mathewhe/aqua_rat huggingface dataset:
Question: The “length of integer x” refers to the number of prime factors, not necessarily distinct, that x has. (If x = 60, the length of x would be 4 because 60 = 2 × 2 × 3 × 5.) What is the greatest possible length of integer z if z < 1,000?
(A) 13
(B) 10
(C) 9
(D) 7
(E) 6
Rationale: To maximize the length of z, we should minimize its prime base. The smallest prime is 2 and since 2^9 = 512 <1,000, then the greatest possible length of integer z is 9.
The answer is C.
Answer: (C) 9
Question: Mona and Sona go around a circular track of length 400 m on a bike at speeds of 18 kmph and 36 kmph. After how much time will they meet for the first time at the starting point?
(A) 120
(B) 80
(C) 60
(D) 136
(E) 150
Rationale: Time taken to meet for the first time at the starting point
= LCM { length of the track / speed of monA , length of the track / speed of sona}
= LCM { 400/ (18 * 5/18) , 400/ (36 * 5 /18) }
= LCM (80, 40) = 80 sec.
Answer: B
Answer: (B) 80
Question: A walks around a circular field at the rate of one round per hour while B runs around it at the rate of five rounds per hour. They start in the same direction from the same point at 7.30 a.m. They shall first cross each other after___ minutes?
(A) 11 min
(B) 12 min
(C) 10 min
(D) 15 min
(E) 16 min
Rationale: Since A and B move in the same direction along the circle, so they will first meet each other when there is a difference of one round between the two.
Relative speed of A and B = 5 - 1 = 4 rounds per hour.
Time taken to complete one round at this speed = 1/4 hr = 15 min.
D
Answer: (D) 15 min
Question: If -4 < x < 7 and -7 < y < 3, which of the following specifies all the possible values of xy?
(A) -42 < xy < 21
(B) -49 < xy < 24
(C) -28 < xy < 18
(D) -24 < xy < 21
(E) -24 < xy < 24
Rationale: The least value of xy is a bit more than 7*(-7)=-49 and the largest value of xy is a bit less than (-4)*(-6)=24.
Therefore -49 < xy < 24.
Answer: B.
Answer: (B) -49 < xy < 24
Question: Find the amount on Rs.5000 in 2 years, the rate of interest being 4% per first year and 5% for the second year?
(A) 5460
(B) 3377
(C) 2776
(D) 2887
(E) 2667
Rationale: 5000 * 104/100 * 105/100 => 5460
Answer: C
Answer: (C) 2776
Question: If n is a natural number, then (6n^2 + 6n) is always divisible by?
(A) 6 only
(B) Both 6 and 12
(C) 12 only
(D) 6 or 12
(E) None
Rationale: 6n^2 + 6n = 6n(n + 1)
n(n + 1) is always even when n is a natural number
Hence 6n^2 + 6n is always divisible by 6 and 12
B)
Answer: (B) Both 6 and 12
Question: Sheila works 8 hours per day on Monday, Wednesday and Friday, and 6 hours per day on Tuesday and Thursday. She does not work on Saturday and Sunday. She earns $396 per week. How much does she earn in dollars per hour?
(A) 2
(B) 8
(C) 9
(D) 11
(E) 2
Rationale: Explanation:
Total hours worked = 8 x 3 + 6 x 2 = 36
Total earned = 396. Hourly wage = 396 / 36 = 11
Answer: D
Answer: (D) 11
Question: If population of certain city increases at the rate of 5%. If population in 1981 was 15000, then population in 1980 was?
(A) 142856
(B) 130000
(C) 261000
(D) 627000
(E) 12690
Rationale: Explanation:
X * (105/100) = 15000
X = 15000/1.05
X = 14285.71=142856
Answer: Option A
Answer: (A) 142856
Question: A 25 cm wide path is to be made around a circular garden having a diameter of 4 meters. Approximate area of the path is square meters is?
(A) 3.34 sq m
(B) 2.98 sq m
(C) 9.98 sq m
(D) 1.98 sq m
(E) 3.78 sq m
Rationale: Area of the path = Area of the outer circle - Area of the inner circle
= ∏{4/2 + 25/100}2 - ∏[4/2]2
= ∏[2.252 - 22]
= ∏(0.25)(4.25) { (a2 - b2
= (a - b)(a + b) }
= (3.14)(1/4)(17/4) = 53.38/16
= 3.34 sq m
Answer: A
Answer: (A) 3.34 sq m
Question: Find the value of (X) in the given equation ?
35% of 1500 + X = 45% of 4200 – 320
(A) 910
(B) 980
(C) 1012
(D) 1045
(E) None of these
Rationale: Explanation:
35% of 1500 + X = 45% of 4200 – 320
(35/100 * 1500) + X = (45/100 * 4200) – 320
525 + X = 1890 – 320
X = 1890 – 320 – 525
X = 1890 – 845
X = 1045
ANSWER: D
Answer: (D) 1045
Question: A is 50% as efficient as B. C does half the work done by A & B together. If C alone does the work in 40 days, then A, B and C together can do the work in how many days?
(A) 11 1/3 days
(B) 13 1/3 days
(C) 12 1/3 days
(D) 15 1/3 days
(E) 16 1/3 days
Rationale: A’s one day’s work : B’s one days work = 150 : 100 = 3 : 2.
Let A’s & B’s one day’s work be 3X and 2X days respectively.
Then C’s one day’s work = 5X/2
= > 5X/2 = 1/40
= > X = ((1/40) x (2/5)) = 1/100
A’s one day’s work = 3/100
B’s one day’s work = 1/50
C’s one day’s work = 1/40
Thus, A, B and C can do the work in 13 1/3 days.
ANSWER:B
Answer: (B) 13 1/3 days
Question: The average of five consecutive odd numbers is 61. What is the difference between the highest and the lowest number?
(A) 8
(B) 2
(C) 5
(D) Cannot be determined
(E) None of these
Rationale: Suppose the consecutive odd numbers are : x, x + 2, x + 4, x + 6 and x + 8
Therefore, the required difference = x + 8 – x = 8
Note that answering the above question does not require the average of the five consecutive odd numbers.
Answer A
Answer: (A) 8
Question: Robert can row a boat at 15 kmph in still water. If the speed of the stream is 4 kmph, what is the time taken to row a distance of 80 km downstream?
(A) 80/15
(B) 80/17
(C) 80/19
(D) 80/21
(E) 80/23
Rationale: Speed downstream = 15+4=19 kmph.
Time required to cover 60 km downstream = d/s = 80/19 hours. Answer:C
Answer: (C) 80/19
Question: At a certain supplier, a machine of type A costs $20,000 and a machine of type B costs $65,000. Each machine can be purchased by making a 20 percent down payment and repaying the remainder of the cost and the finance charges over a period of time. If the finance charges are equal to 40 percent of the remainder of the cost, how much less would 2 machines of type A cost than 1 machine of type B under this arrangement?
(A) $10,000
(B) $11,200
(C) $12,000
(D) $12,800
(E) $33,000
Rationale: Total Cost of 2 Machines of Type A
= 20% of (Cost of 2 machine A) + remainder + 40 % remainder
= 20% of 40000 + (40000 - 20% of 40000) + 40% of (40000 - 20% of 40000)
= 52800
Total Cost of 1 Machine of Type B
= 20% of (Cost of 1 machine B) + remainder + 40 % remainder
= 20% of 65000 + (65000 - 20% of 65000) + 40% of (65000 - 20% of 65000)
= 85800
Diff = 66000 - 85800 = 33000
Hence, E.
Answer: (E) $33,000
Question: In a box, there are 8 red, 7 blue and 6 green balls. One ball is picked up randomly. What is the probability that it is neither red nor green?
(A) 1/3
(B) 3/4
(C) 7/19
(D) 8/21
(E) 9/21
Rationale: Total number of balls = (8 + 7 + 6) = 21.
Let E	= event that the ball drawn is neither red nor green
= event that the ball drawn is blue.
n(E) = 7.
P(E) =	n(E)/n(S)	=	7/21 =	1/3	.
Answer :A
Answer: (A) 1/3
Question: The S.I. on a certain sum of money for 2 years at 6% per annum is half the C.I. on Rs. 4000 for 2 years at 10% per annum. The sum placed on S.I. is?
(A) 2197
(B) 1267
(C) 3500
(D) 2267
(E) 1262
Rationale: Explanation:
C.I. = [4000 * (1 + 10/100)2 - 4000]
= (4000 * 11/10 * 11/10 - 4000) = Rs. 840.
Sum = (420 * 100)/(2 * 6) = Rs. 3500
Answer:C
Answer: (C) 3500
Question: If s and t are positive integers, st + s + t cannot be
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
Rationale: Let st + t + s = x
Add 1 on both sides:
st + t + s + 1 = x + 1
t(s + 1) + s + 1 = x + 1
(s + 1)(t + 1) = x + 1
Minimum value of (s + 1) = 2
Minimum value of (t + 1) = 2
Hence x + 1 cannot be prime
Substitute x from the given options: 6 + 1 = 7 --> prime --> st + t + s cannot be 6
Answer: B
Answer: (B) 6
Question: A certain candy manufacturer reduced the weight of Candy Bar M by 5 percent buy left the price unchanged. What was the resulting percent increase in the price per ounce of Candy Bar M?
(A) 5.5
(B) 5.4
(C) 5.3
(D) 5.2
(E) 5.1
Rationale: assume 1oz candy cost $1 before.
now price remain same $1 but weight of candy reduces to 0.95 oz
new price of candy = 1/0.95 =1.052
price increase 5.2 %
D
Answer: (D) 5.2
Question: The average of 20 numbers is zero. Of them, at the most, how many may be greater than zero?
(A) 0
(B) 1
(C) 10
(D) 19
(E) 20
Rationale: Solution
Average of 20 numbers	= 0
Sum of 20 numbers	=(0 x 20) =0.
It is quite possible that 19 of these numbers may be positive and if there sum id a, then 20th number is (-a).
Answer A
Answer: (A) 0
Question: A number x is 12 times another number y. The percentage that y is less than x is
(A) 91.6%
(B) 87.5%
(C) 80%
(D) 11%
(E) 1%
Rationale: Say y=1 and x=12.
Then y=1 is less than x=12 by (12-1)/12*100=11/12*100=91.6%.
Answer: A.
Answer: (A) 91.6%
Question: At a local beach, the ratio of little dogs to average dogs to enormous dogs is 3:8:9. Late in the afternoon, the ratio of little dogs to average dogs doubles and the ratio of little dogs to enormous dogs increases. If the new percentage of little dogs and the new percentage of average dogs are both integers and there are fewer than 30 total dogs at the beach, which of the following represents a possible new percentage of enormous dogs?
(A) 25%
(B) 40%
(C) 30%
(D) 55%
(E) 70%
Rationale: Little Dogs(L), Average Dogs(A) and Enormous Dogs (E)
The initial ratio for L:A:E :: 3:8:9
Initial Total dogs = 20X ( x assumed; 3+8+9= 20), Since the total dogs are less than 30 therefore initial total value has to be 20
L = 2, A = 5 E = 8
L:A= 2:5
This ratio doubles
Hence New Dog count is
L= 6 , A = 8 E= X: Also 6+8+x<30
We need to Find X*100/(6+8+X)
Now it says that new percentage of little dogs and Average dogs is an integer
%L = 6*100/(14+x) %A = 8*100/(14+x); Only Value for X is 6 ; 14+x<30 and % integer
Therefore, Enormus Dogs % is = 6*100/(20) = 30%
C
Answer: (C) 30%
Question: A man can reach certain place in 10hours. If he reduces his speed by 1/5th, he goes 10km less in time. Find his speed?
(A) 5km/hr
(B) 22.5km/hr
(C) 10.78km/hr
(D) 14km/hr
(E) 43.15km/hr
Rationale: Let the speed be x km/hr
10x-10* 4/5 *x = 10
10x - 8x = 10
2x = 10
x = 5km/hr
Answer is A
Answer: (A) 5km/hr
Question: Shreyas bought an article and sold it for 105% of its cost price. What was the cost price of the article, if Shreyas sold it for Rs.42000/-?
(A) Rs.40000
(B) Rs.45640
(C) Rs.44250/-
(D) Rs.43200
(E) None of these
Rationale: Explanation:
105% of CP = Rs.42000
:. CP = Rs.42000x100/105 = Rs.40000.
Answer: Option A
Answer: (A) Rs.40000
Question: If the product 4864 x 9 P 2 is divisible by 12, then the value of P is:
(A) 3
(B) 2
(C) 1
(D) 6
(E) 5
Rationale: C
1
Clearly, 4864 is divisible by 4.
So, 9P2 must be divisible by 3.
So, (9 + P + 2) must be divisible by 3.
P = 1.
Answer: (C) 1
Question: The average of 11 numbers is 11. If the average of the first six numbers is 10.5 and that of the last six numbers is 11.4, then the middle number is
(A) 10.4
(B) 11.5
(C) 81.5
(D) 11.5
(E) 21.5
Rationale: Explanation:
Middle numbers = [(10.5 x 6 + 11.4 x 6) - 11 x 11] = 10.4.
Answer: A
Answer: (A) 10.4
Question: (2^2-1)(2^2+1)(2^4+1)(2^9+1)=
(A) 2^17 - 1
(B) 2^16 + 1
(C) 2^32 - 1
(D) 2^128 - 1
(E) 2^16(2^16-1)
Rationale: A: is correct
(2^2-1)* (2^2+1)=(2^4-1)
(2^4-1)*(2^4+1)=2^8-1
(2^8-1)*(2^9 +1)=2^17-1
You can apply to this formula: a^2- b^2=(a-b)*(a+b)
Answer: (A) 2^17 - 1
Question: 120 is what percent of 50 ?
(A)  5%
(B)  240%
(C)  50%
(D)  2%
(E)  500%
Rationale: 50*x=120 --> x=2.4 --> 2.4 expressed as percent is 240%.
Answer: B.
Answer: (B)  240%
Question: If x^2=3x+1, then x^3 = ?
(A) 8x+2
(B) 10x+3
(C) 6x+1
(D) 2x+3
(E) 6x+4
Rationale: x^2 = 3x+1
x^3 = x*x^2 = x*(3x+1) = 3x^2 + x = 3(3x+1)+x = 10x+3
The answer is B.
Answer: (B) 10x+3
Question: A reduction of 20% in the price of oil enables a house wife to obtain 10 kgs more for Rs.1500, what is the reduced price for kg?
(A) Rs.20
(B) Rs.25
(C) Rs.30
(D) Rs.35
(E) Rs.40
Rationale: Explanation:
1500*(20/100) = 300 ---- 10
? ---- 1 => Rs.30
Answer: C
Answer: (C) Rs.30
Question: The average number of shirts with Salman, Ambani and Dalmiya is 40, if all of them reached a shopping mall in Delhi and purchased 14 shirts each of them then average number of shirt each of them now has
(A) 66
(B) 54
(C) 67
(D) can't be determined
(E) None of these
Rationale: Answer
Required average
= Old average + New average
= 40 + 14 = 54
Correct Option: B
Answer: (B) 54
Question: The average weight of A, B and C is 60 kg. If the average weight of A and B be 70 kg and that of B and C be 50 kg, then the weight of B is:
(A) 50 kg
(B) 60 kg
(C) 55 kg
(D) 57 kg
(E) 62 kg
Rationale: EXPLANATION
Let A, B, C represent their respective weights. Then, we have:
A + B + C = (60 x 3) = 180 â€¦. (i)
A + B = (70 x 2) = 140 â€¦. (ii)
B + C = (50 x 2) = 100 â€¦.(iii)
Adding (ii) and (iii), we get: A + 2B + C = 240 â€¦. (iv)
Subtracting (i) from (iv), we get : B = 60.
Bâ€™s weight = 60 kg.
Answer B
Answer: (B) 60 kg
Question: If the perimeter of a rectangular garden is 600 m, its length when its breadth is 100 m is?
(A) 299 m
(B) 777 m
(C) 200 m
(D) 167 m
(E) 128 m
Rationale: 2(l + 100) = 600 => l
= 200 m
Answer:C
Answer: (C) 200 m
Question: What will be the ratio of simple interest earned by certain amount at the same rate of interest for 14 years and that for 18 years?
(A) 7 : 9
(B) 8 : 9
(C) 5 : 9
(D) Data inadequate
(E) None of these
Rationale: Let the principal be P and rate of interest be R%.
∴ Required Ratio = [(P×R×14/100) /(P×R×18/100)]=14PR/18PR=14/18=7:9
Answer A
Answer: (A) 7 : 9
Question: 264, 396, 462, 792, 968, 2178, 5184, 6336?
How many of the following numbers are divisible by 132 ?
(A) 7
(B) 3
(C) 5
(D) 9
(E) 4
Rationale: 132 = 4 x 3 x 11
So, if the number divisible by all the three number 4, 3 and 11, then the number is divisible by 132 also.
264 11,3,4 - (/)
396 11,3,4 - (/)
462 11,3 - (X)
792 11,3,4 - (/)
968 11,4 - (X)
2178 11,3 - (X)
5184 3,4 - (X)
6336 11,3,4 - (/)
Therefore the following numbers are divisible by 132 : 264, 396, 792 and 6336.
Required number of number = 4.
ANSWER E
Answer: (E) 4
Question: Out of a classroom of 3 boys and 8 girls, the teacher randomly chooses a president for the student board, a vice president, and a secretary. What is the probability that only girls will be selected for all three positions?
(A) 14/33
(B) 17/33
(C) 48/165
(D) 52/165
(E) 56/165
Rationale: The number of ways to choose three people is 11C3=165.
The number of ways to choose three girls is 8C3=56.
P(only girls are chosen)=56/165
The answer is E.
Answer: (E) 56/165
Question: Maxwell leaves his home and walks toward Brad's house. One hour later, Brad leaves his home and runs toward Maxwell's house. If the distance between their homes is 14 kilometers, Maxwell's walking speed is 4 km/h, and Brad's running speed is 6 km/h. What is the total time it takes Maxwell before he meets up with Brad?
(A) 2
(B) 4
(C) 5
(D) 6
(E) 8
Rationale: Total Distance = 14 kms
Maxwell Speed = 4 kms/hr
Maxwell travelled for 1hour before Brad started , therefore Maxwell traveled for 4 kms in 1 hour.
Time taken = Total Distance / Relative Speed
Total Distance after Brad started = 10 kms
Relative Speed (Opposite side) (As they are moving towards each other speed would be added ) = 6+ 4 = 10 kms/hr
Time taken to meet Brad after Brad Started = 10 / 10 = 1 hrs
Distance traveled by Maxwell = Maxwell's speed * time taken = 4 * 1 = 4+4 = 8 kms...
Therefore Total Time taken by Maxwell to meet Brad = Distance travelled by Maxwell / Maxwell's Speed = 8/4 = 2 hrs ... Answer A
Answer: (A) 2
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 9 hours and 16 hours respectively. The ratio of their speeds is?
(A) 4:6
(B) 4:3
(C) 4:4
(D) 4:7
(E) 4:2
Rationale: Let us name the trains A and B.
Then, (A's speed) : (B's speed)
= √b : √a = √16 : √9 = 4:3
Answer: B
Answer: (B) 4:3
Question: 40% of the employees in a factory are workers. All the remaining employees are executives. The annual income of each worker is Rs. 390. The annual income of each executive is Rs. 420. What is the average annual income of all the employees in the factory together?
(A) 390
(B) 405
(C) 408
(D) 415
(E) None
Rationale: Solution:
Let X be the number of employees.
We are given that 40% of the employees are workers. Now, 40% of X is (40/100)*X =0.4X.
Hence, the number of workers is 2X/5.
All the remaining employees are executives, so the number of executives equals,
(The number of Employees)–(The number of Workers),
= X–(2X/5)
=(3X/5)
The annual income of each worker is Rs. 390.
Hence, the total annual income of all the workers together is,
= (2X/5)*390 =156X.
Also, the annual income of each executive is Rs. 420. Hence, the total income of all the executives together is,
(3X/5)×420 =252X
Hence, the total income of the employees is,
= 156X +252X =408X.
The average income of all the employees together equals,
Answer: Option C
Answer: (C) 408
Question: A highway is to be divided into 3 lanes. For this purpose, two yellow stripes are painted so that stripes divide the highway into 3 lanes. If 3 gallons of paint cover an area of 4P square feet of highway, how many gallons of paint are needed to paint two stripes x inches wide on a stretch of highway m miles long? (1 mile = 5280 feet and 1 feet = 12 inches)
(A) 220P/mx
(B) 660mx/P
(C) 880mx/P
(D) 440P/mx
(E) 330mx/P
Rationale: 1 square foot needs 3/4P gallons of paint.
The width of each stripe is x/12 feet.
The length of each stripe is 5280m feet.
The area of each stripe is (5280m)(x/12) = 440mx square feet.
For two stripes, the total area is 880mx square feet.
The number of gallons needed is (880mx)*(3/4P) = 660mx/P gallons.
The answer is B.
Answer: (B) 660mx/P
Question: WHEN A PERSON SELLS TWO ITEMS $800 each, ONE AT A GAIN OF 20% AND OTHER AT A LOSS OF 20%.THEN THE SELLER INCURES A LOSS OR GAIN OF:
(A) no loss no gain
(B) 4% loss
(C) 5% gain
(D) 2% gain
(E) 1% loss
Rationale: When two items are sold at the same price, one at a profit of a% and other at a loss of a% (which means the cost price of one item was lower than the selling price and the cost price of the other item was higher than the selling price), there will always be a loss of (a^2)/100 %. e.g. Here a = 20, so loss % = (20)^2/100 % = 4%.
Answer : B
Answer: (B) 4% loss
Question: 1500 men have provisions for 17 days. If 320 more men join them, for how many days will the provisions last now?
(A) 12.9
(B) 12.0
(C) 14
(D) 15
(E) 16
Rationale: 1500*17 = 1820*x
x = 14
Answer:C
Answer: (C) 14
Question: Pavan travelled for 11 hours. He covered the first half of the distance at 30 kmph and remaining half of the distance at 25 kmph. Find the distance travelled by Pavan?
(A) 288 km
(B) 886 km
(C) 866 km
(D) 300 km
(E) 261 km
Rationale: Let the distance travelled be x km.
Total time = (x/2)/30 + (x/2)/25 = 11 => x/60 + x/50
= 11 => (5x + 6x)/300 = 11 => x
= 300 km
Answer: D
Answer: (D) 300 km
Question: Out of 5 consonants and 3 vowels, how many words of 3 consonants and 2 vowels can be formed?
(A) 25200
(B) 120
(C) 3600
(D) 300
(E) 2100
Rationale: Required selection = select 3 consonants from 5 and 2 vowels frm 3
= 5C3 * 3C2
= 30
As we have to form 5 letter word the above combination of consonants and vowels can be done in 5! = 120 different ways
Required no. of ways = 30 * 120
= 3600
Ans - C
Answer: (C) 3600
Question: In 1992 a total of 550 earthquakes occurred worldwide, some but not all of which occurred in Asia. If 150 of these earthquakes occurred in Asia, which of the following represents the ratio of the number of earthquakes that occurred in Asia to the number that did NOT occur in Asia?
(A) 2/8
(B) 1/8
(C) 3/8
(D) 5/8
(E) 7/8
Rationale: We're given a couple of facts to work with:
1) There were a total of 550 earthquakes
2) Of those earthquakes, 150 of them occurred in Asia
We're asked for the ratio of the number of earthquakes that occurred IN ASIA to the number of earthquakes that DID NOT occur in Asia.
Thus, there were 400 earthquakes that DID NOT occur in Asia....
The answer to the question is 150/400 = 3/8
Answer : C
Answer: (C) 3/8
Question: Each month a retailer sells 100 identical items. On each item he makes a profit of $40 that constitutes 10% of the item's price to the retailer. If the retailer contemplates giving a 5% discount on the items he sells, what is the least number of items he will have to sell each month to justify the policy of the discount?
(A) 191
(B) 213
(C) 221
(D) 223
(E) 226
Rationale: For this question, we'll need the following formula:
Sell Price = Cost + Profit
We're told that the profit on 1 item is $20 and that this represents 10% of the cost:
Sell Price = Cost + $40
Sell Price = $400 + $40
Thus, the Sell Price is $440 for each item. Selling all 100 items gives the retailer...
100($40) = $2,000 of profit
If the retailer offers a 5% discount on the sell price, then the equation changes...
5%(440) = $22 discount
$418 = $400 + $18
Now, the retailer makes a profit of just $18 per item sold.
To earn $2,000 in profit, the retailer must sell....
$18(X) = $2,000
X = 2,000/18
X = 222.222222 items
You'll notice that this is not among the answer choices.... 221 and 223 are.
Selling 221 items would get us 9(221) = $1989 which is NOT enough money. To get back to AT LEAST $2,000, we need to sell 223 items.
Final Answer:
D
Answer: (D) 223
Question: A committee has 5 men and 6 women. What are the number of ways of selecting a group of eight persons?
(A) 165
(B) 185
(C) 205
(D) 225
(E) 245
Rationale: Total number of persons in the committee = 5 + 6 = 11
Number of ways of selecting group of eight persons = ¹¹C₈ = ¹¹C₃ = (11 * 10 * 9)/(3 * 2) = 165 ways.
ANSWER:A
Answer: (A) 165
Question: The radii of two cones are in the ratio 2:1, their volumes are equal. Find the ratio of their heights.
(A) 1/4
(B) 1/8
(C) 2/4
(D) 4/1
(E) None
Rationale: Sol.
Let their radii be 2x, x and their heights be h and H respectively. Then,
1/3 * ∏ * (2x)² * h = 1/3 * ∏ * x² * H
or
h/H = 1/4.
Answer A
Answer: (A) 1/4
Question: If a card is drawn from a shuffled deck of cards, what is the probability of drawing a red card or a 9?
(A) 14/27
(B) 15/26
(C) 7/13
(D) 7/12
(E) 13/26
Rationale: P(Rá´œ9) = P(R) + P(9) - P(Râˆ©9), where R denotes a red card and 9 denotes a 9 card.
P(Rá´œ9) = 26/52 + 4/52 - 2/52
P(Rá´œ9) = 7/13
Answer: C
Answer: (C) 7/13
Question: The closest approximation of D(69.28 × 0.004)/0.03 is
(A) 0.092
(B) 0.92
(C) 9.2
(D) 92
(E) 920
Rationale: D(69.28 × 0.004)/0.03
1. 0.004 = 4 × 10^(-3)
2. 0.03 = 3 × 10^(-2)
3. (a × b)/c = a × (b/c)
4. 0.004/0.03 = 4 × 10^(-3)/ (3 × 10^(-2)) = 4 × 10^( -3 - (-2))/3 = 4 × 10^(-1) / 3 = (4/3) × 10^(-1) = 1.333 × 10^(-1)
Therefore,
(69.28 × 0.004)/0.03 = 69.28 × (0.004/0.03) = 69.28 × 1.33 × 10^(-1) = 69.28 × 1.33/10 = 6.928*1.33
Now,
7 × 2 = 14
7 × 1 = 7
or better:
6.9 × 1 = 6.9
6.9 × 2 = 13.8
hence,
6.9 <6.928 × 1.33 < 13.8
9.2 is the only answer that satisfies this condition.C
Answer: (C) 9.2
Question: Company C sells a line of 25 products with an average retail price of $1,000. If none of these products sells for less than $400, and exactly 10 of the products sell for less than $1,000, what is the greatest possible selling price of the most expensive product?
(A) 9000
(B) 8000
(C) 7000
(D) 6000
(E) 5000
Rationale: The average price of 25 products is $1,000 means that the total price of 25 products is 25*1,000=$25,000.
Next, since exactly 10 of the products sell for less than $1,000, then let's make these 10 items to be at $400 each (min possible).
Now, the remaining 14 items cannot be priced less than $1,000, thus the minimum possible price of each of these 14 items is $1,000.
Thus the minimum possible value of 24 products is 10*400+14*1,000=$18,000.
Therefore, the greatest possible selling price of the most expensive product is $25,000-$18,200=$7,000.
Answer: C.
Answer: (C) 7000
Question: How many integers between 324,700 and 448,600 have tens digit 1 and units digit 3?
(A) 10,300
(B) 8,030
(C) 1,253
(D) 1,252
(E) 1,239
Rationale: The integers are:
324,713
324,813
etc...
448,513
The number of integers is 4486 - 3247 = 1239
The answer is E.
Answer: (E) 1,239
Question: The greatest possible length which can be used to measure exactly the length 5m ,7m 25cm, 1m 25 cm is?
(A) 25cm
(B) 101cm
(C) 56cm
(D) 42cm
(E) 35cm
Rationale: Required length = H.C.F of 500cm, 725cm, 125cm = 25cm
Answer is A
Answer: (A) 25cm