mathewhe/aqua_rat huggingface dataset:
Question: In a box, there are 10 red, 8 blue and 5 green balls. One ball is picked up randomly. What is the probability that it is neither red nor green?
(A) 4/51
(B) 10/21
(C) 8/23
(D) 11/31
(E) 13/17
Rationale: Total number of balls = 10+8+5 = 23
E = event that the ball drawn is neither red nor green
= event that the ball drawn is red
n(E) = 8
P(E) = 8/23
Answer is C
Answer: (C) 8/23
Question: If 7 gallons of gasoline are added to a tank that is already filled to 3/4 of its capacity, the tank is then filled to 9/10 of its capacity. How many gallons does the tank hold?
(A)  20
(B)  24
(C)  36
(D)  42
(E)  60
Rationale: Let the Capacity of the tank=C
(3/4)C + 7 = (9/10)C
=>(9/10)C - (3/4)C = 7
=>(3/20)C = 7
=>C = (7*20)/3 = 46.66
Number of gallons of gasoline that the tank currently holds = 3/4*C +7 = 34.99+7 = 41.99=42
Answer D
Answer: (D)  42
Question: A small company is planning to rent either computer A or computer B to print customer mailing lists. Both computer A and computer B must be rented on an hourly basis. The rental fee is based only on the amount of time the computer is turned on. It will cost 40 percent more per hour to rent computer A than to rent computer B. Computer B would, however, require 20 hours more than computer A to do the job. If either computer A, or computer B were rented the total cost to rent the computer would be $880.00. What would be the approximate hourly charge to rent computer B?
(A) $9.40
(B) $12.57
(C) $13.20
(D) $17.80
(E) $22.10
Rationale: Pa = price of A
Pb = price of B
Ta = time for A to complete the job
Tb = time for B to complete the job
Given
Pa = 1.4 Pb
Ta+20 = Tb
Pa*Ta = Pb*Tb=880
1.4Pb * (Tb-20) = Pb*Tb
1.4 Pb Tb - Pb Tb = 1.4 Pb * 20
0.4PbTb = 28Pb
Tb = 28/0.4 = 70
Pb=880/70 ~ 12.57
B
Answer: (B) $12.57
Question: There are three prizes to be distributed among eight students. If no students gets more than one prize, then this can be done in?
(A) 10
(B) 45
(C) 56
(D) 20
(E) None of these
Rationale: Explanation :
3 prize among 8 students can be distributed in 8C3 ways = 56 ways.
Answer : C
Answer: (C) 56
Question: What is the difference between the place values of two sevens in the numeral 54179479 ?
(A) 699990
(B) 99990
(C) 69930
(D) 699930
(E) None of these
Rationale: Explanation:
Required Difference
= 70000 - 70 = 69930
Answer is C
Answer: (C) 69930
Question: A train 100 m long crosses a platform 250 m long in 7 sec; find the speed of the train?
(A) 94 kmph
(B) 58 kmph
(C) 54 kmph
(D) 180 kmph
(E) 59 kmph
Rationale: D = 100 + 250 = 350
T = 7
S = 350/7 * 18/5 = 180 kmph
Answer:D
Answer: (D) 180 kmph
Question: If the population of a certain country increases at the rate of one person every 15 seconds, by how many persons does the population increase in 60 minutes?
(A) 80
(B) 100
(C) 150
(D) 240
(E) 300
Rationale: Since the population increases at the rate of 1 person every 15 seconds, it increases by 4 people every 60 seconds, that is, by 4 people every minute. Thus, in 60 minutes the population increases by 60 x 4 = 240 people.
Answer. D.
Answer: (D) 240
Question: In a certain business school class, p students are accounting majors, q students are finance majors, r students are marketing majors, and s students are strategy majors. If pqrs = 1365, and if 1< p < q < r < s, how many students in the class are finance majors?
(A) 3
(B) 5
(C) 8
(D) 11
(E) 17
Rationale: pqrs = 1365 = 3* 5 *7 * 13
Since 1< p < q < r < s, the number of students who are finance majors is q = 5.
The answer is B.
Answer: (B) 5
Question: Fill in the missing number:
? 14 12 11 10.5 10.25
(A) 10.1
(B) 10.4
(C) 10.2
(D) 10.5
(E) 18
Rationale: 18
Divide each number by 2 and then add 5 to it.
ANSWER E
Answer: (E) 18
Question: David earns $7.00 per hour for the first 50 hours he works per week, and twice this rate for overtime. If Michael earned $352 last week, how many hours did he work?
(A) 43
(B) 44
(C) 45
(D) 46
(E) 56
Rationale: $7*40 + $12*x = $352 --> x = 6 hours.
Total working hours = 50 + 6 = 56.
Answer: E.
Answer: (E) 56
Question: How many days will there be from 27th January,1996 to 15th May,1996(both days included)?
(A) 102
(B) 103
(C) 111
(D) 120
(E) 110
Rationale: Explanation:
Number of days from 27-Jan-1996 to 15-May-1996 (both days included)
= 5(Jan) + 29(Feb) + 31 (Mar) + 30(Apr)+ 15(May) = 110
Answer: Option E
Answer: (E) 110
Question: A no. when divided by the sum of 555 and 445 gives 2times their difference as quotient & 80 as remainder. Find the no. is?
(A) 220880
(B) 145778
(C) 220081
(D) 220080
(E) 220030
Rationale: (555 + 445) * 2 * 110 + 80 = 220000 + 80 = 220080
D
Answer: (D) 220080
Question: In given series 1, 2, 6, 15, 31, 56, 91 only one number is incorrect. Find out that wrong number
(A) 91
(B) 92
(C) 90
(D) 60
(E) 61
Rationale: 1,
1 + 12 = 2,
2 + 22 = 6,
6 + 32 = 15,
15 + 42 = 31,
31 + 52 = 56,
56 + 62 = 92
Last number of given series must be 92 not 91.
ANSWER:A
Answer: (A) 91
Question: A car covers a distance of 618 km in 6 ½ hours. Find its speed?
(A) 104 kmph
(B) 103 kmph
(C) 298 kmph
(D) 186 kmph
(E) 268 kmph
Rationale: 618/6
= 103 kmph
Answer:B
Answer: (B) 103 kmph
Question: If a: b = 3:4, b:c = 7:9, c:d = 5:7, find a:d?
(A) 5/12
(B) 5/15
(C) 5/10
(D) 5/11
(E) 5/13
Rationale: a/d = (3/4)*(7/9)*(5/7) => 5/12
Answer: A
Answer: (A) 5/12
Question: 2,400 has how many positive divisors?
(A) 20
(B) 24
(C) 32
(D) 36
(E) 40
Rationale: By factorization, we can write 2400 as 2400=2^5*3*5^2.
The number of factors is (5+1)(1+1)(2+1) = 36
The answer is D.
Answer: (D) 36
Question: pow(1000,9) ÷ pow(10,24) = ?
(A) 10000
(B) 1000
(C) 100
(D) 10
(E) None of these
Rationale: Given Exp. = pow(1000,9) = pow(pow(10,3),9) = pow(10,27) = pow(10, (27-24)) = pow(10,3) = 1000
Answer B
Answer: (B) 1000
Question: In May, the groundskeeper at Spring Lake Golf Club built a circular green with an area of 80π square feet. In August, the groundskeeper doubled the distance from the center of the green to the edge of the green. What is the total area of the renovated green?
(A) 160π
(B) 320π
(C) 400π
(D) 540π
(E) 640π
Rationale: Area = πR^2, so doubling the radius results in an area that is 4 times the original area.
4(80π) = 320π
The answer is B.
Answer: (B) 320π
Question: The ratio of the length and the breadth of a rectangle is 4 : 3 and the area of the rectangle is 6912 sq cm. Find the ratio of the breadth and the area of the rectangle?
(A) 1:96.
(B) 1:90
(C) 1:95
(D) 1:92
(E) 1:93
Rationale: Let the length and the breadth of the rectangle be 4x cm and 3x respectively.
(4x)(3x) = 6912
12x2 = 6912
x2 = 576 = 4 * 144 = 22 * 122 (x > 0)
=> x = 2 * 12 = 24
Ratio of the breadth and the areas = 3x : 12x2 = 1 : 4x
= 1:96.
Answer: A
Answer: (A) 1:96.
Question: 12, 38, 116, 350, 1052, ?
(A) 1800
(B) 2200
(C) 2800
(D) 3158
(E) 3260
Rationale: Explanation :
12
12 × 3 + 2 = 38
38 × 3 + 2 = 116
116 × 3 + 2 = 350
350 × 3 + 2 = 1052
1052 × 3 + 2 = 3158
Answer : Option D
Answer: (D) 3158
Question: A dishonest dealer professes to sell goods at the cost price but uses a weight of 500 grams per kg, what is his percent?
(A) 20%
(B) 25%
(C) 29%
(D) 55%
(E) 100%
Rationale: 500 --- 500
100 --- ? =>100%
Answer: E
Answer: (E) 100%
Question: A bag contains five white and four red balls. Two balls are picked at random from the bag. What is the probability that they both are different color?
(A) 5/6
(B) 5/9
(C) 5/1
(D) 5/2
(E) 5/5
Rationale: Two balls can be picked from nine balls in ways.
We select one white ball and one red ball from five white balls and four red balls. This can be done
The required probability = (5 * 4)/9C2 = 20/36 = 5/9
Answer:B
Answer: (B) 5/9
Question: The length of the rectangular field is double its width. Inside the field there is square shaped pond 8m long. If the area of the pond is 1/98 of the area of the field. What is the length of the field?
(A) 73
(B) 32
(C) 34
(D) 43
(E) 112
Rationale: Explanation:
A/98 = 8 * 8 => A = 8 * 8 * 98
x * 2x = 8 * 8 * 98
x = 56 => 2x = 112
Answer: Option E
Answer: (E) 112
Question: A 600 meter long train crosses a signal post in 40 seconds. How long will it take to cross a 9 kilometer long bridge, at the same speed?
(A) 4 min
(B) 2 min
(C) 10 min
(D) 9 min
(E) 3 min
Rationale: S = 600/40 = 15 mps
S = 9000/15 = 600 sec = 10 min.Answer: C
Answer: (C) 10 min
Question: What is the sum of the numbers between 1 and 10, inclusive?
(A) 85
(B) 95
(C) 100
(D) 105
(E) 55
Rationale: Sol. add all the numbers between 1 and 10.
Final Answer =E, 55.
Answer: (E) 55
Question: A shopkeeper loses 15%,if an article is sold for Rs. 153. What should be the selling price of the article to gain 20%?
(A) s.147
(B) s.248
(C) s.244
(D) s.229
(E) s.216
Rationale: Given that SP = Rs. 153 and loss = 15%
CP = [100(SP)]/(100 - l%) = (100 * 153)/85 = Rs. 180.
To get 20% profit, New SP = [(100 + p%)CP]/100
= (180 * 120)/100
= Rs.216
Answer:E
Answer: (E) s.216
Question: If the volume of the cube is 729 cm3, then the surface area of the cube will be
(A) 486 sq.cm
(B) 456 sq.cm
(C) 446 sq.cm
(D) 476 sq.cm
(E) None of these
Rationale: Explanation:
a3=729; a=9
surface area= (6 x 9 x 9) = 486 cm2
Answer: A
Answer: (A) 486 sq.cm
Question: The U.S. Defense Department has decided that the Pentagon is an obsolete building and that it must be replaced with an upgraded version: the Hexagon. The Secretary of Defense wants a building that is exactly 70 feet high and 200 feet on a side, and that has a hexagonal bull's-eye cutout in the center (somewhat like the current one) that is 35 feet on a side. What will be the volume of the new building in cubic feet?
(A) 3,937,500 cubic feet
(B) 15,750 cubic feet
(C) 11550√3 cubic feet
(D) 15,750√3 cubic feet
(E) 7,051,828 cubic feet
Rationale: Volume of the Hexagon with side 200 and height 70 = Area * height
= 6*(sqrt(3)/4)(200^2)(70)
Volume of the center bull's eye that is similar in shape of a hexagon but side 35
= 6 * (sqrt(3)/4)(35^2)*70
Volume of the building = 6*(sqrt(3)/4)(200^2)(70) - 6 * (sqrt(3)/4)(35^2)*70=7,051,828 cubic feet
Answer is E
Answer: (E) 7,051,828 cubic feet
Question: After spending Rs. 5000 on rent, Rs. 1500 on milk, Rs. 4500 on groceries, Rs.2500 On childrens education Rs. 2000 on petrol and Rs. 6100 on miscellaneous expenses, Mr. Kishore saved 10% of his monthly salary. How much did he save in Rs. ?
(A) 2160
(B) 2350
(C) 2000
(D) 2300
(E) 2400
Rationale: Explanation :
Total Exp = 5000+1500+4500+2500+2000+6100 = 21600
Exp in % = 100-10 = 90%, 21600 = 90%
Saving = 10 % = 21600 X 10/90 = Rs. 2400
Answer : E
Answer: (E) 2400
Question: Which of the following is the equation of the line in the xy-plane that has slope 0
(I) x = 2
(II) y = 5
(III) x + y = 0
(A) I
(B) III
(C) I&II
(D) II
(E) II& III
Rationale: y =mx+c therefore y-c= mx then m =(y-c)/x
m=0 means y = c constant ..= II
D
Answer: (D) II
Question: If set A={2,2,2,....,n times} , set B={3,3,3,3....m times} and set C={11,11,11...k time} , then in terms of m,n and k , how many possible subsets from sets A,B, and C can be created ?
(A) k(n+m+mn)+ k
(B) (1+n+m+mn)(k+1)
(C) k^2(mn+n/m)
(D) kmn(k+m+n)
(E) None of the above
Rationale: The number of subsets is (m + 1)(n + 1)(k + 1). The answer is not given in that form. Instead, the first two factors have been FOILed together:
(mn + m + n + 1)(k + 1).
ANSWER:B
Answer: (B) (1+n+m+mn)(k+1)
Question: Five children — A, B, C, D, and E — are going to sit in five chairs in a row. Child D must be somewhere to the left of child E. How many possible configurations are there for the children?
(A) 60
(B) 180
(C) 240
(D) 360
(E) 720
Rationale: The number of ways to seat 5 people is 5! = 120.
Child D will sit to the left of Child E in exactly half of these arrangements.
The total number of possible arrangements is 120/2 = 60
The answer is A.
Answer: (A) 60
Question: Ada and Paul received their scores on three tests. On the first test, Ada's score was 4 points higher than Paul's score. On the second test, Ada's score was 4 points higher than Paul's score. If Paul's average (arithmetic mean) score on the three tests was 3 points higher than Ada's average score on the three tests, then Paul's score on the third test was how many points higher than Ada's score?
(A) 9
(B) 14
(C) 17
(D) 23
(E) 25
Rationale: My take is Option D (23)
I followed a simple approach (explained below):
Test 1: Ada's score = Paul's score + 10
Test 2: Ada's score = Paul's score + 4
Avg. of Paul's score = 3 points higher than Avg. of Ada's score
This implies that : Sum of Paul's score [3 Tests] = 9 points higher than Sum of Ada's score [3 Tests] (9 points higher since 3 points were given in terms of average of 3 scores)
So, Paul needs to score 17 points higher than Ada in Test 3, since Paul needs to compensate for the lower score in test 1 and Test 2 ( 17 = 4 + 4 + 9)
C
Answer: (C) 17
Question: Shopkeeper rise price by 36% and gives successive discount of 10% and 15%. What is overall % gain or loss?
(A) 5.04%
(B) 4.04%
(C) 3.04%
(D) 6.04%
(E) 7.04%
Rationale: Let d initial price be 100
36% rise
now price = 136/100*100 = 136
10% discount
Then price = 136 * 90/100 = 122.4
15 % discount
Then price = 122.4 * 85/100 = 104.04
So Gain = 104.04 - 100 = 4.04
Gain % = Gain * 100 /CP
==> 4.04 * 100 /100 = 4.04%
ANSWER:B
Answer: (B) 4.04%
Question: Which of the number is the odd one out?
(A) 21165
(B) 17642
(C) 81002
(D) 52832
(E) 72927
Rationale: D
52832
All the others are three digit numbers followed by their square root, eg 729 followed by its square root, 27.
Answer is D
Answer: (D) 52832
Question: There are 20 poles with a constant distance between each pole. A car takes 22 second to reach the 12th pole. How much will it take to reach the last pole.
(A) 38
(B) 41
(C) 28
(D) 88
(E) 22
Rationale: Assuming the car starts at the first pole.
To reach the 12th pole, the car need to travel 11 poles (the first pole doesn't count, as the car is already there).
11 poles 22 seconds
1 pole (22/11) seconds
To reach the last (20th) pole, the car needs to travel 19 poles.
19 pole 19 x (22/11) seconds
=38 seconds
Answer:A
Answer: (A) 38
Question: Neha's mother was four times her age 12 years ago. She will be twice as old as Neha 12 years from now. What is the present age of Neha's mother ?
(A) 60 years
(B) 33
(C) 77
(D) 66
(E) 101
Rationale: Explanation:
Let Neha's present age be 'x' years.
Her age 12 years ago = (x – 12) years
Therefore, her mother's age 12 years ago = 4(x – 12)
Her mother's present age = 4x – 48 + 12 = 4x – 36
Neha's age after 12 years = x + 12
Her mother's age after 12 years = 4x – 36 + 12 = 4x – 24
4x – 24 = 2(x + 12)
4x – 2x = 24 + 24
x = 24
Therefore, Neha's present age = 24
Her mother's present age = 4x – 36 = 4(24) – 36 = 60 years
ANSWER: A
Answer: (A) 60 years
Question: In a fort there was sufficient food for 200 soldiers for 31days. After 27 days, 120 soldiers left the fort. for how many extra days will the rest of the food last for the remaining soldiers?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
Rationale: 200*31=27*200+x*80
x=10
it means that 6 extra days
ANSWER:B
Answer: (B) 6
Question: A train running at the speed of 60 km/hr crosses a pole in 18 seconds. What is the length of the train?
(A) 140
(B) 130
(C) 150
(D) 170
(E) 300
Rationale: Speed=(60x5/18)m/sec = (50/3) m/sec.
Length of the train = (Speed x Time).
Length of the train = (50/3 x 18)m = 300 m.
Answer is E.
Answer: (E) 300
Question: If a sequence of 8 consecutive odd integers with increasing values has 9 as its 7th term, what is the sum of the terms of the sequence?
(A) 22
(B) 32
(C) 36
(D) 40
(E) 44
Rationale: Seventh term, a7 = 9
Number of terms,n = 8
an= a1 + (n-1)d
a7= a1 + 6d
=>9 = a1 + 12
=>a1 = -3
8th term , a8 = 11
Sum of terms of the sequence = n/2[first term + last term]
= 4*[-3 + 11]
= 4*8
= 32
Answer B
Answer: (B) 32
Question: Find the simple interest on Rs. 68,800 at 16 2/3% per annum for 9 months.
(A) s.8600
(B) s.8000
(C) s.7500
(D) s.7000
(E) s.6500
Rationale: P = Rs.68800,R = 50/3% p.a and T = 9/12 years = 3/4years.
S.I. = (P*R*T)/100 = Rs.(68,800*(50/3)*(3/4)*(1/100))
= Rs.8600
Answer is A.
Answer: (A) s.8600
Question: If 4<(7-x)/3, which of the following must be true?
I. 5<x
II. |x+3|>2
III. -(x+3) is positive
(A) II only
(B) III only
(C) I and II only
(D) II and III only
(E) I, II and III
Rationale: 12<7-x
x<-5
x+5<0
1.5<x...not possible
2.True.....Check for values x=-6,-7,-8....... etc
3.True.. Since x+5<0 -(x+5) will always be positive
Hence, Ans is A..
Answer: (A) II only
Question: How much does a watch lose per day, if its hands coincide every 64 minutes?
(A) 35 8/11 mins
(B) 31 8/11 mins
(C) 32 8/11 mins
(D) 30 8/11 mins
(E) 37 8/11 mins
Rationale: 55 min. spaces are covered in 60 min.
60 min spaces are covered in (60/55 * 60)min = 65 5/11 min
Loss in 64 min = ( 65 5/11- 64 ) = 16/11 min
Loss in 24 hrs = ( 16/11 * 1/64 * 24 * 60 ) min
= 32 8/11 min
Answer is C.
Answer: (C) 32 8/11 mins
Question: A batsman scored 120 runs whichincluded 3 boundaries and 8sixes. What % of his total score did he make by running between the wickets
(A) 20%
(B) 50%
(C) 60%
(D) 70%
(E) 80%
Rationale: Number of runs made by running = 110 - (3 x 4 + 8 x 6)
= 120 - (60)
= 60
Now, we need to calculate 60 is what percent of 120.
=> 60/120 * 100 = 50%
B
Answer: (B) 50%
Question: A box contains four cents, of which two centss have heads on both their faces, one cent has tail on both its faces and the fourth cent is a normal one. A cent is picked at random and then tossed. If head is the outcome of the toss, then find the probability that the other face (hidden face) of the cent tossed is also a head.
(A) 4/5
(B) 3/5
(C) 2/5
(D) 3/4
(E) 1/2
Rationale: There are four ways (2 heads in one two-headed cent and 2 heads in the other two-headed cent)
How many ways can you get heads from this entire set of cents? There are five ways (four as identified above and one from the normal coin)
Therefore probability = 4/5
Option A
Answer: (A) 4/5
Question: In an election between two candidates first candidate got 60% of votes polled and second Candidate got 270 votes. The total number of votes polled was
(A) votes
(B) votes
(C) votes
(D) votes
(E) votes
Rationale: Total = 100 %,
First person got 60%
second person got remaining 40 % of votes.
than 40 % = 270
40% = 40×7 = 270
100% =100×7 =700 votes
A)
Answer: (A) votes
Question: The probability of a team winning a match given Matt is playing the match is 0.7. The probability of the team winning a match given Matt is not playing the match is 0.5. The probability of Matt playing any match is 0.8.
If it is known that the team has won the last match, what is the probability that Matt played the match?
(A) A)0.848
(B) B)0.7
(C) C)0.8571
(D) D)0.7531
(E) E)0.8213
Rationale: Out of 100 matches:
Matt is plays in 80 and not plays in 20.
Out of 80 matches Matt plays in, team wins 0.70*80 = 56.
Out of 20 matches Matt does not play in, team wins 0.5*20 = 10.
So, out of 100 matches 56 + 10 = 66 are won.
It is known that the team has won the last match. Out of 66 matches won, Matt is in 56: 56/66 = 0.848...
Answer: A.
Answer: (A) A)0.848
Question: Jayant gets 3 marks for each right sum and loses 2 marks for each wrong sum. He attempts 30 sums and obtains 40 marks. The number of sums attempted correctly is
(A) 25
(B) 20
(C) 26
(D) 27
(E) 28
Rationale: this is linear eqn in 2 variable
the Ist eqn
3x - 2y = 40
x + y = 30
solving
x = 20 (right answer)
y = 10 (wrong answer)
ANSWER:B
Answer: (B) 20
Question: The largest 4 digit number exactly divisible by 66 is?
(A) 9935
(B) 9939
(C) 9944
(D) 9966
(E) 9960
Rationale: Largest 4-digit number = 9999
66) 9999 (151
9966
Largest number : 9966
Answer : D
Answer: (D) 9966
Question: If a function f is defined by f(x)= 3/(x-1) for all non zero numbers x. If f(a) = 3 and f(ab) = 9 then b= ?
(A) 1/3
(B) 1/2
(C) -1/2
(D) -1/3
(E) -2
Rationale: Given that f(x) = 3/(x-1) and f(a) = 3, then f(a) =3/(x-1)=3 ===> x-1=1 ==> x =2, then backsolve using the answer choices:
f(ab) = f(2b) = 3/(2b-1)
A) 1/3 ===> f(2*1/3) = f(2/3) = 3/((2*2/3)-1) = 9 WINS
B) 1/2 ===> f((2*1/2) = f(1) = 3/1-1 = undefined
C) -1/2 ===> f(2*-1/2) = f(-1) = 3/1+1 = 3/2
D) -1/3 ===> f(2*-1/3) = f(-2/3) = 3/(2*-2/3 -1) = -9/7
E) -2 ===> f(2*-2) = f(-4) = 3/(2*-4 -1) = -1/3
Answer: A
Answer: (A) 1/3
Question: Find the sum The difference between the compound and S.I. on a certain sum of money for 2 years at 10% per annum is Rs.15of money?
(A) 1500
(B) 1800
(C) 2100
(D) 1950
(E) 2500
Rationale: Explanation:
P = 15(100/10)2 => P = 1500
ANSWER IS A
Answer: (A) 1500
Question: If n is a positive integer greater than 1, then p(n) represents the product of all the prime numbers less than or equal to n. The second smallest prime factor of p(12)+11 is
(A) 2
(B) 11
(C) 13
(D) 17
(E) 211
Rationale: p(12)+11=2∗3∗5∗7∗11+11=11(2∗3∗5∗7+1)=11∗211. Both 11 and 211 are primes: 11 is the smallest prime of p(12)+11 and 211 is the second smallest prime of p(12)+11.
Answer: E.
Answer: (E) 211
Question: From a seven-member dance group, three will be chosen at random to volunteer at a youth dance event. If Kori and Jason are two of the seven members, what is the probability that both will be chosen to volunteer?
(A) a) 1/42
(B) b) 1/7
(C) c) 4/21
(D) d) 2/7
(E) e) 3/7
Rationale: Total number of ways to choose 3 out of 7 = 7C3 = 420.
Number of ways to choose 2 (any but Kori and Jason) out of 5 (excluding Kori and Jason) = 5C2 = 10.
P = favorable/total = 10/420 = 1/42.
Answer: A.
Answer: (A) a) 1/42
Question: A shopkeeper buys two articles for Rs.1000 each and then sells them, making 20% profit on the first article and 20% loss on second article. Find the net profit or loss percent?
(A) 200
(B) 277
(C) 265
(D) 2987
(E) 212
Rationale: Profit on first article = 20% of 1000 = 200.
This is equal to the loss he makes on the second article. That, is he makes neither profit nor loss.Answer: A
Answer: (A) 200
Question: A small pool filled only with water will require an additional 400 gallons of water in order to be filled to 80% of its capacity. If pumping in these additional 400 gallons of water will increase the amount of water in the pool by 30%, what is the total capacity of the pool in gallons?
(A) 1000
(B) 1250
(C) 1300
(D) 1600
(E) 1750
Rationale: Since pumping in additional 400 gallons of water will increase the amount of water in the pool by 30%, then initially the pool is filled with 1,000 gallons of water.
So, we have that 1,000 + 400 = 0.8*{total} --> {total} = 1,750.
Answer: E.
Answer: (E) 1750
Question: A pack of 52 playing cards, 2cards are drawn together at random. Find the probability of both thecards being queen?
(A) 2/113
(B) 2/115
(C) 1/221
(D) 2/215
(E) 1/265
Rationale: Two cards can be drawn from a pack of 52 playing cards in 52C2 ways. i,e., 52 x 51 / 2 = 1326 ways. The event that two kings appear in a single drawn of cards is 4C2 ways, i.e 6 ways.
∴ The probability that the two cards drawn from a pack of 52 cards are kings = 6/1326 = 1/221
C
Answer: (C) 1/221
Question: By selling 99 pens, a trader gains the cost of 66 pens. Find his gain percentage?
(A) 66 1/3%
(B) 66 7/3%
(C) 66 1/8%
(D) 66 2/3%
(E) 66 1/5%
Rationale: Let the CP of each pen be Rs. 1.
CP of 99 pens = Rs. 99
Profit = Cost of 33 pens
= Rs. 33
Profit% = 66/99 * 100
= 66 2/3%
Answer: D
Answer: (D) 66 2/3%
Question: In the xy-plane, line q passes through point (3,-2) and intersect perpendicularly with line n that passes through points (0,3) and (3,5). What is the equation of line q?
(A) 3x+2y-5=0
(B) 3x+2y+5=0
(C) 2x-3y-12=0
(D) 2x+3y=0
(E) 4x+3y-6=0
Rationale: If two lines intersect perpendicularly, we get -1 when we multiply two slopes together. The slope of a line n is (5-3)/(3-0)=2/3. Hence, the slope of a line q should be -3/2. Since it crosses (3,-2), if we calculate we get 3x+2y=5. Hence, the correct answer is A.
Answer: (A) 3x+2y-5=0
Question: A farmer has an apple orchard consisting of Fuji and Gala apple trees. Due to high winds this year 10% of his trees cross pollinated. The number of his trees that are pure Fuji plus the cross-pollinated ones totals 221, while 3/4 of all his trees are pure Fuji. How many of his trees are pure Gala?
(A) 22
(B) 33
(C) 39
(D) 77
(E) 88
Rationale: Let f = pure fuji , g = pure gala and c - cross pollinated.
c = 10% of x where x is total trees.
c = .1x
also 3x/4 = f and c+f = 221 => .1x + 3/4x = 221 => x = 260
260 - 221 = pure gala = 39.
Answer C
Answer: (C) 39