divelab/Sys2Bench huggingface dataset:
Question: In a class total 34 students, 16 are have a brother, 15 are have sisters, 9 students don't have either brothers or sisters.Find the number of students having both brother and sisters.
Options:
A)4
B)5
C)6
D)7
E)8
Rationale: Total Number of students = 34
Let A be the Number of students have a brothers.
Let B be the number of students have a sisters.
AUB = Number of students have either brothers or sisters=34-9=25
n(AUB)= n(A)+n(B)-n(AnB)
25=16+15-n(AnB)
n(AnB)=31-25
n(AnB)=6
The number of students having both brother and sisters = 6
ANSWER:C
Answer: C
Question: What is the greatest 5-digit number when divided by 6, 7 ,8 , 9, and 10 leaves a remainder of 4, 5, 6, 7, and 9 respectively?
Options:
A)56780
B)78910
C)97479
D)97918
E)97920
Rationale: When you divide a positive integer by 10, the remainder will just be the units digit. We know the remainder is 9 when we divide by 10, so C is the only possible answer.
Answer: C
Question: The inverse ratio of 6: 2: 1 is?
Options:
A)2:3:7
B)2:3:9
C)2:3:2
D)1:3:6
E)2:3:1
Rationale: 1/6: 1/2: 1/1 = 1:3:6
Answer:D
Answer: D
Question: If f(x) = ax^5 – 3x^2 + ax^2 – x, then f(b) – f(-b) will equal:
Options:
A)0
B)2ab
C)2ab^4 – 6
D)2ab^5-2b
E)ab^5
Rationale: f(x)=ax^5 – 3x^2 + ax^2 – x
f(b) = ab^5 – 3b^2 + ab^2 – b
f(-b) = -ab^5 – 3b^2 + ab^2 + b
f(b) - f(-b) = ab^5 – 3b^2 + ab^2 – b + ab^5 + 3b^2 - ab^2 – b
=2ab^5-2b
Answer D
Answer: D
Question: For the set { 3, 3, 4, 4, 5, 5, x}, which of the following values of x will most increase the standard deviation?
Options:
A)(-3)^2
B)2
C)3
D)4
E)5
Rationale: Standard Deviation Step 1, as pointed out by others, is to find out the mean = 4
Step 2, For each number: subtract the Mean and square the result =
(1-4)^2=(-3)^2
(2-4)^2=(-2)^2
(3-4)^2 =(-1)^2
(4-4)^2=(.0)^2
(5-4)^2=(1)^2
Clearly (1-4)^2=(-3)^2 will give you the greatest value among all the other options.
Hence A
Answer: A
Question: Gold is 10 times as heavy as water and copper is 5 times as heavy as water. In what ratio should these be mixed to get an alloy 9 times as heavy as water?
Options:
A)3:2
B)1:2
C)4:1
D)5:2
E)4:3
Rationale: G = 10W
C = 5W
Let 1gm of gold mixed with x gm of copper to get 1+x gm of the alloy
1gm gold + x gm copper = x+1 gm of alloy
10W+5Wx = x+1 * 9W
10+5x = 9(x+1)
x = 1/4
Ratio of gold with copper = 1:1/4 = 4:1
Answer is C
Answer: C
Question: Media companies sell their magazine through a distributor, which take a commission of 3% of the price set by the media company. The distributor obtains the magazines through each company at the price of $12 per subscription. What is the price that the buyer observers if the distributor wants to maintain a 3% profit on the cost of a subscription?
Options:
A)11.13
B)11.72
C)11.74
D)12.72
E)12.74
Rationale: Magazine price = $12;The distributor wants to maintain a 3% profit on the cost of each magazine subscription, thus he must get $12*1.03 = $12.36 after the distributor takes a commission of 3% of the final price --> (final price)*0.97 = $12.36 --> (final price) = $12.74Answer: E.
Answer: E
Question: How many 6 digit telephone numbers can be formed if each number starts with 35 and no digit appears more than once?
Options:
A)720
B)360
C)1420
D)1680
E)1780
Rationale: 6 digit number where first 2 digit are fixed .
1*1*8*7*6*5 =1680
ANSWER:D
Answer: D
Question: The number of arrangement of letters of the word BANANA in which the two N's do not appear adjacently is:
Options:
A)40
B)50
C). 60
D)80
E)100
Rationale: Total # of arrangements of BANANA is 6!/(3!2!) = 60 (arrangement of 6 letters {B}, {A}, {N}, {A}, {N}, {A}, where 3 A's and 2 N's are identical).
The # of arrangements in which the two N's ARE together is 5!/3!=20 (arrangement of 5 units letters {B}, {A}, {A}, {A}, {NN}, where 3 A's are identical)..
The # of arrangements in which the two N's do not appear adjacently is {total} - {restriction} = 60 - 20 = 40.
Answer: A.
Answer: A
Question: Bill has a small deck of 14 playing cards made up of only 2 suits of 7 cards each. Each of the 7 cards within a suit has a different value from 1 to 7; thus, there are 2 cards in the deck that have the same value. Bill likes to play a game in which he shuffles the deck, turns over 4 cards, and looks for pairs of cards that have the same value. What is the chance that Bill finds at least one pair of cards that have the same value?
Options:
A)8/67
B)61/130
C)17/33
D)63/143
E)25/88
Rationale: P(no pairs) = 12/13*10/12*8/11 = 80/143
P(at least one pair) = 1 - 80/143 = 63/143
The answer is D.
Answer: D
Question: In a theater, the first row has 15 seats and each row has 2 more seats than previous row. If the last row has 53 seats, what is the total number of seats in the theater?
Options:
A)600
B)640
C)680
D)720
E)760
Rationale: The number of seats in the theater is
15 + (15+2) + ...+ (15+38)=
20(15) + 2(1+2+...+19)=
20(15) + 2(19)(20)/2=
20(15+19) = 20(34) = 680
The answer is C.
Answer: C
Question: In an xy-coordinate plane, a line is defined by y = kx + 1. If (4, b), (a,3), and (a, b+1) are three points on the line, where a and b are unknown, then k = ?
Options:
A) 1/2
B) 1/4
C) 3/2
D) 2
E) 5/2
Rationale: b=4k+1...(1)
b+1=ak+1...(2)
3=ak+1...(3)
Taking (2) and (3)
3=b+1
b=2
Taking (1)
2=4k+1
k=1/4
Answer : B
Answer: B
Question: What is the greatest prime factor of 8^13 - 2^30?
Options:
A)23
B)37
C)59
D)73
E)107
Rationale: 8^13 - 2^30
=(2^3)^13 - 2^30
= 2^39 - 2^30
= 2^30 (2^9 -1)
= 2^30 * (512-1)
= 2^30 * 511
= 2^30 * 7 * 73
The greatest prime factor is 73.
The answer is D.
Answer: D
Question: Ten identical machines, running continuously at the same constant rate, take 6 days to complete a shipment. How many additional machines, each running at the same constant rate, would be needed to reduce the time required to complete a shipment by four days?
Options:
A)25
B)20
C)14
D)9
E)5
Rationale: From the question you know that 10R = 1/6. The question asks you (partially) to make the rate from 1/6 to 1/2 (drop from 6 day to 2). So the only thing that you need to do is to find the magic number than can convert 1/6 to 1/2.
So 1/6 * x = 1/2 (1 equation with one unknown). So by solving this you get x = 6/2 or 3/1. Thats it then! Take the magic number 3/1 and multiply BOTH sides of the original equation and you have:
10*(3/1)*R = (3/1) * 1/6
10 * 3 * R = 1/2, Hence 30R = 1/2, therefore 20 more machines!
B
Answer: B
Question: If S is the sum of the reciprocals of the consecutive integers from 91 to 100, inclusive, which of the following is less than S?
I. 1/8
II. 1/9
III. 1/10
Options:
A)None
B)I only
C)III only
D)II and III only
E)I, II, and III
Rationale: Since we summarize the reciprocals from 100 to 91, we can say also that we add ten numbers who are all (with one exception 1/100) greater than 1/100, so that the sum must be greater than 1/10.
On the other side we can say that we add the reciprocals from 91 to 100, so that the sum has to be less than the sum of ten times 1/91.
We can conclude that the sum has to be less than 1/9 but more than 1/10. That leaves us C as the only possible answer.
Answer: C
Question: A cistern 9m long and 4 m wide contains water up to a depth of 1 m 25 cm. The total area of the wet surface is:
Options:
A)49 m2
B)50 m2
C)53.5 m2
D)68.5 m2
E)57 m2
Rationale: Area of the wet surface	= [2(lb + bh + lh) - lb]
= 2(bh + lh) + lb
= [2 (4 x 1.25 + 9 x 1.25) + 9 x 4] m2
= 68.5 m2.
Answer: Option D
Answer: D
Question: A delegation of 5 members has to be formed from 3 ladies and 5 gentlemen. In how many ways the delegation can be formed, if 2 particular ladies are always included in the delegation?
Options:
A)20
B)30
C)37
D)40
E)39
Rationale: There are three ladies and five gentlemen and a committee of 5 members to be formed.
Number of ways such that two ladies are always included in the committee
= ⁶C₃ = (6 * 5 * 4)/6 = 20.
Answer:A
Answer: A
Question: A and B start a business jointly. A invests Rs.16000 for 8 months and B remains in the business for 4 months. Out of the total profit B claims 2/7th share. How much money is contributed by B?
Options:
A)12288
B)12800
C)27636
D)19287
E)19281
Rationale: Explanation:
16*8: x*4 = 5:2
x = 12.8 => Rs.12800
Answer: B
Answer: B
Question: In the first 10 overs of a cricket game, the run rate was only 3.2. What should be the rate in the remaining 40 overs to reach the target of 252 runs?
Options:
A)6.25
B)6.22
C)5.5
D)6.39
E)6.13
Rationale: Required run rate
= [252 - (3.2 * 10)]/40
= 220/40
= 5.5
Answer: C
Answer: C
Question: A bag contains 14 wool scarves, exactly one of which is red and exactly one of which is green. If Deborah reaches in and draws three scarves, simultaneously and at random, what is the probability that she selects the red scarf but not the green scarf?
Options:
A)2/15
B)11/23
C)18/121
D)33/182
E)51/273
Rationale: Total possible ways to choose three scarves is 14C3 = 364
We need to choose the red scarf and two of 12 other scarves (not the green scarf).
The number of successful possibilities is 12C2 = 66
P(red scarf but not green scarf) = 66/364 = 33/182
The answer is D.
Answer: D
Question: Rs.630/- distributed among A,B and C such that on increasing their shares by RS.10,RS.5 and RS.15 respectively, The balance money would be divided among them in the ratio 3:4:5. Then, A’s share is:?
Options:
A)Rs.155
B)Rs.145
C)Rs.150
D)Rs.140/-
E)Rs.160
Rationale: A:B:C = 3:4:5
Total parts = 12
A's share is = 3 parts
12 -----> Rs.600/-
3 -----> Rs.150/-
A's total = 150 - 10 = Rs.140/-
D)
Answer: D
Question: Five years ago the average of the ages of A and B was 40 years and now the average of the ages of B and C is 48 years. What will be the age of the B ten years hence?
Options:
A)22
B)27
C)96
D)51
E)2
Rationale: Let the present ages of A, B and C be a, b and c respectively.
Given, [(a - 5) + (b - 5)] / 2 = 40 => a + b = 90 --- (1)
(b + c)/2 = 48 => b + c = 96 --- (2)
From (1) and (2), we cannot find b.
Answer:D
Answer: D
Question: Two persons start running simultaneously around a circular track of length 200 m from the same point at speeds of 10 km/hr and 15 km/hr. When will they meet for the first time any where on the track if they are moving in opposite directions?
Options:
A)28 sec
B)19.2 sec
C)17 sec
D)23 sec
E)27 sec
Rationale: Time taken to meet for the first time anywhere on the track
= length of the track / relative speed
= 200 / (10 + 15)5/18 = 300* 18 / 25 * 5 = 19.2 seconds.
Answer : B
Answer: B
Question: A car covers a distance of 1728 km in 6 hours. Find its speed?
Options:
A)104
B)288
C)271
D)276
E)128
Rationale: 1728/6 = 288 kmph
Answer: B
Answer: B
Question: A certain candy manufacturer reduced the weight of Candy Bar M by 25 percent buy left the price unchanged. What was the resulting percent increase in the price per ounce of Candy Bar M?
Options:
A)20
B)30
C)34
D)35
E)33.33
Rationale: assume 1oz candy cost $1 before.
now price remain same $1 but weight of candy reduces to 0.75 oz
new price of candy = 1/0.75 =1.3333
price increase 33.33 %
E
Answer: E
Question: a renowned battery sells six different-sized wedding cakes. Each cake costs x dollars more than the next one below it in size, and the price of the largest cake is $24.50. If the sum of the prices of the six different cakes is $109.50, what is the value of x?
Options:
A) 1.50
B) 1.75
C) 2.00
D) 2.50
E) 3.00
Rationale: Since the price of the largest cake (6th) is $24.50, then the price of the smallest cake (1st) is $(24.50-5x). Now, the prices of the cakes are evenly spaced so the sum of the prices is (average price)*(# of cakes)=(first+last)/2*(# of cakes). So, (24.50-5x+24.50)/2*6=109.50 --> x=2.5.
Answer: D.
Answer: D
Question: Fifteen more than three times a number is the same as ten less than six times the
number. What is the number
Options:
A)20/2
B)15/4
C)30/5
D)25/3
E)9/6
Rationale: 3x+15 First, addition is built backwards
6x−10 Then, subtraction is also built backwards
3x+15=6x−10 Is between the parts tells us theymust be equal
−3x −3x Subtract 3x so variable is all on one side
15=3x−10 Nowwe have a two−step equation
+10 +10 Add 10 to both sides
25=3x The variable ismultiplied by 3
3 3 Divide both sides by 3
25/3=x Our number is
25/3
correct answer D
Answer: D
Question: Mandrake has to choose from 4 from 10 people. There are 3 girls, 5 boys , 2 children. What is total probability that he will choose 1G , 2B , 1C?
Options:
A)1/7
B)2/7
C)3/7
D)4/7
E)5//7
Rationale: (3C1 * 5C2 * 2C1)/ 10C4 = 3*10*2/210 = 60/210=2/7
ANSWER:B
Answer: B
Question: Maddie has 48 apples, if she give 22 to mike, how many does she have left?
Options:
A)12
B)21
C)26
D)22
E)5
Rationale: 48-22=26
C. 26
Answer: C
Question: Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is?
Options:
A)3/7
B)3/2
C)3/5
D)3/1
E)3/3
Rationale: Let the speeds of the two trains be x m/sec and y m/sec respectively. Then, length of the first train = 27 x meters, and length of the second train = 17 y meters. (27 x + 17 y) / (x + y) = 23
==> 27 x + 17 y = 23 x + 23 y ==> 4 x = 6 y ==> x/y
= 3/2.
Answer: B
Answer: B
Question: The sume of the ages of a father and his son is 45 years.Five years ago,the product of their ages was 34 .The ages of the son and the father are respectively :
Options:
A)6 and 39
B)7 and 38
C)9 and 36
D)11 and 34
E)12 and 74
Rationale: Solution
Let the ages of father and son be x and (45 - x) years respectively.
Then,(x - 5)(45 - x - 5)=34 ⇔ (x - 5) (40 - x)=34 ⇔x2 - 45x + 234 = 0
⇔ (x - 39)(x - 6)= 0 ⇔ x = 39 or x =6.
∴ Father's age = 39 years and son's age =6 years. Answer A
Answer: A
Question: Divide Rs. 5500 among A, B and C so that A receives 1/3 as much as B and C together and B receives 1/5 as A and C together. A's share is?
Options:
A)1227
B)1268
C)1375
D)1200
E)1210
Rationale: A+B+C = 5500
A = 1/3(B+C); B = 1/5(A+C)
A/(B+C) = 1/3
A = 1/4 * 5500 => 1375
Answer: C
Answer: C
Question: There are 2 sections with 4 questions each. If three questions are selected from each section, the chance of getting different questions is________
Options:
A)10
B)214
C)300
D)216
E)245
Rationale: we have to select three questions from each section so the chances are 4C2.4C2.4C2=216
ANSWER:D
Answer: D
Question: Samantha's investment portfolio consists of three stocks: an airline, a bank, and a computer company. In the month of February, the price of the airline's stock rose by 10%, that of the bank decreased by 15% and that of the computer company also decreased by 12%, but the overall value of her portfolio increased. If Samantha owns equal amounts of all three stocks, which of the following could be the initial prices of the three stocks in the order airline, bank, and computer company respectively?
Options:
A)$75, $25, $20
B)$65, $60, $60
C)$65, $55, $90
D)$55, $85, $40
E)$25, $60, $70
Rationale: Since Samantha owns equal amounts of stocks, the 10% increase alone should set off the 15% decrease in each of the other two stocks. i.e The stock which increased should have a substantially higher value than the two stocks which decreased. Between B and A, A is obviously the safer bet and is the right answer.
Answer is A.
Answer: A
Question: A boat having a length 3 m and breadth 2 m is floating on a lake. The boat sinks by 1.5 cm when a man gets on it. The mass of man is
Options:
A)12 kg
B)90 kg
C)72 kg
D)96 kg
E)None
Rationale: Solution
Volume of water displaced	= (3 x 2 x 0.015)m3
= 0.09m3.
Mass of man	=Volume of water displaced ×Density of water
= (0.09×1000) kg
= 90 kg.
Answer B
Answer: B
Question: Tough and Tricky questions: Ratios
4/5 of a certain class left on a field trip. 1/3 of the students who stayed behind did not want to go on the field trip (all the others did want to go). When another vehicle was located, 1/2 of the students who did want to go on the field trip but had been left behind were able to join. What fraction of the class ended up going on the field trip?
Options:
A)1/2
B)2/3
C)13/15
D)23/30
E)4/5
Rationale: let total no. of students be 30
students left on a field trip = 4/5(30) =24
thus 6 students left behind
1/3(6)=2 students did not want to go. thus 4 students want to go on the trip
1/2(4)=2 were able to join the other students on the field trip.
thus total number of students that went on a field trip =24+2 =26
thus required fraction = 26/30 =13/15
C
Answer: C
Question: What is M : N if M is 40% of N
Options:
A)2:3
B)5:2
C)3:2
D)2:5
E)1:2
Rationale: Solution:
M = 40% of N = 40*N/100 = 2*N/5 = 5M = 2N ; M : N = 2 : 5
ANSWER IS D
Answer: D
Question: A group of people were given 2 puzzles. 70% people solved puzzle X and 89% people solved puzzle Y. What is the maximum and minimum percentage of people who could have solved both the puzzles?
Options:
A) 11%, 0%
B) 49%, 33%
C) 70%, 57%
D) 79%, 68%
E) 89%, 79%
Rationale: To solve this question, we don't need any formulas. Just read the question carefully. If 70% of the people solved puzzle X and 89% solved puzzle Y, then maximum % that can solve both correctly can only be 70%. From the given options, only D looks good
Answer C
Answer: C
Question: A tradesman by means of his false balance defrauds to the extent of 30%? in buying goods as well as by selling the goods. What percent does he gain on his outlay?
Options:
A)17%
B)77%
C)44%
D)16%
E)69%
Rationale: g% = 30 + 30 + (30*30)/100
= 69%
Answer: E
Answer: E
Question: If a train, travelling at a speed of 180 kmph, crosses a pole in 6 sec, then the length of train is?
Options:
A)300
B)125
C)288
D)266
E)121
Rationale: D = 180 * 5/18 * 6
= 300 m
Answer: A
Answer: A
Question: Let A be the positive integer satisfying the following equation.
9/10
+
99/102th +
999/103rd + · · · +
9999999999/1010th =
A/1010th
How many 8’s appear in the decimal representation of A ?
Options:
A)0
B)1
C)5
D)8
E)9
Rationale: The sum equals (1- 0.1) + (1- .01) +...+ (1 - .0000000001) = 10 .1111111111 =
9:8888888889. Thus A = 98888888889
correct answer E
Answer: E
Question: A man was asked to state his age in years. His reply was , "Take my age 6 years hence, multiply it by 6 and subtract 6 times my age 6 years ago and you will know how old I am." What was the age of the person ?
Options:
A)18
B)92
C)72
D)26
E)19
Rationale: Explanation:
Let the present age of person be x years.
Then, 6(x + 6) - 6(x - 6 ) = x <=> (6x + 36) - (6x - 36) = x <=> x = 72..
Answer: C
Answer: C
Question: In what time will a railway train 120 m long moving at the rate of 36 kmph pass a telegraph post on its way?
Options:
A)12 sec
B)7 sec
C)8 sec
D)9 sec
E)10 sec
Rationale: T = 120/36 * 18/5
= 12 sec
Answer:A
Answer: A
Question: Given that there are 8 cricket players per team, how many ways can you select 10 cricket players from 2 teams if no more than 3 players can be selected from each team?
Options:
A)2456
B)3136
C)1452
D)3565
E)2134
Rationale: Now from each group we have to select 5 persons only: 8C3 * 8C3 = 56 * 56 = 3136
Total ways=3136 ways.
Answer B
Answer: B
Question: The two trains of lengths 400 m, 600 m respectively, running at same directions. The faster train can cross the slower train in 180 sec, the speed of the slower train is 48 km. then find the speed of the faster train?
Options:
A)76 Kmph
B)68 Kmph
C)79 Kmph
D)25 Kmph
E)28 Kmph
Rationale: Length of the two trains = 600m + 400m
Speed of the first train = X
Speed of the second train= 48 Kmph
1000/X - 48 = 180
1000/x - 48 * 5/18 = 180
50 = 9X - 120
X = 68 Kmph
Answer: B
Answer: B
Question: In a certain store, the profit is 320% of the cost. If the cost increases by 25% but the selling price remains constant, approximately what percentage of the selling price is the profit?
Options:
A)30%
B)40%
C)70%
D)80%
E)90%
Rationale: C
70%
Let C.P. = $ 100. Then, profit = $ 320, S.P. = $ 420
New C.P. = 125% of $ 100 = $ 125.
New S.P. = $ 420
Profit = 420 - 125 = $ 295
Required percentage = 295/420 * 100 = 1475/21 = 70%
Answer: C
Question: Find the area of trapezium whose parallel sides are 20 cm and 18 cm long, and the distance between them is 15 cm?
Options:
A)827 cm2
B)216 cm2
C)285 cm2
D)178 cm2
E)176 cm2
Rationale: Area of a trapezium = 1/2 (sum of parallel sides) * (perpendicular distance between them)
= 1/2 (20 + 18) * (15)
= 285 cm2
Answer:C
Answer: C
Question: P has $35 more than what Q and R together would have had if both B and C had 1/7 of what P has. How much does P have?
Options:
A)$45
B)$47
C)$49
D)$51
E)$53
Rationale: P = (2/7)*P+35
(5/7)*P=35
P=49
The answer is C.
Answer: C
Question: The total expense of a boarding house is partly fixed and partly variable with the number of boarders. When the number of boarders is 25, then the charge is Rs 70 per head and the same is Rs 60 when the number of boarders is 50. What would be the charge per head if there are 100 boarders?
Options:
A)51
B)52
C)53
D)54
E)55
Rationale: consider x as partly fixed and y as partly variable.
as number of boarders has been changing consider it as y.
sum(total expense including fixed n change)=x+25y=1750(25*70)
x+60y=3000(60*50)
by solving those equations v get x as 500 and y as 50
now do for 100 boarders 100y=100*50=5500
per head consists of 5500/100=55.
ANSWER:E
Answer: E
Question: If YWVSQ is 25 - 23 - 21 - 19 - 17, Then MKIGF
Options:
A)13 - 11 - 9 - 7 - 9
B)13 - 11 - 9 - 7 - 6
C)13 - 11 - 9 - 7 - 7
D)13 - 11 - 9 - 7 - 3
E)13 - 11 - 9 - 7 - 1
Rationale: MKIGF = 13 - 11 - 9 - 7 - 6
Note: this is a dummy question. Dont answer these questions
Answer:B
Answer: B
Question: The salary of a person was reduced by 25%. By what percent should his reduced salary be raised so as to bring it at par with his original salary?
Options:
A)10%
B)33.33%
C)20%
D)25%
E)50%
Rationale: Let the original salary be $100
new salary = $75
increase on 75 = 25
increase on 100 = [(25/75)100]% = 33.33%
Answer is B
Answer: B
Question: Find the numbers which are in the ratio 5:2:4 such that the sum of the first and the second added to the difference of the third and the second is 18?
Options:
A)4,3,22
B)4,4,22
C)10,4,8
D)9,6,12
E)9,2,23
Rationale: Let the numbers be a, b and c.
a:b:c = 5:2:4
Given, (a + b) + (c - b) = 21
=> a + c = 21
=> 5x + 4x = 18 => x = 2
a, b, c are 5x, 2x, 4x
a, b, c are 10, 4, 8.
Answer:C
Answer: C
Question: If m and n are even integers, which of the following is an odd integer?
Options:
A)mn + 2
B)m(n − 1)
C)m(m + 5)
D)3m + 4n
E)(m + 3)(n − 1)
Rationale: If m and n are even integers, then:
A. mn + 2: even + even = even
B. m(n − 1): even(odd) = even
C. m(m + 5): even(odd) = even
D. 3m + 4n: even + even = even
E. (m + 3)(n − 1): (odd)(odd) = odd.
Answer is E.
Answer: E
Question: By how much does the larger root of the equation 2a^2+5a = 12 exceed the smaller root?
Options:
A) 5/2
B) 10/3
C) 7/2
D) 14/3
E) 11/2
Rationale: For 2a^2+5a = 12 Roots are [-5 + sqrt(25 + 96)]/4 OR [-5 - sqrt(25 + 96)]/4
= 1.5 OR -4
Hence larger root 1.5 is 1.5 - (-4) = 5.5 = 11/2 greater than smaller root (-4).
Hence option (E).
Answer: E
Question: The cross-section of a water channel is a trapezium in shape. If the channel is 14 meters wide at the top and 8 meters wide at the bottom and the area of cross-section is 880 square meters, what is the depth of the channel (in meters)?
Options:
A)50
B)60
C)70
D)80
E)90
Rationale: 1/2 * d * (14 + 8) = 880
d = 80
The answer is D.
Answer: D
Question: At what time between 5 and 6 o' clock are the hands of a 3 minutes apart ?
Options:
A)24
B)55
C)66
D)88
E)21
Rationale: In this type of problems the formuae is
(5*x+ or - t)*12/11
Here x is replaced by the first interval of given time. Here x is 5.
t is spaces apart
Case 1 : (5*x + t) * 12/11
(5*5 + 3) * 12/11
28 * 12/11 = 336/11= min
therefore the hands will be 3 min apart at 31 5/11 min past 5.
Case 2 : (5*x - t) * 12/11
(5*5 -3 ) * 12/11
22 *12/11 = 24 min
therefore the hands will be 3 min apart at 24 min past 5
Answer: A) 24min
Answer: A
Question: Benny goes to the market for buying some apples to be distributed between her nine kids equally.She takes 360 dollars with her .The cost of each apple is 3 dollars .How many apples does she buy to share them equally between her six kids?
Options:
A)20
B)9
C)15
D)7
E)10
Rationale: cost of each apple = 3 dollars
Apples that Benny can buy with the amount she has=360/3 = 120.
Apples that each kid gets evenly = 120/6 =20 Apples.
So the answer is A=20
Answer: A