C and in half of these cases to the left, hence the final answer would be 3360/2=1680
Answer: A.
Answer: A
Question: Smitty Farm picks 9866 cherries a day. If Smitty distributes their apples evenly across 9 different retail shops, how many cherries would remain with him.
Options:
A)1 cherry
B)7 cherry
C)2 cherry
D)4 cherry
E)5 cherry
Rationale: This is equivalent to finding the first number that is divisible by 9 that occurs before 9,866.
In order to divide the sum in 9 parts, the amount must be divisible by 9
Divisibility rule of 9: The sum of the digits must be divisible by 9
Sum of digits of 9+8+6+6 = 29. If we add 7, then it is divisible by 9.
Hence, we need to add 7 to this number for it to be divisible by 9
Correct Option : B
Answer: B
Question: It rained as much as on Wednesday as on all the other days of the week combined. If the average rainfall for the whole week was 4 cms, How much did it rain on Wednesday?
Options:
A)14
B)10.5
C)10.2
D)10.1
E)10.6
Rationale: Explanation:
Let the rainfall on wednesday = 6x.
âˆ´ Rainfall on the remaining days = 6x
Given,
(6x + 6x )/7 = 4
â‡’12x = 28
â‡’6x = 14
Answer: A
Answer: A
Question: Find the next number in the Sequence
2, 9, 30, 65,?
Options:
A)114
B)165
C)167
D)122
E)126
Rationale: +7 =>9
+21 =>30
+35 =>65
+49 =>114
Answer is A
Answer: A
Question: Of the 3,600 employees of Company X, 1/4 are clerical. If the clerical staff were to be reduced by 1/4, what percent of the total number of the remaining employees would then be clerical?
Options:
A)25%
B)22.2%
C)20%
D)12.5%
E)11.1%
Rationale: Let's see, the way I did it was
1/4 are clerical out of 3600 so 900 are clerical
900 reduced by 1/4 is 900*1/4
so it reduced 225 people , so there is 675 clerical people left
but since 225 people left, it also reduced from the total of 3600 so there are 3375 people total
since 675 clerical left / 3375 people total
you get (C) 20%
Answer: C
Question: Prathik purchased 40 shirts for rs 3000.he spends 10% for transportation. What should be the selling price per shirt to earn profit of 20% ?
Options:
A)96 rs
B)97 rs
C)98 rs
D)99 rs
E)100 rs
Rationale: total CP = 3000 + 3000*10/100 = 3300
to gain 20% profit, SP = (100+20)*3300/100 = 3960
selling price per shirt = 3960/40 = 99 rs/shirt
ANSWER:D
Answer: D
Question: A girl scout was selling boxes of cookies. In a month, she sold both boxes of chocolate chip cookies ($1.25 each) and boxes of plain cookies ($0.75 each). Altogether, she sold 1,585 boxes for a combined value of $1,585.75. How many boxes of plain cookies did she sell?
Options:
A)0
B)233
C)500
D)695
E)791
Rationale: Let #plain cookies sold be X then #chocolate cookies = (total cookies-X)
Equating for X
(0.75)*X +(1.25)*(1585-X)=1585.75
=>x=791
E
Answer: E
Question: How many five-digit numbers that do not contain the digits 4 or 7 are there?
Options:
A)44648
B)27844
C)28642
D)16864
E)32458
Rationale: We can have 7 digits ( 1,2,3,5,6,8,9) for the first place ( ten thousand's place).
and similarly 8 digits for thousand's, hundred's, tenth's and unit digit. ( 0,1,2,3,5,6,8,9)
So in total 7*8*8*8*8= 28672
Hence C
Answer: C
Question: The slant height of a cone is 15 cm and radius of the base is 3cm, find the curved surface of the cone?
Options:
A)26
B)134
C)141
D)190
E)28
Rationale: π * 15 * 3
= 141
Answer:C
Answer: C
Question: A container holding 12 ounces of a solution that is 1 part alcohol to 2 parts water is added to a container holding 12 ounces of a solution that is 1 part alcohol to 3 parts water. What is the ratio of alcohol to water in the resulting solution?
Options:
A)2:5
B)3:7
C)3: 5
D)4:7
E)7:17
Rationale: Container 1 has 12 ounces in the ratio 1:2
or,
x+2x=12 gives x(alcohol)=4 and remaining water =8
container 2 has 12 ounces in the ratio 1:3
or,
x+3x=12 gives x(alcohol)=3 and remaining water =9
mixing both we have alcohol=4+3 and water =8+9
ratio thus alcohol/water =7/17
Answer E
Answer: E
Question: If 3 boys can do 3 times of a particular work in 3 days, then, 7 boys can do 7 times of that work in?
Options:
A)days
B)days
C)days
D)days
E)days
Rationale: That is, 1 boys can do one time of the work in 3 days.
Therefore, 7 boys can do 7 times work in the same 3 days itself.
B)
Answer: B
Question: In an election contested by two parties, Party B secured 20% of the total votes more than Party C. If party C got 144,000 votes, by how many votes did it lose the election?
Options:
A)14,000
B)72,000
C)78,000
D)24,000
E)30,000
Rationale: B + C = 100 ---- (1)
B - C = 20 ---- (2)
Solving (1) and (2) B = 60% and R = 40%
40% of Total = 144000
Total = 360000
B = 216000
Difference = 216000 - 144000 = 72000
Answer: B
Answer: B
Question: A cistern has a leak which would empty the cistern in 20 minutes. A tap is turned on which admits 4 liters a minute into the cistern, and it is emptied in 24 minutes. How many liters does the cistern hold?
A. 480 liters
Options:
A)480
B)489
C)486
D)482
E)483
Rationale: 1/x - 1/20 = -1/24
x = 120
120 * 4 = 480
Answer: A
Answer: A
Question: Tough and Tricky questions: Coordinate Geometry.
Line L contains the points (2,3) and (p,a). If a = 2, which of the following could be the equation of line m, which is perpendicular to line L?
Options:
A) 2x + y = px + 7
B) 2x + y = –px
C) x + 2y = px + 7
D) y – 7 = x ÷ (p – 2)
E) 2x + y = 7 – px
Rationale: we need m=p-2, so we should gety=mx+bform in answer choices
(A) 2x+y=px+7 => y=px-2x+7 => y=x(p-2)+7. It is what we need
(B) 2x + y = –px => y=-px-2x => y=x(-p-2). Wrong
(C) x + 2y = px + 7 => y=x(p-1/2)+7/2. Wrong
(D) y – 7 = x ÷ (p – 2) => y=(1/p-2)x+7. Wrong
(E) 2x + y = 7 – px => y=-px-2x+7 => y=x(-p-2)+7. Wrong
A=Answer
Answer: A
Question: Mr. Thomas invested an amount of Rs. 13,900 divided in two different schemes A and B at the simple interest rate of 14% p.a. and 11% p.a. respectively. If the total amount of simple interest earned in 2 years be Rs. 3508, what was the amount invested in scheme B?
Options:
A)6400
B)2878
C)2899
D)2660
E)2701
Rationale: Let the sum invested in scheme A be Rs. x and that in scheme B be Rs. (13900 - x). Then,
(x * 14 * 2)/100 + [(13900 - x) * 11 * 2]/100 = 3508
28x - 22x = 350800 - (13900 * 22)
6x = 45000 => x = 7500
So, sum invested in scheme B = (13900 - 7500) = Rs. 6400.Answer:A
Answer: A
Question: A can give B 100 meters start and C 200 meters start in a kilometer race. How much start can B give C in a kilometer race?
Options:
A)111.12 m
B)111.13 m
C)117.12 m
D)111.92 m
E)141.12 m
Rationale: A runs 1000 m while B runs 900 m and C runs 800 m.
The number of meters that C runs when B runs 1000 m,
= (1000 * 800)/900 = 8000/9 = 888.88 m.
B can give C = 1000 -888.88 =111.12 m.
Answer:A
Answer: A
Question: A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 sec. The speed of the train is?
Options:
A)65 km/hr
B)50 km/hr
C)76 km/hr
D)56 km/hr
E)87 km/hr
Rationale: Speed of the train relative to man = 125/10 = 25/2 m/sec.
= 25/2 * 18/5 = 45 km/hr
Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr.
x - 5 = 45 => x = 50 km/hr.
Answer:B
Answer: B
Question: 1,2,4,7,_,16
Options:
A)11
B)9
C)10
D)12
E)13
Rationale: Each new number is the same as the last number with the adder growing by 1. This would yield 11.
Answer: A
Question: Eddy and Freddy start simultaneously from city A and they travel to City B and City C respectively. Eddy takes 3 hours and Freddy takes 3 hours to complete the journey. If the distance between City A and City B is 600 kms and City A and City C is 300 kms. What is the ratio of their average speed of travel? (Eddy: Freddy)
Options:
A)2/1
B)3/8
C)8/5
D)5/8
E)5/3
Rationale: Distance traveled by Eddy = 600 km
Time taken by Eddy = 3 hours
Average speed of Eddy = 600/3 = 200 km/hour
Distance traveled by Freddy = 300 km
Time taken by Freddy = 3 hours
Average speed of Freddy = 300/3 = 100 km/hour
Ratio of average speed of Eddy to Freddy = 200/100 = 2/1
Answer A
Answer: A
Question: In a rectangular coordinate system, what is the area of a rhombus whose vertices have the coordinates (0, 3.5), (9, 0), (0, -3.5), (-9, 0)?
Options:
A)63
B)88
C)112
D)116
E)120
Rationale: Ares of rhombus= 1/2* D1 *D2
Length of 1st diagonal = 9+9= 18
Length of 2nd diagonal= 3.5+3.5= 7
Area= 1/2*18*7= 63
A is the answer
Answer: A
Question: A woodworker normally makes a certain number of parts in 24 days. But he was able to increase his productivity by 5 parts per day, and so he not only finished the job in only 22 days but also he made 80 extra parts. How many parts does the woodworker normally makes per day and how many pieces does he make in 24 days?
Options:
A)360
B)350
C)340
D)370
E)380
Rationale: Let x be the number of parts the woodworker normally makes daily. In 24 days he makes 24⋅x pieces. His new daily production rate is x+5 pieces and in 22 days he made 22⋅(x+5) parts. This is 80 more than 24⋅x. Therefore the equation is:
24⋅x+80=22(x+5)
30=2x
x=15
Normally he makes 15 parts a day and in 24 days he makes 15⋅24=360 parts.
So answer is A.
Answer: A
Question: A vendor bought bananas at 6 for Rs.10 and sold them at Rs.4 for Rs.6 .Find his gain or loss percent .
Options:
A)13%
B)10%
C)47%
D)36%
E)52%
Rationale: Suppose , number of bananas bought = LCM of 6 and 4=12
CP=Rs.[(10/6)*12]=Rs.20 ; SP= Rs[(6/4)*12]=Rs.18
Loss%=[(2/20)*100]%=10%
Ans:B
Answer: B
Question: Which of the following has 35^70 as a factor?
Options:
A)70^70
B)30^40
C)40^70
D)60^60
E)90^70
Rationale: Here 35^70 = 5^70 * 7^70 Only Option A has both .
Smash A
Answer: A
Question: Three taps A,B and C can fill a tank in 10,20 and 30. If A is open all the time and B and C are open for one hour each alternately, the tank will be full in?
Options:
A)6hour 20min
B)7hour 10min
C)7hour 30min
D)8hour 15min
E)9hours 05 min
Rationale: A+B 1 hour work = 1/10 + 1/20 = 3/20
A+C 1 hour work = 1/12 + 1/30 = 7/60
Part filled in 2 hours = 3/20 + 7/60 = 4/15
Part filled in 6 hours = 3* 4/15 = 4/5
Remaining part = 1 - 4/5 = 1/5
Now it is the turn of A and B and 1/5 part is filled by A and B in 1hour 30min
Total time taken to fill the tank = 6+1.5 = 7hours 30min
Answer is C
Answer: C
Question: At what time between 5.30 and 6 will the hands of a clock beat right angles?
Options:
A)43 5⁄11 min. past 5
B)43 7⁄11 min. past 5
C)40 min. past 5
D)45 min. past 5
E)None of these
Rationale: At 5 o’clock, the hands are 25 min. spaces apart.
To be at right angles and that too between 5.30 and 6, the minute hand has to gain (25 + 15) = 40 min. spaces
55 min.spaces are gained in 60 min.
40 min. spaces are gained in (60⁄55 × 40) min = 43 7⁄11 min.
∴ Required time = 43 7⁄11 min. past 5
Answer B
Answer: B
Question: A mixture of 150 liters of wine and water contains 20% water. How much more water should be added so that water becomes 25% of the new mixture?
Options:
A)11 liters
B)12 liters
C)10 liters
D)15 liters
E)18 liters
Rationale: Number of liters of water in150 liters of the mixture = 20% of 150 = 20/100 * 150 = 30 liters.
P liters of water added to the mixture to make water 25% of the new mixture.
Total amount of water becomes (30 + P) and total volume of mixture is (150 + P).
(30 + P) = 25/100 * (150 + P)
120 + 4P = 150 + P => P = 10 liters.
Answer:C
Answer: C
Question: Simplify: 45205 x 95
Options:
A)4520500
B)4294470
C)4294475
D)4068450
E)226025
Rationale: 45205 x 95 = 45205 x (100 - 5)
= 4520500 - 226025
= 4294475
Answer is C
Answer: C
Question: The annual birth and death rate in a country per 1000 are 39.4 and 19.4 respectively . the number of years K in which the population would be doubled assuming there is no emigration or immigration is
Options:
A)20
B)K=25
C)30
D)K=35
E)40
Rationale: Suppose the population of the country in current year is 1000.
So annual increase is 1000 + 39.4 - 19.4=1020
Hence every year there is an increase of 2%.
2000=1000(1+ (2/100))^n
n=35 Answer is D.
Answer: D
Question: A began business with Rs.45000 and was joined afterwards by B with Rs.36000. When did B join if the profits at the end of the year were divided in the ratio of 2:1?
Options:
A)1.5
B)6
C)7.5
D)8.5
E)2
Rationale: 45*12 : 36*x = 2: 1
x = 7.5
12 -7.5 = 4.5
Answer: C
Answer: C
Question: If 144/0.144 = 14.4/x, then the value of x is:
Options:
A)0.0414
B)0.144
C)0.0144
D)0.414
E)None of them
Rationale: =144/0.144 = 14.4/x
=144 x 1000/144
=14.4/x
=x = 14.4/1000
= 0.0144
Answer is C.
Answer: C
Question: The factorial expression 9!/2! is not divisible by which of the following integers?
Options:
A)3
B)2
C)6
D)7
E)11
Rationale: 9!/2! => 9 x 8 x 7 x 6 x 5 x 4 x 3
(A) 3 Can divide 12 or 9
(B) 2 Can divide 8 or 6 or 4
(C) 6 Can divide 6
(D) 7 Can divide 7
(E) 11 None of the Multiplicands present
Hence answer will be (E)
Answer: E
Question: A man can row 12 Kmph in stil water and the river is running at 4 Kmph. If the man takes 2 hour to row to a place and back how far is the place?
Options:
A)3 Km
B)2.66 Km
C)10.66 Km
D)9 Km
E)10 km
Rationale: Explanation:
Man's rate down stream = 12 + 4 = 16 kmph
Man's rate upstream = 12 - 4 = 8 kmph
Let the required distence be x Km
then, x/16 +x/8 = 2
3x = 32
x = 10.66 Km.
Answer: Option C
Answer: C
Question: x is what percent of y percent of z, in terms of x, y and z? k be the value expressed in terms of x,y and z.
Options:
A)xyz
B)1/xyz
C)100xyz
D)10^4*x/yz
E)10^3 x/yz
Rationale: Algebraically, y% of z is just (y/100)*z, or yz/100. So we want to answer the question: x is what percent of yz/100? Say x is equal to k% of yz/100; then we have:
x = (k/100)*(yz/100)
10,000x/yz = k
D
Answer: D
Question: In how many different ways can the letters of the word DETAIL be arranged in such a way that the vowels occupy only the odd positions?
Options:
A)120
B)60
C)48
D)32
E)None of these
Rationale: 3 vowels can be arranged in three odd places in 3! ways.
Similarly, 3 consonants can be arranged in three even places in 3! ways.
Hence, the total number of words in which vowels occupy odd positions = 3! × 3! = 6 × 6 = 36 ways.
Answer E
Answer: E
Question: The product Q of the first 10 prime numbers is closest to which of the following?
Options:
A)6.5 x 10^7
B)6.5 x 10^8
C)6.5 x 10^9
D)6.5 x 10^10
E)6.5 x 10^11
Rationale: The first 10 primes are: 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29.
So, we need to find approximate value Q of 2*3*5*7*11*13*17*19*23*29.
# of different approximations are possible. For example:
2*5=10
3*17=~50 (actually more than 50);
7*13=~100 (actually less than 100);
11*19=~200 (actually more than 200)
23*29=667
2*3*5*7*11*13*17*19=~10*50*100*200*667=10^7*667=6.67*10^9.
Answer: C.
Answer: C
Question: A will was written such that an estate would be divided among three guys with the remainder donated to charity. One stipulation in the will is that no one from the guys can receive an amount within 30% of another's amount. If one of the guys received $20,000, what is the smallest possible range between the highest and lowest amounts (rounded to the nearest dollar) among the three guys?
Options:
A)$4096
B)$5904
C)$7892
D)$10052
E)$20736
Rationale: 1st - 20,000.
2nd - 0.7*20,000 = 14,000
3rd - 0.7*14,000 = 9,800
Range = 20,000 - 9800 = 10,200.
Answer: D.
Answer: D
Question: A company wants to spend equal amounts of money for the purchase of two types of computer printers costing $400 and $350 per unit, respectively. What is the fewest number of computer printers that the company can purchase?
Options:
A)11
B)13
C)15
D)17
E)19
Rationale: The smallest amount that the company can spend is the LCM of 400 and 350, which is 2800 for each, which is total 5600.
The number of 1st type of computers which costing $400 = 2800/400 = 7.
The number of 2nd type of computers which costing $350 = 2800/350 = 8.
Total = 7+8 = 15
Answer is C.
Answer: C
Question: The number x of cars sold each week varies with the price y in dollars according to the equation x = 800,000 – 50y. What would be the total weekly revenue E, in dollars, from the sale of cars priced at $ 15,000?
Options:
A)50,000
B)750,000
C)850,000
D)7,500,000
E)E=750,000,000
Rationale: number of cars sold = x=800000-50y
y=15000
x=800000-750000=50000
revenue from 50000 cars= 15000*50000=750000000 E
Answer: E
Question: A qualified worker digs a well in 5 hours. He invites 3 apprentices, both capable of working 3/4 as fast and 2 trainees both working 1/5 as fast as he. If the five-person team digs the same well, how much time does the team need to finish the job?
Options:
A)1:24
B)1:34
C)1:44
D)1:41
E)2:14
Rationale: and answer is correct as you have calculated : 100/56 hrs that is 1.62 hrs - 1 hr and 41 minutes, so 1:41, hence, D.
Answer: D
Question: A book is bought for $600 and sold for $624. What is the profit in percentage?
Options:
A)2
B)4
C)6
D)8
E)10
Rationale: 624/600 = 1.04
The answer is B.
Answer: B
Question: 10 men, working 5 hours a day can complete a work in 18 days. How many hours a day must 15 men work to complete the work in 12 days ?
Options:
A)4 hours a day
B)5 hours a day
C)6 hours a day
D)7 hours a day
E)8 hours a day
Rationale: Explanation:
More Men, Less Hours {Indirect Proportion}
Less Days, More Hours {Indirect Proportion}
[men 15 10
days 12 18] ::5:x
=>xâˆ—15âˆ—12=10âˆ—18âˆ—6
=>x=10âˆ—18âˆ—5/ 15âˆ—12
=>x=5
Option B
Answer: B
Question: What is the sum of odd integers from 25 to 85
, inclusive?
Options:
A)1,705
B)1,500
C)1,240
D)1,120
E)1,100
Rationale: Number of odd integers = (85-25)/2 + 1
= 60/2 + 1
= 31
Sum of odd integers = (25+85)/2 * 31
= 1705
Answer A
Answer: A
Question: Peter invested an amount of Rs. 12,000 at the rate of 10% p.a simple interest and another amount at the rate of 20% p.a. simple interest. The total interest earned at the end of one year on the total amount invested became 14% p.a. Find the total amount invested?
Options:
A)20,000
B)72888
C)27899
D)27891
E)27712
Rationale: Let the second amount be Rs. x. Then,
(12000 * 10 * 1)/100 + (x * 20 * 1)/100 = [(12000 + x) * 14 * 1] / 100
120000 + 20x = 16800 + 14x
x = 8000
Total investment = 12000 + 8000 = Rs. 20,000.
Answer:A
Answer: A
Question: The manager at a health foods store mixes a unique superfruit juice cocktail that costs $1399.45 per litre to make. The cocktail includes mixed fruit juice and açai berry juice, which cost $262.85 per litre and $3104.35 per litre, respectively. The manager has already opened 35 litres of the mixed fruit juice. How many litres of the açai berry juice does he need to add?
Options:
A)17 litres
B)23.3 litres
C)11 litres
D)07 litres
E)38 litres
Rationale: 262.85(35)+3,104.35x = 1,399.45(35 + x)
Solve the equation.
262.85(35)+3,104.35x = 1,399.45(35 + x)
9,199.75 + 3,104.35x = 48980.75 + 1,399.45x
9,199.75 + 1,704.9x = 48980.75
1,704.9x = 39,781
x ≈ 23.3
Answer is B.
Answer: B
Question: Rectangle ABCD is constructed in the coordinate plane parallel to the x- and y-axes. If the x- and y-coordinates of each of the points are integers which satisfy 4 ≤ x ≤ 11 and -5 ≤ y ≤ 5, how many possible ways are there to construct rectangle ABCD?
Options:
A)396
B)1260
C)1540
D)7920
E)15840
Rationale: As the rectangle is parallel to coordinate axes, the coordinates of the points of the rectangle would be
(X1, Y1), (X2, Y1), (X2, Y2), (X1,Y2)
given that X1, X2 lie between 4 and 11..ie., 8 possible numbers
Possible combinations for X1,X2 would be 8C2 = 28
Similarly, Possible combinations for Y1, Y2 would be 11C2 = 55
Possible ways of constructing rectangle is by selecting any of the combination of X1,X2 and Y1,Y2
= 28 * 55 = 1540
Ans. C
Answer: C
Question: The ratio of two quantities is 2 to 3. If each of the quantities is increased by 4, what is the ratio of these two new quantities?
Options:
A)5/5
B)It cannot be determined from the information given.
C)11/5
D)12/5
E)13/5
Rationale: let the actual ratio be 2k/3k, increase numerator and denominator by 4=> 2k+4/3k+4
Until the value of k is unknown we can not determine the actual ratio.
OR
let the actual be 3/4. After increasing 4 => 7/8
let the actual be 6/8. After increasing 4 => 10/12
Therefore without actual quantities we cannot determine the actual ratio.
Answer : B
Answer: B
Question: There are 11 teams in a certain league and each team plays each of the other teams exactly once. What is the total number of games played?
Options:
A)35
B)45
C)55
D)65
E)75
Rationale: 11C2 = 55
The answer is C.
Answer: C