divelab/Sys2Bench huggingface dataset:
Question: A and B are two stations 125km apart. A train starts from A at 6a.m. and travels towards B at 50kmph. Another train starts from B at 7a.m. and travels towards A at 25kmph. At what time do they meet?
Options:
A)7a.m.
B)8a.m.
C)9a.m.
D)9.30a.m.
E)10a.m.
Rationale: Suppose they meet x hours after 6 a.m.
Distance moved by first train in x hours + distance moved by 2nd train in x-1 hrs = 125
50x+25(x-1) = 125
x = 2hr
So they meet 2hr after 6a.m. is at 8a.m.
Answer is B
Answer: B
Question: In the x-y plane, point (x, y) is a lattice point if both x and y are integers. A rectangle has a center at (1, 2) and width (x), length (y), 6", 4", respectively. Some points, such as the center (1, 2), are inside the rectangle, but a point such as (4, 2) is on the rectangle, but not in the rectangle. How many lattice points are in the rectangle?
Options:
A)7
B)71
C)72
D)17
E)27
Rationale: The lattice points that are in the rectangle can be calculated as follows: divide the rectangle into 4 quadrants. Now we solve for one quadrant, multiply by 4, and subtract the repeating points along the vertical and horizontal lines that lie along the center point.
For one quadrant we have:
vertical = (1, 2), (1, 3),
horizontal = (2, 2), (3, 2), (don't count center again),
others = (2, 2), (3, 3).
There are 6 points. So, 6 * 4 = 24. Subtract repeating points, 7, we get 17.
There are a total of 17 lattice points in the square.
Answer: D
Answer: D
Question: A password of a computer used three digits where they are from 0 and 9. What is the probability that the password solely consists of prime numbers and zero?
Options:
A)1/32
B)1/16
C)1/8
D)2/5
E)1/2
Rationale: We have three digits can be used for password -0,2,3,5,7.
Assuming that the numbers can be repeated any number of times in the password, probability of selecting any one of them is 5/10 (out of 10 digits from 0-9)
So, 5/10 * 5/10 * 5/10 =1/8 (C)
Answer: C
Question: A boy can reach a certain place in 30 hours. If he reduces his speed by 1/30th, he goes 3 km less in that time. Find his speed.
Options:
A)3 km/hr.
B)6 km/hr
C)8 km/hr
D)14 km/hr
E)None of these
Rationale: Explanation :
Solution: Let the speed be x km/hr. then,
30x - (30 * 29x/30) = 3
=> x = 3 km/hr.
Answer : A
Answer: A
Question: A money lender lent a total of $1400 to two of his customers. He charged at the rate of 5%p.a. to one of them and 6% p.a. to the other. If he earned an average of 5.67% on $1400, how much did he lend to each of the two customers?
Options:
A)700; 1100
B)938; 462
C)1000; 800
D)1200; 800
E)None of the above
Rationale: The method given above is the one given in the book.
However the method I used was
(1*x*5)/100 + (1400-x)*6/100 = 1400*5.67/100
Simplifying we get x=462
B
Answer: B
Question: A man can row with a speed of 20 kmph in still water. If the stream flows at 11 kmph, then the speed in downstream is?
Options:
A)28
B)26
C)31
D)87
E)24
Rationale: M = 20
S =11
DS = 20 + 11
=31
Answer: C
Answer: C
Question: A three digit number consists of 9,5 and one more number . When these digits are reversed and then subtracted from the original number the answer yielded will be consisting of the same digits arranged yet in a different order. What is the other digit
Options:
A)3
B)4
C)5
D)6
E)7
Rationale: 954
-459
---------
495
Rearrenge=954
ANSWER:B
Answer: B
Question: Arun borrowed a certain sum from Manish at a certain rate of simple interest for 2 years. He lent this sum to Sunil at the same rate of interest compounded annually for the same period. At the end of two years, he received Rs. 2400 as compound interest but paid Rs. 2000 only as simple interest. Find the rate of interest.
Options:
A)40%
B)30%
C)20%
D)10%
E)15%
Rationale: Explanation:
Let the sum be x
Simple interest on x for 2 years = Rs.2000
Simple interest = PRT/100
2000 = x Ãƒâ€” R Ãƒâ€” 2100
Ã¢â€¡â€™ x R = 100000 --- (1)
Compound Interest on x for 2 years = 2400
P(1+R/100)T Ã¢Ë†â€™ P = 2400
x (1+R/100)2 Ã¢Ë†â€™ x = 2400
x (1 +2R/100+R210000)Ã¢Ë†â€™x=2400x(2R100+R210000)=2400
2xR/100 + xR2/10000 = 2400--- (2)
Substituting the value of xR from (1) in (2) ,we get
(2Ãƒâ€”100000)/100 + 100000 Ãƒâ€” R10000 = 2400
2000+10R = 2400
10R=400
R=40%
ANSWER IS A
Answer: A
Question: The 100-milliliter solution of sugar and water is 21% sugar. How much water (in milliliters) must be added to make a solution that is 12% sugar?
Options:
A)55
B)60
C)65
D)70
E)75
Rationale: In the original solution the amount of sugar is 0.21*100=21 ml.
Let the volume of the new solution be V.
0.12V=21 ml.
V=175 ml.
The amount of water we need to add is 175 - 100 = 75 ml.
The answer is E.
Answer: E
Question: In a coconut grove, (x + 2) trees yield 60 nuts per year, x trees yield 120 nuts per year and (x – 2) trees yield 180 nuts per year. If the average yield per year per tree be 100, find x.
Options:
A)3
B)4
C)5
D)6
E)7
Rationale: (x+2)×60+x×120+(x−2)×180 /(x+2)+x+(x−2)=100
⇒ 360x−240 /3x = 100
⇒ 60x = 240 ⇒ x = 4
Answer E
Answer: E
Question: Reena took a loan of 1200 with simple interest for as many years as the rate of interest. If she paid 432 as interest at the end of the loan period, what was the rate of interest?
Options:
A)3.6
B)6
C)18
D)Cannot be determined
E)None
Rationale: Explanation: Let rate = R% and time = R years.
Then, (1200 x R x R)/100 = 432
12R² = 432
R² = 36
R = 6.
Answer: Option B
Answer: B
Question: Three candidates contested an election and received 1136, 7636 and 12628 votes respectively. What percentage of the total votes did the winning candidate got?
Options:
A)55%
B)56%
C)57%
D)58%
E)59%
Rationale: Total number of votes polled = (1136 + 7636 + 12628) = 21400
So, Required percentage = 12628/21400 * 100 = 59%
ANSWER : E
Answer: E
Question: Tough and Tricky questions: Exponents.
If 3^(x+1)*5^(y-1) = 9^x*125^y, then 2x + y =
Options:
A)-3/4
B)-2/5
C)-5/2
D)2/5
E)5/2
Rationale: Here is my solution.
3^(x+1)*5^(y-1) = 9^x*125^y
Here RHS 9^x*125^y= 3^(2x)*5^(3y)
Equating powers on both sides-->
x+1=2x , thus x=-1 and
y-1=3y giving y=-1/2
So, x+y=-5/2
Option: C
Answer: C
Question: Mixture A is 20 percent alcohol, and mixture B is 50 percent alcohol. If the two are poured together to create a 15 gallon mixture that contains 30 percent alcohol, approximately how many gallons of mixture A are in the mixture?
Options:
A)3 gallons
B)4 gallons
C)5 gallons
D)10 gallons
E)12 gallons
Rationale: Let A = number of gallons on Mixture A in 15 gallon mixture
B = number of gallons on Mixture B in 15 gallon mixture
(20/100)A + (50/100)B= (30/100)(A+B) --1
A+B=15 -- 2
On solving equations 1 and 2 , we get
A=10
B=5
Answer D 10 gallons
Answer: D
Question: A dishonest dealer professes to sell his goods at Cost Price but still gets 20% profit by using a false weight. What weight does he substitute for a kilogram?
Options:
A)835 1/3 grams
B)833 1/3 grams
C)833 1/9 grams
D)836 1/3 grams
E)843 1/3 grams
Rationale: If the cost price is Rs.100, then to get a profit of 20%, the selling price should be Rs.120.
If 120kg are to be sold, and the dealer gives only 100kg, to get a profit of 20%.
How many grams he has to give instead of one kilogram(1000 gm).
120 gm ------ 100 gm
1000 gm ------ ?
(1000 * 100)/120 = 2500/3 = 833 1/3 grams.
Answer: B
Answer: B
Question: Calculate 56581 ÷ ? = 137
Options:
A)113
B)213
C)413
D)417
E)414
Rationale: Answer
Let 56581/X = 137
Then X = 56581/137= 413
Option: C
Answer: C
Question: If 60 honey bees make 60 grams of honey in 60 days, then 1 honey bee will make 1 gram of honey in how many days?
Options:
A)1
B)3.5
C)20
D)49
E)60
Rationale: Explanation :
Let the required number days be x.
Less honey bees, More days (Indirect Proportion)
Less honey, Less days (Direct Proportion)
Honey bees 1 : 60 :: 60 : x
Honey 60 : 1
=> 1 x 60 x x = 60 x 1 x 60
=> x = 60.
Answer : E
Answer: E
Question: The average earning of a mechanic for the first-four days of a week is Rs. 16 and for the last four days is Rs. 24. If he earns Rs . 27 on the fourth day, his average earning for the whole week is ?
Options:
A)Rs . 18.95
B)Rs 16
C)Rs. 19
D)Rs. 25.71
E)None of these
Rationale: Answer
Total earning for the week = Sum of earning of first four days + Sum of earning of last four days - Earning of 4th day
= 4 x16 + 4 x 24 -27
= Rs. 133
âˆ´ Average earning = 133 / 7
= Rs. 19
Correct Option: C
Answer: C
Question: A can do a piece of work in 3 hours; B and C together can do it in 3 hours, while A and C together can do it in 2 hours. How long will B alone take to do it?
Options:
A)12
B)9
C)8
D)6
E)5
Rationale: A's 1 hour's work = 1/3;
(B + C)'s 1 hour's work = 1/3 ;
(A + C)'s 1 hour's work = 1/2 .
(A + B + C)'s 1 hour's work = ( 1/3 + 1/3 ) =2/3 .
B's 1 hour's work = ( 2/3 - 1/2 ) = 1/6.
Therefore A alone will take 6 hours to do the work.
D
Answer: D
Question: Ten cards numbered 1 to 10 are placed in a box, mixed up thoroughly and then one card is drawn
randomly. If it is known that the number on the drawn card is more than 3, what is the probability
that it is an even number?
Options:
A)4/7
B)1/2
C)1/3
D)1/7
E)2/7
Rationale: Let A be the event ‘the number on the card drawn is even’ and B be the
event ‘the number on the card drawn is greater than 3’. We have to find P(A|B).
Now, the sample space of the experiment is S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
Then A = {2, 4, 6, 8, 10}, B = {4, 5, 6, 7, 8, 9, 10}
and A n B = {4, 6, 8, 10}
Also P(A) = 5/2, P(B) = 7/10 and P(A n B) = 4/10
Then P(A|B) = P(A n B)/P(B) = (4/10)/(7/10) = 4/7
A
Answer: A
Question: A pair of prime numbers that can be expressed in the form W{p, (p + 6)} is deﬁned as a pair of “sexy primes.” A “sexy triplet” is a group of three primes that can be expressed in the form {p, (p + 6), (p + 12)}. All of the following prime numbers are the middle term of a sexy triplet EXCEPT
Options:
A) 11
B) 13
C) 17
D) 19
E) 23
Rationale: definetly a sitter.plug in the values for middle term and calculate.We can see clearly that W for 19 , 19+6 gives 25 which is not a prime
therefore correct answer D
Answer: D
Question: If the radius of a circle is decreased 30%, what happens to the area?
Options:
A)51% decrease
B)20% decrease
C)36% decrease
D)40% decrease
E)50% decrease
Rationale: Area of Square = Pi* radius^2
New Radius = 0.7 * old radius
so new area = (0.7)^2 old area => 0.49 of old area => 49% old area
Ans : A
Answer: A
Question: Lucy is traveling from one end of a forest to the other. In order to find her way back, she is leaving morsels of bread in the following pattern: 2 morsels of wheat, 3 morsels of rye, and 1 morsel of white. The pattern repeats after she leaves the morsel of rye. If Lucy drops 2,000 morsels of bread, what are the last 3 morsels of bread that she drops?
Options:
A)white − wheat − wheat
B)wheat − wheat − rye
C)rye − white− wheat
D)rye − rye − rye
E)rye − rye − white
Rationale: In a single round Lucy drops 6 morsels.
Remainder (2000/6) = 2
Final action = 2 drops of Wheat --> Options B, C, D and E can be eliminated
Answer: A
Answer: A
Question: The angles of a triangle have ratios 3:4:5 relative to each other. Determine which angle below corresponds to one of the angles of this triangle.
Options:
A)40Â°
B)60Â°
C)80Â°
D)100Â°
E)120Â°
Rationale: The three angles of a triangle add up to 180Â°. Knowing the ratios, we can formulate this expression:
3x + 4x + 5x = 180Â°
12x = 180Â°
x = 15Â°
Now, find the angles within the triangle.
3x = 3(15Â°) = 45Â°
4x = 4(15Â°) = 60Â°
5x = 5(15Â°) = 75Â°
Therefore, the answer is 60Â°, or B.
Answer: B
Question: What is the sum of the greatest common factor and the lowest common multiple of 16 and 72?
Options:
A)142
B)152
C)124
D)160
E)184
Rationale: Prime factorization of 16 = 2 x 2 x 2 x 2.
Prime factorization of 72 = 2 x 2 x 2 x 3 x 3
GCF = 8
LCM = 144
Sum = 152.
Answer B.
Answer: B
Question: Fred and Sam are standing 35 miles apart and they start walking in a straight line toward each other at the same time. If Fred walks at a constant speed of 2 miles per hour and Sam walks at a constant speed of 5 miles per hour, how many miles has Sam walked when they meet?
Options:
A)5
B)9
C)25
D)30
E)45
Rationale: relative distance =35 miles
relative speed =2+5 =7 miles per hour
time taken =35/7=5 hours
distance travelled by sam =5*5=25 miles=C
Answer: C
Question: At what price must an article costing Rs.47.50 be marked in order that after deducting 5% from the list price. It may be sold at a profit of 25% on the cost price?
Options:
A)62.5
B)62.8
C)62.1
D)62.9
E)32.5
Rationale: Explanation:
CP = 47.50
SP = 47.50*(125/100) = 59.375
MP*(95/100) = 59.375
MP = 62.5
Answer: A
Answer: A
Question: In how many ways, a committee of 6 members can be selected from 7 men and 4 ladies, consisting of 4 men and 2 ladies?
Options:
A)210
B)180
C)200
D)310
E)250
Rationale: (4 men out 7) and (2 ladies out of 4) are to be chosen
Required number of ways = 7C4*4C2 = 210
Answer is A
Answer: A
Question: A Table is bought for Rs.1600/- and sold at a loss of 20% find its selling price?
Options:
A)s.1280/-
B)s.1560/-
C)s.1580/-
D)s.1250/-
E)s.1300/-
Rationale: 100 % ------> 1600 (100 * 16 = 1600)
80 % ------> 1280 (80 * 16 = 1280)
Selling price = Rs.1280/-
Option 'A'
Answer: A
Question: What sum of money put at C.I amounts in 2 years to Rs.8820 and in 3 years to Rs.9261?
Options:
A)Rs.8000
B)Rs.8400
C)Rs.7500
D)Rs.7800
E)None of these
Rationale: Explanation:
8820 ---- 441
100 ---- ? => 5%
x *105/100 * 105/100 = 8820
x*1.1025=8820
x=8820/1.1025 => 8000
Answer is A
Answer: A
Question: The ratio of two numbers is 2:3 and the sum of their cubes is 945. The difference of number is?
Options:
A)3
B)4
C)5
D)6
E)8
Rationale: 2x 3x
8x cube + 27x cube = 945
35x cube = 945
x cube = 27 => x = 3.Answer: A
Answer: A
Question: The diagonal of a rectangle is 41 cm and its area is 20 sq. cm. The perimeter of the rectangle must be:
Options:
A)18 cm
B)28 cm
C)30 cm
D)38 cm
E)42 cm
Rationale: l2 + b2 = 41.
Also, lb = 20.
(l + b)2 = (l2 + b2) + 2lb = 41 + 40 = 81
(l + b) = 9.
Perimeter = 2(l + b) = 18 cm.
A)
Answer: A
Question: At the starting of 2012, 60% of the population of Town Y lived in the north and the rest lived in the south. During the year 2012, the population of Town Y grew by 5.5%. If the population in the north grew by 4.5%, by how much did the population in the south grow?
Options:
A)7%
B)9%
C)1%
D)1.5%
E)3.8%
Rationale: Here I prefer the weighted average method over dealing with creating and solving the algebraic expression:
Ratio of population in the Town Y -North:South :: 60%:40% = 3:2
Mean growth = 5.5%
South Growth: 4.5%
North Growth = ??
North-------------Average--------------South
4.5% __(2n)_____5.5%_____(3n)_____??
Since:
4.5 + 2n = 5.5
n = 1/2 (this is the multiplier of the ratio)
Therefore:
South = 5.5 + 3n
South = 5.5 + 3(0.5) = 7%
Answer: A
Question: Three 6 faced dice are thrown together. The probability that all the three show the same number on them is?
Options:
A)1/39
B)1/36
C)1/32
D)1/31
E)1/30
Rationale: Explanation:
It all 3 numbers have to be same basically we want triplets. 111, 222, 333, 444, 555 and 666. Those are six in number. Further the three dice can fall in 6 * 6 * 6 = 216 ways.
Hence the probability is 6/216 = 1/36
Answer: B
Answer: B
Question: A started a business with Rs.25000 and is joined afterwards by B with Rs.30,000. After how many months did B join, if profit per annum is divieded equally?
Options:
A)2 months
B)4 months
C)5 months
D)7 months
E)9 months
Rationale: Given their profits are equal per annum so
25000*12=30000*x
x=10 months
12-10=2 months
ANSWER:A
Answer: A
Question: If k is a non-negative integer and 15^k is a divisor of 759,325 then 3^k - k^3 =
Options:
A)0
B)1
C)37
D)118
E)513
Rationale: At first we should understand whether 759325 divisible by 15.
15 is equal to 3 * 5 so 759325 should be divisible on these integers
759325 is divisible by 5 because of last digit 5
but not divisible by 3 because sum of its digits doesn't divisible by 3: 7 + 5 + 9 + 3 + 2 + 5 = 31 and 31 doesn't divisible by 3
so 759325 can be divisible by 15^k only if k = 0 and 15^k = 1
so 3^k - k^3 = 1 - 0 = 1
Answer is B
Answer: B
Question: Two trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 10 hours and 8 hours respectively. The ratio of their speeds is
Options:
A)4 : 9
B)4 : 3
C)4 : 12
D)4 : 8
E)4 : 5
Rationale: Let us name the trains as A and B. Then, (A's speed) : (B's speed) = b : a = 8 : 10 = 4 : 5.Answer: E
Answer: E
Question: J and M were each paid x dollars in advance to do a certain job together. J worked on the job for 12 hours and M worked for 2 hours less than J. If M gave J y dollars of her payment so that they would have received the same hourly wage, what was the dollar amount, in terms of y, that J was paid in advance?
Options:
A)a)4y
B)b)5y
C)c)6y
D)d)11y
E)e)10y
Rationale: J and M were both paid x dollars
If M gave Y dollars from her X to J then at the end
J will have X+Y dollars
M will have X- Y dollars
Now since the hourly wages have to be same then
Hourly wage of J = (X+Y) / 12 (Since J worked for 12 hrs)
Hourly wage of M = (X-y) /10 (Since M worked 2 hrs less than J)
Equating both
(X+Y)/12=(X-Y)/10
on simplifying X=11y
Answer D
Answer: D
Question: A bowl contains pecans, cashews, and almonds in a ratio of 7 : 12 : 18, respectively. If some of the nuts of one of the three types are removed, which of the following could be the ratio of pecans to cashews to almonds remaining in the bowl? i. 1 : 2 : 3 ii. 2 : 3 : 4 iii. 4 : 7 : 10
Options:
A)I only
B)III only
C)I,II only
D)II only
E)II,III only
Rationale: i. The ratio 2 : 3 is the same as the given ratio 12 : 18. If one pecan were removed, the new ratio would be 6 : 12 : 18, or 1 : 2 : 3.
ii. None of the nuts currently have a ratio of 3 : 4. The cashews and almonds do have a ratio of 2 : 3, but there are not enough pecans in the bowl to complete the ratio.
iii. The ratio 4 : 10 is the same as the given ratio 6 : 15. To see this, multiply the ratio by 3/2 . The new ratio is 6 : 10.5 : 15. Unfortunately, this means that there are fewer cashews that this ratio would require. Removing cashews won’t create the desired ratio.
Answer : A
Answer: A
Question: Current ages of Rahim and Thomas are in the ratio of 5 : 4 correspondingly. 0.2 decades hence, the ratio of their ages will become 11 : 9 correspondingly, What is Thomasâ€™s current age in years?
Options:
A)24 years
B)44 years
C)34 years
D)64 years
E)16 years
Rationale: 16 years
If current ages of Rahim and Thomas be 5A years and 4A years correspondingly
Then, 5A + 2 = 11
4A + 2 = 9
9(5A + 2)=11(4A + 2)
A = 4
Thomasâ€™s current age = 4A
= 16 years.
E
Answer: E
Question: Four milkmen rented a pasture. A grazed 24 cows for 3 months; B 10 for 5 months; C 35 cows for 4 months and D 21 cows for 3 months. If A's share of rent is Rs. 2160, find the total rent of the field.
Options:
A)3750
B)3550
C)4250
D)9750
E)3250
Rationale: Ratio of shares of A, B, C, D = (24 x 3) : (10 x 5) : (35 x 4) : (21 x 3) = 72 : 50 : 140 : 63.
Let total rent be Rs. x. Then, A’s share = Rs. (72x)/325
(72x)/325=2160 = x=(2160 x 325)/72 = 9750
Hence, total rent of the field is Rs. 9750.
Answer is D.
Answer: D
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 seconds. The speed of the train is ?
Options:
A)45 kmph
B)25 kmph
C)30 kmph
D)50 kmph
E)None of these
Rationale: Explanation:
Speed of the train relative to man = (125/10) m/sec = (25/2) m/sec.
[(25/2) x (18/5)] km/hr = 45 km/hr.
Let the speed of the train be 'S' km/hr.
Then, relative speed = (S - 5) km/hr.
S - 5 = 45 => S = 50 km/hr.
ANSWER IS D
Answer: D
Question: Sreedhar and Sravan together can do a work in 25 days. With the help of Pavan, they completed the work in 8 days and earned Rs. 225. What is the share of Sravan, if Sreedhar alone can do the work in 75 days?
Options:
A)22
B)26
C)48
D)77
E)12
Rationale: Sravan's one day's work = 1/25 - 1/75 = 2/75
Sravan worked for 8 days. So, his 8 days work = 8 * 2/75 = 16/75
Sravan completed 16/75th of total work.
So, his share is 16/75 * 225 = Rs. 48.
Answer:C
Answer: C
Question: An examiner rejects 0.16% of the meters as defective. How many will be examine to reject 4?
Options:
A)500
B)4000
C)2500
D)5500
E)None of these
Rationale: Explanation :
Solution: let the number of meters to be examined be x. then, 0.16% of x = 4
=>(16/100 * 1/100 * x) = 4
=>x = (4*100*100)/16 = 2500.
Answer : C
Answer: C
Question: An object thrown directly upward is at a height of h feet after t seconds, where h = -14 (t-3)^2 + 150. At what height, in feet, is the object 2 seconds after it reaches its maximum height?
Options:
A)80
B)88
C)94
D)112
E)124
Rationale: We see that h will be a maximum h=150 when t-3=0, that is when t=3.
At t=5, h = -14(5-3)^2 + 150 = -14(4) + 150 = 94
The answer is C.
Answer: C
Question: In a forest 150 deer were caught, tagged with electronic markers, then released. A week later, 50 deer were captured in the same forest. Of these 50 deer, it was found that 10 had been tagged with the electronic markers. If the percentage of tagged deer in the second sample approximates the percentage of tagged deer in the forest, and if no deer had either left or entered the forest over the preceding week, what is the approximate number of deer in the forest?
Options:
A)150
B)750
C)3,000
D)1,500
E)2,500
Rationale: The percentage of tagged deer in the second sample = 10/50*100=20%.
So, 150 tagged deers comprise 10% of total # of deers --> total # of deers = 150*20 = 3,500.
Answer: C
Answer: C
Question: There are 15 points in a given plane, no three of which are on the same line. If one of the points is represented as 'Y', then how many triangles can be determined with the 15 points that contain the point Y?
Options:
A)91
B)105
C)182
D)210
E)455
Rationale: Fist point is A which is fixed so can be selected in 1 way
Second point can be selected in 14 ways
Third point can be selected in 13 ways
so total ways = 1x14x13 = 182
but answer is 91 which is 182/2=C
Answer: C
Question: if 70% of (x-y) = 30% of (x+y) then what percent of x is y?
Options:
A)2.5%
B)40%
C)5%
D)15%
E)25%
Rationale: 70% of (x-y)=30% of(x+y)
(70/100)(x-y)=(30/100)(x+y)
7(x-y)=3(x+y)
4x=10y
x=5/2y
therefore required percentage
=((y/x) X 100)% = ((y/(5/2)y) X 100) =40%
Answer is B.
Answer: B
Question: A and B can do a work in 8 hours and 12 hours respectively. A starts the work at 6AM and they work alternately for one hour each. When will the work be completed?
Options:
A)9.6 days
B)7.6 days
C)4 days
D)8.6 days
E)6.6 days
Rationale: Work done by A and B in the first two hours, working alternately = First hour A + Second hour B = 1/8+ 1/12 = 5/24.
Total time required to complete the work = 2 * 24/5 = 9.6 days.
ANSWER:A
Answer: A
Question: If KING is coded as 17 and DON is coded as 18 Then MASS is coded as
Options:
A)21
B)20
C)19
D)29
E)None
Rationale: KING = 11+9+14+7=41 i.e (4*4)+(1*1)=17
MASS = 13+1+19+19=52 i.e (5*5)+(2*2)=29
DON = 4+14+15=33 i.e(3*3)+(3*3)=18
ANSWER:D
Answer: D
Question: Judges will select 5 finalists from the 7 contestants entered in a singing competition. The judges will then rank the contestants and award prizes to the 3 highest ranked contestants: a blue ribbon for first place, a red ribbon for second place, and a yellow ribbon for third place. How many different arrangements of prize-winners are possible?
Options:
A)10
B)21
C)210
D)420
E)1,260
Rationale: First Select 5 from 7 contestants and then select top 3 from those 5 =
7C5*5C3 = 42 * 5 = 210
ANS:C
Answer: C
Question: A student took five papers in an examination, where the full marks were the same for each paper. His marks in these papers were in the proportion of 6 : 7 : 8 : 9 : 10. In all papers together, the candidate obtained 60% of the total marks. Then the number of papers in which he got more than 40% marks is
Options:
A)5
B)4
C)3
D)2
E)1
Rationale: Here we can assume that one subject is of 100 marks so total there are 5 subjects => 100*5 = 500.
Now according to the question he secured 60 % of those which is 60%of 500 = 300 marks in total.
The ratio between the marks is given as 6 : 7 : 8 : 9 : 10 , so now we can distribute 300 marks according to the ratio.
Total ratio = 40
For 6 : (300/40)*6 = 45
Similarly , we will get for others as 52.5 , 60 , 62.5 , 75.
Hence , there are 4 subject where he secured more that 40 %.
The answer is 5.
A
Answer: A