divelab/Sys2Bench huggingface dataset:
Question: The average price of three items of furniture is Rs. 15000. If their prices are in the ratio 3:5:7, the price of the cheapest item is :
Options:
A)6000
B)7000
C)8888
D)9000
E)None of these
Rationale: Explanation:
Let their prices be 3x, 5x and 7x.
Then, 3x + 5x + 7x = (15000 * 3) or x = 3000.
Cost of cheapest item = 3x = Rs. 9000. Answer: D
Answer: D
Question: A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. How far is the place?
Options:
A)1.99 km
B)2.88 km
C)4.49 km
D)2.99 km
E)7.88 km
Rationale: M = 6
S = 1.2
DS = 6 + 1.2 = 7.2
US = 6 - 1.2 = 4.8
x/7.2 + x/4.8 = 1
x = 2.88
Answer: B
Answer: B
Question: A runs times as fast as B. If A gives B a start of 80 m, how far must the winning post be so that A and B might reach it at the same time?
Options:
A)200
B)378
C)277
D)298
E)797
Rationale: Explanation:
Ratio of the speeds of A and B =5 : 1 = 5 :3
Thus, in race of 5 m, A gains 2 m over B.
2 m are gained by A in a race of 5 m.
80 m will be gained by A in race of \inline \fn_jvn {\color{Black} \left ( \frac{5}{2}\times 80 \right )} m =200m
\inline \fn_jvn {\color{Black} \therefore }Winning post is 200 m away from the starting point.
Answer: A) 200 m
Answer: A
Question: 2, 4, 6, 8, 10, ... ?
Options:
A)8
B)5
C)7
D)3
E)12
Rationale: Each number increases by 2.
2+2=4
4+2=6
6+2=8
8+2=10
10+2=12
ANSWER:E
Answer: E
Question: A is twice as good a work man as B and together they finish the work in 14 days. In how many days A alone can finish the work?
Options:
A)20
B)21
C)22
D)23
E)24
Rationale: Explanation:
WC = 2:1
2x + x = 1/14 => x = 1/42
2x = 1/21
A can do the work in 21 days.
Answer: B
Answer: B
Question: What is the value of 10^8- 6^4?
Options:
A)9,99,98,623
B)9,99,98,704
C)9,99,98,800
D)9,99,99,521
E)9,99,99,932
Rationale: As 10^n will always have last digit as 0 AND 6^n will always as last digit 6.. hence difference of such sum should always be ending with 4 and there is only on option ..
Answer B
Answer: B
Question: Which of the following is a parallelogram?
Options:
A)130,50,130,50(angle in deg)
B)120,30,130,20(angle in deg)
C)95,95,95,95(angle in deg)
D)a & c
E)none
Rationale: sum of adjacent angles is 180 degrees.
ANSWER:A
Answer: A
Question: If N is the greatest number that will divide 1305, 4665 and 6905, leaving the same remainder in each case.What is the sum of the digits of N ?
Options:
A)1
B)2
C)3
D)5
E)4
Rationale: N = H.C.F. of (4665 - 1305), (6905 - 4665) and (6905 - 1305)
= H.C.F. of 3360, 2240 and 5600 = 1120.
Sum of digits in N = ( 1 + 1 + 2 + 0 ) = 4
ANSWER:E
Answer: E
Question: The cost of producing x tools by a company is given by
C(x) = 2000 x + 5500 (in $)
a) What is the cost of 100 tools?
Options:
A)215500 $
B)205800 $
C)125900 $
D)226500 $
E)205500 $
Rationale: Solution
C(100) = 2000*100 + 5500 = 205500 $
Answer E
Answer: E
Question: Each digit in the two-digit number G is halved to form a new two-digit number H. Which of the following could be the sum of G and H
Options:
A)153
B)150
C)137
D)132
E)89
Rationale: let the number be x, now x is halved => x/2..the question asks what is x?
x(number) + x/2 (half of that number) = something
=> 3x/2 = something
=> x = 2 (something) / 3
so the answer choice must be divisible by 3
eliminate C, E right away
check the rest
D satisfies
3x/ 2 = 132
=> x = 88
Verify. 88 + 44 = 132
Answer is D
Answer: D
Question: What is the next term in the below series.
1/5 , 1/2 , 1/3 , 2/5 ,1, 2/3, 3/5, 1 1/2 ,1, 4/5,?
Options:
A)1/5
B)0
C)2
D)2/5
E)3/5
Rationale: 1/5 2/5 3/5 4/5
1/2 1 1 1/2 ?
1/3 2/3 1 4/3
ans :2
ANSWER:C
Answer: C
Question: The price of an item changed from $120 to $100. Then later the price decreased again from $100 to $80. Which of the two decreases was larger in percentage term?
Options:
A)10%
B)20%
C)30%
D)40%
E)50%
Rationale: First decrease in percent
part / whole = (120 - 100) / 120 = 0.17 = 17%
Second decrease in percent
part / whole = (100 - 80) / 100 = 0.20 = 20%
The second decrease was larger in percent term. The part were the same in both cases but the whole was smaller in the second decrease.
Answer B
Answer: B
Question: The distance traveled by eagle in one year approximately 150,000,000 miles.The distance traveled by eagle in 50 years?
Options:
A)10<8>
B)10<16>
C)10<4>
D)10<12>
E)10<11>
Rationale: The distance traveled by eagle in one year = 150,000,000 miles.
The distance traveled by eagle in 50 years = 150,000,000 miles * 50 years = 7,500,000,000 miles
(ie) 75*10<8> exponent Answer : A
Answer: A
Question: A committee of 5 people is to be selected from 8 people. How many different committees are possible?
Options:
A)28
B)40
C)56
D)168
E)336
Rationale: Because the order does not matter in selecting 5 people for the committee, this is a combination question.
The number of ways to select 5 people from 8 = 8C5 = 8!/5!*3! = 56. Hence C.
Answer: C
Question: In what time will a train 100 m long cross an electric pole, it its speed be 144 km/hr?
Options:
A)2.5
B)3
C)4
D)5
E)6
Rationale: Speed = 144 * 5/18 = 40 m/sec
Time taken = 100/40 = 2.5 sec.
Answer: Option A
Answer: A
Question: The area of the square formed on the diagonal of a rectangle as its side is 108 1/3 % more than the area of the rectangle. If the perimeter of the rectangle is 28 units, find the difference between the sides of the rectangle?
Options:
A)3m
B)5m
C)8m
D)2m
E)1m
Rationale: Let the sides of the rectangle be l and b respectively.
From the given data,
(√l2 + b2) = (1 + 108 1/3 %)lb
=> l2 + b2 = (1 + 325/3 * 1/100)lb
= (1 + 13/12)lb
= 25/12 lb
=> (l2 + b2)/lb = 25/12
12(l2 + b2) = 25lb
Adding 24lb on both sides
12l2 + 12b2 + 24lb = 49lb
12(l2 + b2 + 2lb) = 49lb
but 2(l + b) = 28 => l + b = 14
12(l + b)2 = 49lb
=> 12(14)2 = 49lb
=> lb = 48
Since l + b = 14, l = 8 and b = 6
l - b = 8 - 6 = 2m.
Answer:D
Answer: D
Question: Three friends James, David and Charlie divide $1230 amongs them in such a way that if $5, $10 and $15 are removed from the sums that James, David and Charlie received respectively, then the share of the sums that they got will be in the ratio of 9: 10 : 11. How much did Charlie receive?
Options:
A)$600
B)$575
C)$550
D)$580
E)$615
Rationale: A+B+C = 1230
Given ratio 9:10:11
Let us say the shares of A,B,C deducting 5,10,15 be a,b,c
a+b+c = 1230-30= 1200 = 30K
c share = (1200X30)/60 = 600
C = charlie share = 600+15= 615
Option E
Answer: E
Question: A water tank is three-fifths full. Pipe A can fill a tank in 15 minutes and pipe B can empty it in 6 minutes. If both the pipes are open, how many minutes will it take to empty or fill the tank completely?
Options:
A)2
B)4
C)6
D)8
E)10
Rationale: The combined rate of filling/emptying the tank = 1/15 - 1/6 = -1/10
Since the rate is negative, the tank will be emptied.
A full tank would take 10 minutes to empty.
Since the tank is only three-fifths full, the time is (3/5) * 10 = 6 minutes
The answer is C.
Answer: C
Question: The speed of a car increases by 2 kms after every one hour. If the distance travelling in the first one hour was 30 kms. what was the total distance traveled in 12 hours?
Options:
A)252 kms
B)152 kms
C)492 kms
D)752 kms
E)152 kms
Rationale: Explanation:
Total distance travelled in 12 hours =(30+32+34+.....upto 12 terms)
This is an A.P with first term, a=30, number of terms,
n= 12,d=2.
Required distance = 12/2[2 x 30+{12-1) x 2]
= 6(82)
= 492 kms.
Answer: C
Answer: C
Question: While driving from A-ville to B-town, Harriet drove at a constant speed of 95 kilometers per hour. Upon arriving in B-town, Harriet immediately turned and drove back to A-ville at a constant speed of 155 kilometers per hour. If the entire trip took 5 hours, how many minutes did it take Harriet to drive from A-ville to B-town?
Options:
A)138
B)148
C)150
D)162
E)186
Rationale: 5hr = 300min.
If harriet spend equal hrs on each leg she will spend 150min on each. Since speed A-B is less than speed B-A and distance on each leg is the same, time spent on A-B is more than 150min, which mean we can eliminate ans. A, B and C.
Now let plug in ans. D or E and verify which one give same distance on each leg.
E. t= 186min
* leg A-B ---> d = 95.186/60 = 17670/60
* leg B-A ----> d = 155*114/60 = 17670/60
so the correct ans. isE
Answer: E
Question: A train ,155 meters long travels at a speed of 45 km/hr crosses a bridge in 30 seconds. The length of the bridge is
Options:
A)270 m
B)245 m
C)235 m
D)220 m
E)240 m
Rationale: Explanation:
Assume the length of the bridge = x meter
Total distance covered = 155+x meter
total time taken = 30s
speed = Total distance covered /total time taken = (155+x)/30 m/s
=> 45 Ã— (10/36) = (155+x)/30
=> 45 Ã— 10 Ã— 30 /36 = 155+x
=> 45 Ã— 10 Ã— 10 / 12 = 155+x
=> 15 Ã— 10 Ã— 10 / 4 = 155+x
=> 15 Ã— 25 = 155+x = 375
=> x = 375-155 =220
Answer: Option D
Answer: D
Question: There are 7 players in a bowling team with an average weight of 112 Kg. If two new players join the team, one weighs 110 Kg and the second weighs 60 Kg, what will be the new average weight?
Options:
A)115 Kg.
B)110 Kg.
C)106 Kg.
D)105 Kg.
E)100 Kg.
Rationale: The New average will be= (112*7+110+60)/9= 106 kgs
C is the answer
Answer: C
Question: A can have a piece of work done in 5 days, B can work three times faster than the A, C can work four times faster than A. How many days will they take to do the work together ?
Options:
A)3 days
B)8/9 days
C)3/2 days
D)can't say
E)none
Rationale: A's 1 day work is 1/12
B's 1 day work is 3/12
C's 1 day work is 4/12
(A+B+C)'s 1 day work(1/12+3/12+4/12) is 2/3
so, they can finish the work in 3/2 days
ANSWER:C
Answer: C
Question: There are 20 people among whom two are sisters. Find the number of ways in which we can arrange them around a circle so that there is exactly one person between the two sisters ?
Options:
A)18!
B)2! x 19!
C)19!
D)17!
E)None of these
Rationale: First arrange the two sisters around a circle in such a way that there will be one seat vacant between them. [This can be done in 2! ways since the arrangement is not circular.]
Then, the other 18 people can be arranged on 18 seats in 18! ways.So, total number of ways = 18! x 2! ways
ANSWER:E
Answer: E
Question: In a camp,there is a meal for 120 men or 200 children.If 180 children have taken the meal,how many men will be catered to with the remaining meal ?
Options:
A)20
B)30
C)12
D)50
E)60
Rationale: Solution
There is a metal for 200 children. 180 children have taken the meal.
Remaining meal is to be catered to 20 children.
Now, 200 children = 120 men
20 children =( 120/200x20)men= 12 men. Answer C
Answer: C
Question: A fires 5 shots to B's 3 but A kills only once in 3 shots while B kills once in 2 shots. When B has missed 27 times, A has killed:
Options:
A)10
B)20
C)30
D)40
E)50
Rationale: Let the total number of shots be x. Then,
Shots fired by A = 5/8x
Shots fired by B = 3/8x
Killing shots by A = 1/3 of 5/8x = 5/24x
Shots missed by B = 1/2 of 3/8x = 3/16x
Therefore, 3x/16 = 27 or x = (27 x 16/3)= 144.
Birds killed by A = 5x/24 = (5/24 x 144)= 30.
Answer is C.
Answer: C
Question: A shopkeeper professes to sell his goods at cost price but uses a weight of 800 gm instead of kilogram weight.Thus, he makes a profit of
Options:
A)20%
B)22%
C)25%
D)None of these
E)Cannot be determined
Rationale: Solution
Therefore,Profit	=(200/800×100)%
= 25%.
Answer C
Answer: C
Question: A baker makes chocolate cookies and peanut cookies. His recipes allow him to make chocolate cookie in batches of 7 and peanut cookies in batches of 6. If he makes exactly 99 cookies, what is the minimum number of chocolate chip cookies he makes?
Options:
A)7
B)14
C)21
D)28
E)35
Rationale: 7C+6P=99
We need to maximize P to minimize C so that the eq is also satisfied
Try substitution for CP to solve so that eqn is satisfied
The least value of C for which equation gets satisfied is 5
i.e. 7*3+6*13=21+78=99
Hence C is the answer
Answer: C
Question: You are renting an apartment and you need √784 for each side, how many feet are you looking to measure?
Options:
A)21
B)22
C)23
D)24
E)28
Rationale: Try filling the numbers into the answer y x y =
Find the closest to 784.
Answer E
Answer: E
Question: A farmer spent $35 on feed for chickens and goats. He spent 40% money on chicken feed, which he bought at a 10% discount off the full price, and spent the rest on goat feed, which he bought at full price. If the farmer had paid full price for both the chicken feed and the goat feed, what amount would he have spent on the chicken feed and goat feed combined?
Options:
A)$36.55
B)$38.50
C)$39.20
D)$39.50
E)$40.60
Rationale: A farmer spent 40% money on chicken feed, so he spent 0.4*$35=$14 on chicken feed, thus he spent the remaining 35-14=$21 on goat feed.
Now, since he bought chicken feed at a 20% discount then the original price of it was x*0.9=$14 --> x=$15.55.
Therefore if the farmer had paid full price for both the chicken feed and the goat feed, then he would he have spent 15.55+21=$36.55.
Answer: A.
Answer: A
Question: If -2/(a - 6) = 4/(a + 4), then a = ?
Options:
A)2/3
B)1/2
C)5/3
D)8/3
E)7/3
Rationale: Multiply all terms of the given equation by (a - 6)(a + 4), simplify and solve
(a - 6)(a + 4)[ -2/(a - 6) ] = (a - 6)(a + 4) [ 4/(a + 4) ]
- 2 (a + 4) = 4 (a - 6)
a = 8/3
correct answer D
Answer: D
Question: A cube of sides 9 is first painted red and then cut into smaller cubes of side 3. How many of the smaller cube have painted on exactly 2 sides?
Options:
A)30
B)24
C)12
D)8
E)9
Rationale: n=side of big cube/side of small cube
and no. Of smaller cubes with two surfaces painted is (n-2)*12
(3-2)*12=12 ans
ANSWER:C
Answer: C
Question: 25 binders can bind 1400 books in 21 days. How many binders will be required to bind 1600 books in 20 days?
Options:
A)87
B)18
C)17
D)16
E)30
Rationale: Binders Books Days
25 1400 21
x 1600 20
x/25 = (1600/1400) * (21/20) => x = 30
Answer:E
Answer: E
Question: Given that E and F are events such that P(E) = 10 P(F) = 2 and P(E n F) = 10,
find P (E|F) and P(F|E)
Options:
A)1
B)69
C)24
D)5
E)12
Rationale: Here, E and F are events
P(E|F) = P(EnF)/P(F) = 10/10= 1
P(F|E) = P(EnF)/P(E) = 10/2 = 5.
D)
Answer: D
Question: A sum was put a simple interest at a certain rate for 7 years. Had it been put at 2% higher rate, it would have fetched Rs. 350 more. The sum is:
Options:
A)s.500
B)s.1000
C)s.1500
D)s.2000
E)s.2500
Rationale: Explanation :
Let the sub be Rs.x and the initial rate be R%.Then
x Ã— (R+2) Ã— 7/100âˆ’xÃ—RÃ—7/100=350
â‡’x Ã— 2Ã—7/100=350
â‡’x Ã— 7 /100=175
â‡’7x=17500
â‡’x=2500
Answer : Option A
Answer: A
Question: Assuming i have an infinite supply of coins.
What is the fewest number of coins would be required in order to make sure each and every coin touched exactly three other coins.
Options:
A)3
B)7
C)4
D)8
E)2
Rationale: C
4
Three placed flat on the table in a triangle(touching each other) and put the fourth one on top of them in the middle.
Answer: C
Question: Birbal is a witty trader who trade of a mystical fruit grown far in north. He travels from one place to another with three sacks which can hold 30 fruits each. None of the sack can hold more than 30 fruits. On his way, he has to pass through thirty check points and at each check point, he has to give one fruit for each sack to the authorities.
How many mystical fruits remain after he goes through all the thirty check points?
Options:
A)25
B)26
C)27
D)28
E)29
Rationale: Solution:
25 Fruits
Remember we told you that Birbal is a witty trader. So his sole motive is to get rid of the sacks as fast as he can.
For the first sack:
He must be able to fill fruits from one sack to other two sacks. Assume that he is able to do that after M check points. Now to find M,
(Space in first sack) M + (Space in second sack) M = (Remaining fruits in Third Sack) 30 – M
M = 10
Thus after 10 checkpoints, Birbal will be left with only 2 sacks containing 30 fruits each.
Now he must get rid of the second sack.
For that, he must fill the fruits from second sack to the first sack. Assume that he manages to do that after N checkpoints.
(Space in First Sack) N = (Remaining fruits in second sack) 30 – N
N = 15
Thus after he has crossed 25 checkpoints, he will be left be one sack with 30 fruits in it. He has to pass five more checkpoints where he will have to give five fruits and he will be left with twenty five fruits once he has crossed all thirty check points.
Answer A
Answer: A
Question: 25% of 30% of 45% is equal to?
Options:
A)0.03375
B)0.03372
C)0.03379
D)0.03372
E)0.03328
Rationale: (25/100) * (30/100) * (45/100)
1/4 * 3/10 * 9/20
27/800 = 0.03375
Answer: A
Answer: A
Question: Reena took a loan of Rs. 1200 with simple interest for as many years as the rate of interest. If she paid Rs. 432 as interest at the end of the loan period, what was the rate of interest?
Options:
A)2
B)6
C)5
D)4
E)8
Rationale: Explanation:
Explanation:
Let rate = R% and time = R years.
Then,
Answer: B) 6
Answer: B
Question: The average age of students of a class is 15.8 years. The average age of boys in the class is 16.4 years and that of the girls is 15.1 years, The ratio of the number of boys to the number of girls in the class is
Options:
A)7 : 6
B)2 : 3
C)9 : 3
D)6 : 3
E)2 : 5
Rationale: Explanation:
Let the ratio be k : 1. Then,
k * 16.4 + 1 * 15.1 = (k + 1) * 15.8
<=> (16.4 - 15.8) k = (15.8 - 15.1) <=> k = 0.7/0.6 = 7/6.
Required ratio = 7/6 : 1 = 7 : 6.
Answer: A
Answer: A
Question: A small table has a length of 12 inches and a breadth of b inches. Cubes are placed on the surface of the table so as to cover the entire surface. The maximum side of such cubes is found to be 4 inches. Also, a few such tables are arranged to form a square. The minimum length of side possible for such a square is 24 inches. Find b.
Options:
A)8
B)16
C)24
D)32
E)48
Rationale: From the info that the maximum sides of the cubes is 4, we know that the GCF of 12 (=2^2*3) andbis 4 (=2^2), sob=2^x, where x>=2.
From the second premise, we know that the LCM of 12 (2^2*3) andbis 24 (2^3*3), sob=2^3 or 2^3*3 (8 or 24).
Combining 2 premises shows the answer is A(8).
Answer: A
Question: Two trains leave a station traveling the same direction. Train A leaves the station traveling at a constant speed of 60 mph, and train B leaves the station traveling at a constant speed of 80 mph. If both trains maintain constant speeds, in how many minutes will train B overtake train A if train A left 40 minutes prior to train B?
Options:
A)90
B)100
C)110
D)120
E)130
Rationale: We can use D=RT [distance=rate*time]
Train A will have traveled for 40 minutes longer than train B when B overtakes A, so
time of train A: T+40minutes = T+(2/3) hours (use hours since the rate is in hours)
time of train B: T
rate of train A: 60 mph
rate of train B: 80 mph
the distances traveled by each will be equal when train B overtakes train A, so we can set the right sides of D=RT equal for the two trains
(rate of train A)*(time of train A) = (rate of train B)*(time of train B)
60*(T+2/3)=80*T
60T + 40 = 80T
40 = 20T
2 = T
2 hours = 120 minutes
D
Answer: D
Question: 10 - [9 - {8 - (7 - 6)}] - 5 is equal to ?
Options:
A)-5
B)1
C)3
D)9
E)8
Rationale: Answer
Given expression = 10 - [ 9 - {8 - 1}] - 5
= 10 - [9 - 7] - 5
= 10 - 2 - 5
= 3
Option: C
Answer: C
Question: By selling an umbrella for Rs. 300, a shop keeper gains 200%. During a clearance sale, the shopkeeper allows a discount of 10% on the marked price. His gain percent during the sale is?
Options:
A)50
B)25
C)400
D)200
E)150
Rationale: Marked price = Rs. 300
C.P. = 100/300 * 300 = Rs. 100
Sale price = 90% of Rs. 300 = Rs. 270
Required gain % = 200/100 * 100 = 200%.
Answer:D
Answer: D
Question: The MegaTek Corporation is displaying its distribution of employees by department in a circle graph. The size of each sector of the graph representing a department is proportional to the percentage of total employees in that department. If the section of the circle graph representing the manufacturing department takes up 72° of the circle, what percentage of MegaTek employees are in manufacturing?
Options:
A)20%
B)25%
C)30%
D)35%
E)72%
Rationale: 72° divided by 360° equals 0.2, therefore the sector is equal to 20% of the total
ANSWER: A
Answer: A
Question: The compound interest earned by Sunil on a certain amount at the end of two years at the rate of5% p.a. was Rs.246. Find the total amount that Sunil got back at the end of two years in the form of principal plus interest earned.
Options:
A)Rs.2535
B)Rs.2646
C)Rs.2546
D)Rs.2656
E)Rs.2565
Rationale: Let the sum be Rs.P
P{ [ 1 + 5/100]2 - 1 } = 246
P(5/100)(2 +5/100) = 246 [a2 - b2 = (a - b) ( a + b)] P = 246 / (0.05)(2.05) = 2400. Amount =Rs.2646 Answer :B
Answer: B
Question: Victor gets 92 % marks in examinations. If these are 184 marks, find the maximum marks.
Options:
A)334
B)500
C)200
D)288
E)271
Rationale: Let the maximum marks be m
Then 92 % of m = 184
⇒ 92/100 × m = 184
⇒ m = (184 × 100)/92
⇒ m = 18400/92
⇒ m = 200
Therefore, maximum marks in the examinations are 200.
Answer: C
Answer: C
Question: Which of the following equations is NOT equivalent to 4x^2 = z^2 - 9 ?
Options:
A) 4x^2 + 9 = z^2
B) 4x^2 - z^2 = -9
C) 4x^2= (z + 3)(z - 3)
D) 2x = z - 3
E)x^2 = (z^2-9)/4
Rationale: 4X^2 = z^2 - 9
The basic rule when dealing with equations is that you can do ANYTHING to both sides of an equation as long as you do it EQUALLY to BOTH sides. Everything gets a bit more complex when you're dealing with variables in the denominator of a fraction and/or inequalities, but neither of those subjects is a factor in this prompt.
Looking at Answer D, we have....
2X = z - 3
While you COULD take the square root of both sides of the original equation, it's important to note that the square root of z^2 - 9 is NOT (z-3).
z^2 - 9 can be factored into (z-3)(z+3), but neither of these parentheses is the square root of z^2 - 9.
You can see the proof when you square either of the two parentheses:
(z-3)^2 = z^2 - 6X + 9
(z+3)^2 = z^2 + 6x + 9
Thus, D is NOT equivalent to the prompt.
Answer: D
Question: From a pack of 52 cards, two cards are drawn together at random. What is the probability that the one is heart and other two is diamond?
Options:
A)238/5525
B)176/5534
C)253/5523
D)234/5525
E)1/5525
Rationale: Solution
Let S be the sample space. Then,
n(S) = 52C3	= 22100
Let E = event of getting 1 face card.
n(E) = number of ways of choosing 1 face card out of 26
=13C1 * 13C2= 13*72 = 936
P(E) = n(E) / n(S)	= 936 / 22100 = 234/5525
= 234/5525.
Answer D
Answer: D
Question: In a recent election, Ms. Robbins received 6,000 votes cast by independent voters, that is, voters not registered with a specific political party. She also received 15 percent of the votes cast by those voters registered with a political party. If N is the total number of votes cast in the election and 40 percent of the votes cast were cast by independent voters, which of the following represents the number of votes that Ms. Robbins received?
Options:
A)0.06N + 3,200
B)0.09N + 6,000
C)0.4N + 7,200
D)0.1N + 8,000
E)0.06N + 8,000
Rationale: I will go with option B
According to question 40 percent of total votes (N) cas were cast by independent voters. This implies 60 percent of N are voters that belong to political party. And she received 6000 votes from independent voters and 15 percent from registered voters (i.e 0.15 * 0.6 * N = 0.09N). Hence total votes = 6000 + 0.09N ....option B
Answer: B
Question: There were 400 ducks in a pond and 15 percent of them just left. How many ducks are remaining?
Options:
A)300
B)280
C)220
D)340
E)250
Rationale: 400/100 = 4
4 x 15 = 60
400 - 60 = 340
Answer is D
Answer: D
Question: A student was asked to find the arithmetic mean of the number 3,11,7,9,15,13,8,19,17,21,14 and x. He found the mean to be 12. what should be the number in place of x ?
Options:
A)3
B)7
C)17
D)31
E)32
Rationale: Solution
Clearly, we have(3+11+7+9+15+13+8+19+17+21+14+X/12) = 12
or 137+x = 144 or x = 144-137 = 7. Answer B
Answer: B
Question: If 76 is divided into four parts proportional to 7,5,3,4 then the smallest part is
Options:
A)12
B)15
C)16
D)19
E)None
Rationale: Sol.
Given ratio = 7 : 5 : 3 : 4, sum of ratio terms = 19.
∴ Smallest part = (76 x 3/19) = 12.
Answer A
Answer: A
Question: What is the smallest integer b for which 27^b> 3^24?
Options:
A)7
B)8
C)9
D)10
E)12
Rationale: 27^b> 3^24
Converting into the same bases:
27^b> 27^8
Therefore for the equation to hold true, b> 8 or b = 9
Option C
Answer: C