divelab/Sys2Bench huggingface dataset:
Question: A car covers a distance of 1932 km in 7 hours. Find its speed?
Options:
A)104
B)288
C)271
D)276
E)128
Rationale: 1932/7 = 276 kmph
Answer: D
Answer: D
Question: If point A coordinates are (-4, -3) point B coordinates are (8 ,4 ) if C is along the line A-B so that AC = 1/2 CB. What are the coordinates of point C.
Options:
A)(-2, - 2/3)
B)(2, -2/3)
C)(2/3, -2)
D)(0, 2)
E)(2, 2/3)
Rationale: Look at the diagram below:
Line segment.pngSince, AC= 1/2 CB, then AC = 1/3 AB. This implies that point C is closer to A than to B, which on the other hand implies that the x-coordinate of C must be less than (-4+8)/2=0.5. Only D and A fits, but as (0 , 2) is clearly not on line segment AB, then the answer must be A.
Answer: A.
Answer: A
Question: Kim purchased n items from a catalog for $8 each. Postage and handling charges consisted of $4 for the first item and $1 for each additional item. Which of the following gives the total dollar amount for Kim’s purchase, including postage and handling, in terms of n ?
Options:
A)8n + 2
B)8n + 4
C)9n + 2
D)9n + 3
E)9n + 4
Rationale: its C
n items for $8 each
total price $8n
postage and handling of $3 for 1st item and $1 for the rest
total postage and handling = $ [4+ (n-1)]
= $ n+3
total cost
8n+n+3 = 9n+3
D
Answer: D
Question: Mr. Hanson has a pool of money from which to give out Christmas bonuses to his 5 employees. He wants all his employees to have identical bonuses, but when he divides them out, he finds he has 2 dollars left over, as the payroll system will only accept whole dollar amounts. The next Christmas, Mr. Hanson discovers the pool for the bonuses is 3 times the size. This time, how much money will be left over?
Options:
A)0
B)1
C)2
D)3
E)4
Rationale: Set x = to amount of money for bonuses, and y to be the amount of each individual bonus.
x = 5*y +2.
3x = 15*y+6
3x = 3*5*y + 6
3x = 5(3(y+1))+1
Remainder is then 1, so option B.
Answer: B
Question: In a drawer of shirts 8 are blue, 6 are green and 4 are magenta. If Mason draws 2 shirts at random, what is the probability E at least one of the shirts he draws will be blue?
Options:
A)25/153
B)28/153
C)5/17
D)E=4/9
E)E=12/17
Rationale: P(at least one blue) = 1 - P(0 blue) = 1 - 10/18*9/17 = 12/17.
Answer: E.
Answer: E
Question: Katie has 9 employees that she must assign to 3 different projects. If 3 employees are assigned to each project and no one is assigned to multiple projects, how many different combinations L of project assignments are possible?
Options:
A)252
B)1,680
C)2,340
D)362,880
E)592,704
Rationale: The ways to select three employees out of 9 for first project = 9C3
The ways to select three employees out of Remaining 6 for Second project = 6C3
Third Project already has the group of three to be assigned to it so need to select that
So total ways to assign 3 employees to each of 3 projects L= 9C3 * 6C3 * 1 = 1,680
Answer: Option B
Answer: B
Question: A lady grows cabbage in her garden that is in the shape of a square. Each cabbage takes 1 square foot of area in her garden. This year, she has increased her output by 127 cabbages when compared to last year. The shape of the area used for growing the cabbage has remained a square in both these years. How many cabbages did she produce this year?
Options:
A)4096
B)4098
C)5000
D)5096
E)Cannot be determined
Rationale: Explanatory Answer
The shape of the area used for growing Cabbage has remained a square in both the years.
Let the side of the square area used for growing Cabbage this year be X ft.
Therefore, the area of the ground used for cultivation this year = X2 sq.ft.
Let the side of the square area used for growing Cabbage last year be Y ft.
Therefore, the area of the ground used for cultivation last year = Y2 sq.ft.
As the number of cabbage grown has increased by 127, the area would have increased by 127 sq ft because each cabbage takes 1 sq ft space.
Hence, X2 - Y2 = 127
(X + Y)(X - Y) = 127.
127 is a prime number and hence it will have only two factors. i.e., 127 and 1.
Therefore, 127 can be expressed as product of 2 numbers in only way = 127 * 1
i.e., (X + Y)(X - Y) = 127* 1
So, (X + Y) should be 127 and (X - Y) should be 1.
Solving the two equations we get X = 64 and Y = 63.
Therefore, number of cabbage produced this year = X2 = 642 = 4096.
Alternative Approach : Use answer choices
The area in both the years are squares of two numbers.
That rules out choice B,C and D. as 4098,5000 and 5096 are not the square of any number.
Check Choice A: If this year's produce is 4096, last year's produce would have been 4096 - 127 = 3969
3969 is the square of 63.
So, 4096 is the answer.
Choice A
Answer: A
Question: The total age of A and B is 13 years more than the total age of B and C. C is how many years younger than A.?
Options:
A)16
B)12
C)15
D)20
E)13
Rationale: (A+B)-(B-C)=13
A-C=13
Answer is E
Answer: E
Question: Out of 15 consecutive numbers, 2 are chosen at random. The probability that they are both odds or both primes is?
Options:
A)1/2
B)1/7
C)1/8
D)1/1
E)1/3
Rationale: A leap year has 52 weeks and two days
Total number of cases = 7
Number of favourable cases = 1
i.e., {Saturday, Sunday}
Required Probability = 1/7
Answer:B
Answer: B
Question: What is the probability that when a hand of 5 cards is drawn from a well shuffled deck of 52 cards,
it contains all Queens?
Options:
A)192/379017
B)192/379015
C)379015/192
D)1/379015
E)2/379015
Rationale: nCr = n!/(n-r)!r!
Total number of possible hands = 52C5
52C5 = 2274090
Number of hands with 4 Queens = 4C4 × 48C1
4C4 = 24
48C1 = 48
(other 1 card must be chosen from the rest 48 cards)
Hence P (a hand will have 4 Queens) = (4C4 × 48C1)/52C5 = 192/379015.
B
Answer: B
Question: Kiran travels from A to B by car and returns from B to A by cycle in 7 hours. If he travels both ways by car he saves 3 hours. What is the time taken to cover both ways by cycle?
Options:
A)10
B)16
C)15
D)15
E)12
Rationale: Let the time taken to cover from A to B in car and cycle be x hours and y hours respectively.
x + y = 7 --- (1) ; 2x = 4 --- (2)
solving both the equations, we get y = 5
So, time taken to cover both ways by cycle = 2y hours = 10 hours.
Answer: A
Answer: A
Question: For the past n days, the average (arithmetic mean) daily production at a company was 60 units. If today's production of 90 units raises the average to 65 units per day, what is the value of n ?
Options:
A)30
B)18
C)10
D)9
E)5
Rationale: (average production for n days) * n = (total production for n days) --> 60n=(total production for n days);
(total production for n days) + 90 = (average production for n+1 days) * (n+1) --> 60n + 90 = 65 * (n+1) --> n=5.
Or as 30 extra units increased the average for n+1 days by 5 units per day then 30/(n+1)=5 --> n=5.
Answer: E.
Answer: E
Question: Two trains are traveling on parallel tracks in the same direction. The faster train travels at 130 miles per hour, while the slower train travels at 100 miles per hour. At 2 o’clock the faster train is 15 miles behind the slower one. How far apart are the two trains at 5 o'clock?
Options:
A)60 miles
B)80 miles
C)75 miles
D)120 miles
E)400 miles
Rationale: Answer = C. 75 miles
Relational speed = 130 - 100 = 30 miles per hour
In 3 hours, difference = 30 * 3 = 90 miles
Fast train trailing 15 miles, so effective difference = 90 - 15 = 75 miles
Answer: C
Question: Two cars cover the same distance at the speed of 60 and 64 kmps respectively. Find the distance traveled by them if the slower car takes 1 hour more than the faster car.
Options:
A)873
B)838
C)960
D)838
E)939
Rationale: Explanation:
60(x + 1) = 64x
X = 15
60 * 16 = 960 km
Answer: Option C
Answer: C
Question: The average earning of amechanic for the first 4days of a week is Rs.18 and for the last four days is Rs.22. If heearns Rs.20 on the fourth day, his average earning forthe whole week is?
Options:
A)Rs. 10
B)Rs. 20
C)Rs. 30
D)Rs. 40
E)Rs. 50
Rationale: Total earning for the week = Sum of earning of first four days + Sum of earning of last four days - Earning of 4th day
= 4 x18 + 4 x 22 -20
= Rs. 140
∴ Average earning = 140 / 7
= Rs. 20
B
Answer: B
Question: By selling 50 meters of cloth. I gain the selling price of 20 meters. Find the gain percent?
Options:
A)42 7/7%
B)42 5/8%
C)42 6/4%
D)42 6/8%
E)66 2/3%
Rationale: SP = CP + g
50 SP = 50 CP + 20 SP
30 SP = 50 CP
30 --- 20 CP gain
100 --- ? => 66 2/3%
Answer: E
Answer: E
Question: A Sum of Rs.2600, is lent out in 2 parts SI at 10% for 5yrs is equal to SI on 2nd part at 9% rate for 6 yrs. find the ratio of parts.
Options:
A)23:21
B)27:25
C)25:27
D)23:29
E)21:19
Rationale: Solution :
Given SI1 = SI 2
P1 : P2 = 1/R1T1 : 1/R2T2
= 1/(10*5) : 1/(9:6)
27:25
B
Answer: B
Question: In a kilometer race, A beats B by 50 meters or 10 seconds. What time does A take to complete the race?
Options:
A)347
B)190
C)388
D)277
E)281
Rationale: Time taken by B run 1000 meters = (1000 * 10)/50 = 200 sec.
Time taken by A = 200 - 10 = 190 sec.
Answer: B
Answer: B
Question: In a park there are two ponds with both brown ducks and green ducks. In the smaller pond there are 20 ducks and in the larger pond there are 80 ducks. If 20% of the ducks in the smaller pond are green and 15% of the ducks in the larger pond are green, then what percentage of ducks are green?
Options:
A)13%
B)14%
C)15%
D)16%
E)17%
Rationale: Number of ducks in small pond = 20
green ducks in small pond = 20 % of 20 = 4 ducks
Number of ducks in large pond = 80
green ducks in large pond = 15 % of 80 = 12 ducks
Total number of ducks = 20 + 80 = 100
total number of green ducks = 4 + 12 = 16 ducks
percentage of green ducks = 16/100 * 100 = 16%
Answer: D
Answer: D
Question: At a party, everyone shook hands with everybody else. There were 66 handshakes.
How many people were at the party?
Options:
A)15
B)18
C)11
D)12
E)19
Rationale: D
12
If there are n people,
the first person will shake hand with n-1 persons,
the second with n-2,
the third with n-3,
and
the (n-1)th person with n-(n-1)=1 person means the last person.
Hence, total handshakes are (n-1)+(n-2)+(n-3)+….+3+2+1
Which can be equated using n(n-1)/2=66
Hence, n=12
Answer: D
Question: Find the area of the square, one of whose diagonals is 5.9 m long ?
Options:
A)37.14m^2
B)17.4m^2
C)8.96m^2
D)7.8m^2
E)27.14m^2
Rationale: Area of the square= 1/2(diagonal)^2
=(1/2*5.9*5.9)m^2
= 17.4 m^2
Answer (B)
Answer: B
Question: During a trip on an expressway, Don drove a total of x miles. His average speed on a certain 5-mile section of the expressway was 30 miles per hour, and his average speed for the remainder of the trip was 60 miles per hour. His travel time for the x-mile trip was what percent greater than it would have been if he had traveled at a constant rate of 40 miles per hour for the entire trip?
Options:
A)8.5%
B)50%
C)200/x%
D)60/x%
E)500/x%
Rationale: Say x = 5 miles (so no remainder of the trip).
Time to cover x = 5 miles at 30 miles per hour = (time) = (distance)/(rate) = 5/30 = 1/6 hours = 10 minutes.
Time to cover x = 5 miles at 60 miles per hour = (time) = (distance)/(rate) = 5/60 = 1/12 hours = 5 minutes.
(Or simply, half rate will result in doubling the time.)
So, we can see that the time to cover x = 5 miles at 30 miles per hour (10 minutes) is 100% greater than the time to cover x = 2 miles at 40 miles per hour (5 minutes).
Now, plug x = 2 miles into the answer choices to see which one yields 100%. Only answer E works.
Answer: C.
Answer: C
Question: ACME’s manufacturing costs for sets of horseshoes include a $22,450 initial outlay, and $30per set. They can sell the sets $70. If profit is revenue from sales minus manufacturing costs, and the company producessells 1000 sets of horseshoes, what was their profit?
Options:
A)$16550
B)$18550
C)$17000
D)$20550
E)$17550
Rationale: Total Manufacturing cost = 22,450+1000*30 = 52450
Total Selling cost = 1000*70= 70000
Profit = 70000-52450 = 17550
Answer : E
Answer: E
Question: The inverse ratio of 9: 2: 1 is?
Options:
A)1:9:18
B)2:9:18
C)2:7:18
D)2:13:18
E)2:9:15
Rationale: 1/9: 1/2: 1/1 = 2:9:18
ANSWER:B
Answer: B
Question: The price of a commodity was raised by 25%. So what is % amount of commodity would be reduced by family so that the amount spent on the commodity remains same
Options:
A)10%
B)20%
C)30%
D)40%
E)50%
Rationale: say price of commodity is 100
after raising price by 25% new price=125
to make it 100 again,
25=125*x/100, x% has to be reduced ie:20%
ANSWER:B
Answer: B
Question: An investor bought 200 shares of stock in ABCD company in 1990. By 1992, the investment was worth only 2/3 of its original value. By 1995, the 200 shares were worth only 1/4 of their value in 1990. By what percent did the value of the investment drop from 1992 to 1995?
Options:
A)62.5%
B)25%
C)33 1/3%
D)50%
E)66 2/3%
Rationale: Let price of each share in 1990 = X.
Total cost in 1990 = 200X
Now Price in 1992 = 2/3 * 200X = 400/3 * X
Now price in 1995 = 1/4 *200X= 50X
%Change in 1995 from 1992 = [(400/3* X -50X) / (400/3 *X) ] *100 = 62.5%
Answer A
Answer: A
Question: A train 300 m long is running at a speed of 68 kmph. How long does it take to pass a man who is running at 8 kmph in the same direction as the train?
Options:
A)5 sec
B)9 sec
C)12 sec
D)18 sec
E)19 sec
Rationale: Speed of the train relative to man = (68 - 8) kmph
= (60* 5/18) m/sec = (50/3)m/sec
Time taken by the train to cross the man
= Time taken by It to cover 300 m at 50/3 m / sec = 300 *3/ 50 sec = 18 sec
Answer : D.
Answer: D
Question: A trader has 1600 kg of sugar. He sells a part at 8% profit and the rest at 12% profit. If he gains 11% on the whole , find the quantity sold at 12%?
Options:
A)1000
B)1200
C)1400
D)1450
E)1500
Rationale: By rule of alligation,
% Profit by selling part1	% Profit by selling part2
8	12
Net % Profit
11
12 - 11 = 1	11 - 8 = 3
=> Quantity of part1 : Quantity of part2 = 1 : 3
Given that total quantity = 1600 kg
Hence, quantity of part2 (quantity sold at 12% profit)
=
1600
×
3
4
=1200
B)
Answer: B
Question: The price of the jewel, passing through three hands, rises on the whole by 65%. If the first and the second sellers 20% and 25% profit respectively find the percentage profit earned by the third seller.
Options:
A)20
B)10
C)15
D)25
E)30
Rationale: Let the original price of the jewel be $ p and let the profit earned by the third seller be x% Then, (100+x)% of 125% of 120% of P =165% Of P ((100+X)/100*125/100*120/100*P)=(165/100*P)
==> (100+X)=(165*100*100)/(125*120)=110=>X=10%
Answer B) 10
Answer: B
Question: Juan is a gold medalist in athletics. In the month of May, if Juan takes 12 seconds to run y yards, how many seconds will it take him to run x yards at the same rate?
Options:
A)10x/y
B)11x/y
C)9x/y
D)12x/y
E)13x/y
Rationale: velocity=distance/time;
since he ran at same rate both d tyms,
y/12=x/t
so t=12x/y
ANSWER:D
Answer: D
Question: x^2 + dx + 72 = 0 has two distinct integer roots; how many values are possible for d?
Options:
A)3
B)6
C)8
D)12
E)24
Rationale: For a quadratic equation ax^2+dx+c=0, we know that -d/a is sum of roots and c/a is product of roots.
The quadratic equation here is x^2 + dx + 72 = 0, where product of roots is 72.
If we find all the factors of 72, we have the answer.
By prime factorization, we get 72= 2^3*3^2.
We know that total factors are (3+1)*(2+1) = 12 (Reason: with 2^n, we have n+1 possibilities. n^0 to n^n. so n+1)=D
Answer: D
Question: 1,257
1,275
1,527
........
........
+7,521
The addition problem above shows four of the 24 different integers that can be formed by using each of the digits 1,2,5 and 7 exactly once in each integer. What is the sum Q of the 24 integers ?
Options:
A) 26,996
B) 44,406
C) 60,444
D) 66,660
E) 99,990
Rationale: This is the way i solved it :
Total no. of different combos = 24, total digits 4 therefore each digit must repeat 24/4 = 6 times in each row .. So the right most row would add up to 1x6 + 2x6 + 5x6 + 7x6 = 6+12+30+42 = 90 .. Each row would add up to 90, so 90 in the first means we have 9 that carries over and we get 0 , the second time its 90+9 and 9 stays and one 9 goes to the row to the left, so the last two digits of the SUM Q should be 90 (E) .. We could go on and solve the exact number but since only one answer choice has the last digits as 90 we needn't go any further..
Answer: E
Question: 495 x 495 = ?
Options:
A)250000
B)250025
C)5000
D)245025
E)240000
Rationale: 495 x 495 = (495 )2
= (500 - 5)2
= (500)2 + (5)2 - (2 x 500 x 5)
= 250000+ 25 - 5000
= 250025 - 5000
=245025.
D)
Answer: D
Question: An gun can take a maximum of four shotsat an enemyplane moving away from it. The probability of hitting the plane at the 1st, 2nd, third and 4th shots are 1.4, 1.3, 1.2 & 1.1 respectively. What is the probability that the plane is hit when all the four shots are fired?
Options:
A)0.6976
B)0.7893
C)0.8212
D)0.7541
E)0.9847
Rationale: Required probability:
=(0.4×0.7×0.8×0.9)+(0.6×0.3×0.8×0.9)+(0.6×0.7×0.2×0.9)+(0.6×0.7×0.8×0.1)+(0.4×0.3×0.8×0.9)+(0.4×0.7×0.2×0.9)+(0.4×0.7×0.8×0.1)+(0.6×0.3×0.2×0.9)+(0.6×0.3×0.8×0.1)+(0.6×0.7×0.2×0.1)+(0.4×0.3×0.2×0.9)+(0.6×0.3×0.2×0.1)+(0.4×0.3×0.8×0.1)+(0.4×0.7×0.2×0.1)+(0.4×0.3×0.2×0.1)=(0.4×0.7×0.8×0.9)+(0.6×0.3×0.8×0.9)+(0.6×0.7×0.2×0.9)+(0.6×0.7×0.8×0.1)+(0.4×0.3×0.8×0.9)+(0.4×0.7×0.2×0.9)+(0.4×0.7×0.8×0.1)+(0.6×0.3×0.2×0.9)+(0.6×0.3×0.8×0.1)+(0.6×0.7×0.2×0.1)+(0.4×0.3×0.2×0.9)+(0.6×0.3×0.2×0.1)+(0.4×0.3×0.8×0.1)+(0.4×0.7×0.2×0.1)+(0.4×0.3×0.2×0.1)
=0.2016+0.1296+0.756+0.336+0.864+0.504+0.224+0.324+0.144+0.0084+0.0216+0.0036+0.0096+0.0056+0.002=0.2016+0.1296+0.756+0.336+0.864+0.504+0.224+0.324+0.144+0.0084+0.0216+0.0036+0.0096+0.0056+0.002
=0.6976=0.6976
Edit: Thank you Vaibhav for providing an alternative method.
Alternate Method:
probability that the plane is hit when all the four shots are fired,
P=1−probability of not hitting the targetP=1−probability of not hitting the target
=1−(0.6×0.7×0.8×0.9)=1−(0.6×0.7×0.8×0.9)
=1−0.3024=1−0.3024
=0.6976
A
Answer: A
Question: If j and k are two positive integers and j/k = 1.05, then j can equal which one of the following?
Options:
A) 15
B) 21
C) 20
D) 22
E) 23
Rationale: j/k = 1.05 = 105/100 = 21/20
So, j COULD equal 21
Answer: 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 2 cms, How much did it rain on Wednesday?
Options:
A)10.9
B)7
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 = 2
â‡’12x = 14
â‡’6x = 7
Answer: B
Answer: B
Question: A rectangular grass field is 95 m * 55 m, it has a path of 2.5 m wide all round it on the outside. Find the area of the path and the cost of constructing it at Rs.2 per sq m?
Options:
A)1350
B)1550
C)9676
D)1679
E)2691
Rationale: Area = (l + b +2d) 2d
= (95 + 55 +2.5 * 2) 2*2.5 => 775
775 * 2 = Rs.1550
Answer:B
Answer: B
Question: Anmol can eat 27 pastries in a hour.
Aakriti can eat 2 pastries in 10 minutes.
Divya can eat 7 pastries in 20 minutes.
How long will it take them to eat a 360 pastries ?
Options:
A)6 hours.
B)1 hours.
C)5 hours.
D)4 hours.
E)3 hours.
Rationale: In one hour, Anmol eats 27 pastries, Aakriti eats 12, and Divya eats 21. A total of 60 pastries. Therefore 360 pastries would take 360 ÷ 60 = 6 hours.
ANSWER A
Answer: A
Question: In a simultaneous throw of pair of dice .find the probability of getting the total more than 7
Options:
A)3/7
B)12/5
C)5/12
D)5/7
E)2/5
Rationale: Here n(S)=(6*6)=36
let E=event of getting a total more than 7
={(2,6),(3,5),(3,6),(4,4),(4,5),(4,6),(5,3),(5,4),(5,5),(5,6),(6,2),(6,3),(6,4),(6,5),(6,6)}
P(E)=n(E)/n(S)=15/36=5/12.
Ans: C
Answer: C
Question: ACME’s manufacturing costs for sets of horseshoes include a $11,450 initial outlay, and $19.75 per set. They can sell the sets $52.00. If profit is revenue from sales minus manufacturing costs, and the company producessells 987 sets of horseshoes, what was their profit?
Options:
A)$20,380.75
B)$30,943.25
C)$41,308.50
D)$51,817.50
E)$53,624.25
Rationale: its A
since options are not so close we can solve this by uniting calculation and guessing
total sales will be bit lower than 52000
from that initial outlay will get deducted 11500 so we left with 31500
variable cost say 20 X 1000 = 20000 will be deducted so finally we left with 20500
since we have considered the price greater than it actually is, the correct answer will certainly not cross the threshold of 20500.
Answer: A
Question: Of the 12 temporary employees in a certain company, 4 will be hired as permanent employees. If 5 of the 12 temporary employees are women, how many of the possible groups of 4 employees consist of 3 women and one man?
Options:
A)22
B)35
C)56
D)70
E)105
Rationale: Possible groups = Possible groups of 3 women * possible groups of 1 men
Since order does not matter, its a combination problem.
=[5!/(3!2!)} * [7!/(6!1!)]
=70
ANSWER:D
Answer: D
Question: The average (arithmetic mean) of the integers from 100 to 200, inclusive, is how much lesser than the average of the integers from 150 to 950, inclusive?
Options:
A) 350
B) 475
C) 300
D) 425
E) 400
Rationale: For an AP the mean or average of series is average of first and last term.
So, average of numbers between 150 to 950, inclusive = (150+950)/2 = 550
average of numbers between 100 to 200, inclusive = (100+200)/2 = 150
difference = 550 - 150 = 400
Answer is E
Answer: E
Question: In a throw of dice what is the probability of getting number greater than 5
Options:
A)1/2
B)1/3
C)1/5
D)1/6
E)None of these
Rationale: Explanation:
Number greater than 5 is 6, so only 1 number
Total cases of dice = [1,2,3,4,5,6]
So probability = 1/6
Option D
Answer: D
Question: Points A and B are both in the line segment PQ and on the same side of its midpoint. A divides PQ in the ratio 2:3, and B divides PQ in the ratio 3:4. If AB=2, then the length of PQ is:
Options:
A)70
B)75
C)80
D)85
E)90
Rationale: Explanation :
Let, PA=2x and AB=3x and PB=3y and BQ=4y
PB:BQ=3:4
PA:QA=2:3
PQ=5x=7y
x=7/5 -------------------(i)
From equation (i) and (ii), we have
=>AB=PQ−PA−BQ.
=>7y−4y−2x,
=>3y−2x=2. (AB = 2 ) --------------------(ii)
=>y=10 and Hence, PQ = 70.
Answer : A
Answer: A
Question: Jake, Lena, Fred, John and Inna need to drive home from a corporate reception in an SUV that can seat 7 people. If only Inna, Lena or Jake can drive, how many seat allocations are possible?
Options:
A)30
B)42
C)120
D)360
E)1080
Rationale: 5 people ,7 seats, only 3 can drive
if inna is in one seat remaining, 4 people can be arranged in 4p4 i.e 4! =24 ways
since any one can drive total ways = 24 *3= 72 ways
4 seats can be chosen out of remaining 6 seats in 6c4 ways = 6!/(4!*2!)= 15 ways
72*15=1080
E
Answer: E
Question: In a six-sided polygon EQRSTV ∠E measures 48° less than the average (arithmetic mean) of the remaining five angles. What does ∠E equal to, in degrees?
Options:
A) 72
B) 80
C) 88
D) 96
E) 104
Rationale: The sum of interior angle in a polygon is (n-2)*180
so for a six sided figure, (6-2)*180 = 720
let the A.M of the other 5 angles be 'm'
--> m*5 + ∠E = 720, we know ∠E=m-48
--> m*5 + m - 48 = 720, solving we get m=128
hence ∠E= 128-48 = 80
Ans B.
Answer: B
Question: The average weight of 16 boys in a class is 50.25 kg and that of the remaining 8 boys is 45.15 kg. Find the average weights of all the boys in the class.
Options:
A)48.0
B)48.55
C)49.05
D)49.0
E)45.0
Rationale: Average weight of 16 boys = 50.25
Total weight of 16 boys = 50.25 × 16
Average weight of remaining 8 boys = 45.15
Total weight of remaining 8 boys = 45.15 × 8
Total weight of all boys in the class = (50.25 × 16)+ (45.15 × 8)
Total boys = 16 + 8 = 24
Average weight of all the boys = ((50.25×16)+(45.15×8))/24
=(50.25×2)+(45.15×1)/3
=(16.75×2)+15.05
=33.5+15.05=48.55
Answer is B.
Answer: B
Question: When a number is divided by 6 &then multiply by 12 the answer is 9 what is the no.?
Options:
A)4.5
B)5
C)5.5
D)5.8
E)6
Rationale: if $x$ is the number, x/6 * 12 = 9
=> 2x = 9
=> x = 4.5
A
Answer: A