mathewhe/aqua_rat huggingface dataset:
Question: The perimeter of a rectangle is 60 mete(132)7 × (132)? = (132)11.5.
(A) 3
(B) 3.5
(C) 4
(D) 4.5
(E) 5
Rationale: 7+x=11.5
x=11.5-7
x=4.5
ANSWER:D
Answer: (D) 4.5
Question: 122 * 252 - 12234 = ?
(A) 15310
(B) 18870
(C) 24510
(D) 18510
(E) 42510
Rationale: D
? = 122 * 252 - 12234
= 30744 - 12234
= 18510
Answer: (D) 18510
Question: A photography dealer ordered 75 Model X cameras to be sold for $250 each, which represents a 20 percent markup over the dealer’s initial cost for each camera. Of the cameras ordered, 6 were never sold and were returned to the manufacturer for a refund of 50 percent of the dealer's initial cost. What was the dealer's approximate profit or loss as a percent of the dealer’s initial cost for the 75 cameras?
(A) 7% loss
(B) 13% loss
(C) 7% profit
(D) 13% profit
(E) 14.4% profit
Rationale: Total cost 75*($250/1.2)=62.5*250;
# of cameras sold is 60-6=54 total revenue is 69*250;
# of cameras returned is 6 total refund 6*(250/1.2)*0.5;
So, total income 69*250+ 6*(250/1.2)*0.5
The dealer's approximate profit is (69*250+ 6*(250/1.2)*0.5-62.5*250)/(62.5*250)*100=14.4%
Answer: E.
Answer: (E) 14.4% profit
Question: Anil can do a work in 12 days while Sunil can do it in 25 days. How long will they take if both work together?
(A) 10 1/10 days
(B) 18 1/10 days
(C) 7 1/10 days
(D) 8 1/10 days
(E) 9 1/10 days
Rationale: 1/12 + 1/25 = 37/300
300/37 = 8 1/10 days
ANSWER:D
Answer: (D) 8 1/10 days
Question: The original price of a television is 350$. What percent of the original price has been taken off if the retailer offers a discount of 122,50$ on the television?
(A) 35%
(B) 30%
(C) 40%
(D) 45%
(E) 25%
Rationale: Explanation :
Total cost of the television: 350
Required percentage = (122,5/350) Ã— 100 = 35%
Answer : Option A
Answer: (A) 35%
Question: There are different 45 circles. What is the number of the greatest possible points with which the circles intersect?
(A) 1950
(B) 2000
(C) 1980
(D) 1580
(E) 2600
Rationale: Maximum points of intersection between n different circles = n*(n - 1) = 45*44 = 1980
Answer: C
Answer: (C) 1980
Question: The sum of two numbers is 45. The sum of their quotient and is reciprocal is 2.05, the product of the numbers is?
(A) 300
(B) 400
(C) 500
(D) 600
(E) 700
Rationale: a + b = 45
a/b+b/a = 2.05
=>(a^2+b^2)/ab = 2.05
=>((a+b)^2−2ab)/ab=2.05
=>(a+b)^2 = 2.05ab + 2ab = 4.05ab
=> ab = 45^2 / 4.05 = 500
ANSWER:C
Answer: (C) 500
Question: 4 baseball players each stand at different corners of a baseball diamond. The sides of the diamond are all of equal length. Two arrangements of baseball players are considered different only when the relative positions of the players differ. How many different ways can the baseball players arrange themselves around the diamond?
(A) 4
(B) 6
(C) 16
(D) 24
(E) 256
Rationale: it is like a circular arrangement.
total ways for n people to arrange in a circle is = factorial (n-1)
in this case n= 4
hence ans = 3 factorial = 6
hence B
Answer: (B) 6
Question: A boat travels upstream from B to A and downstream from A to B in 3 hours. If the speed of the boat in still water is 9 km/hour and the speed of the current is 3 km/hour, the distance between A and B is
(A) 4 km
(B) 8 km
(C) 6 km
(D) 12 km
(E) None of these
Rationale: Let D is the distance travelled. Then,
D/(9+3) + D/(9-3) = 3 => D = 12
Answer: D
Answer: (D) 12 km
Question: A 300 meter long train crosses a platform in 51 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform?
(A) 550
(B) 289
(C) 350
(D) 882
(E) 281
Rationale: Speed = [300 / 18] m/sec = 50/3 m/sec.
Let the length of the platform be x meters.
Then, x + 300 / 51 = 50/3
3(x + 300) = 2550 è x = 550m.
Answer: A
Answer: (A) 550
Question: A football coach must choose 5 freshers from a team of 12players. How many different ways can the coach choose the freshers?
(A) 567
(B) 687
(C) 729
(D) 790
(E) 821
Rationale: Choose 5 starters from a team of 12 players. Order is not important.
\inline {\color{Black} 12C_{5}}= 729
C
Answer: (C) 729
Question: A certain mixture of nuts consists of 5 parts almonds to 2 parts walnuts, by weight. What is the number of pounds of almonds in 210 pounds of the mixture ?
(A)  150
(B)  84
(C)  40
(D)  28
(E)  20
Rationale: Almonds : Walnuts = 5 : 2
Total mixture has 7 parts
In a 210 pound mixture, Almonds are 5/7 (total mixture)
= 5/7 * 210 = 150 pounds
Answer (A)
Answer: (A)  150
Question: 12.5% of 192 = 50% of ?
(A) 48
(B) 96
(C) 24
(D) None of these
(E) Cannot be determined
Rationale: Answer
Let 12.5% of 192 = 50% of A,
⇒(12.5 x 192) / 100 = (50 x A) / 100
∴ A = (12.5 x 192) / 50 = 48
Correct Option: A
Answer: (A) 48
Question: The speeds of three motor bikes are in the ratio 24 : 12 : 6. The ratio between the time taken by them to travel the same distance is :
(A) 1 : 3 : 4
(B) 1 : 2 : 6
(C) 1 : 4 : 4
(D) 1 : 2 : 3
(E) 1 : 2 : 4
Rationale: Ratio of time taken :
1/24 :1/12 : 1/6 = 1 : 2 : 4
ANSWER:E
Answer: (E) 1 : 2 : 4
Question: Which of the following fractions is smaller twice greater than 9/50?
(A) 2/5
(B) 10/34
(C) 43/99
(D) 8/21
(E) 9/20
Rationale: Answer B
9/50=0.18
10/34=0.2941 which is 0.01 smaller than two times of 0.18
Answer: (B) 10/34
Question: A team of eight entered for a shooting competition. The best marks man scored 82 points. If he had scored 92 points, the average scores for. The team would have been 87. How many points altogether did the team score?
(A) 686
(B) 672
(C) 652
(D) 642
(E) 721
Rationale: 8 * 87 = 696 – 10 = 686
ANSWER:A
Answer: (A) 686
Question: Mary's income is 50 percent more than Tim's income, and Tim's income is 40 percent less than Juan's income. What percent of Juan's income is Mary's income?
(A)  124%
(B)  120%
(C)  96%
(D)  90%
(E)  64%
Rationale: Juan's income = 100 (assume);
Tim's income = 60 (40 percent less than Juan's income);
Mary's income = 90 (50 percent more than Tim's income).
Thus, Mary's income (90) is 90% of Juan's income (100).
Answer: D.
Answer: (D)  90%
Question: The number of girls in a class are 7 times the number of boys, which value can never be the of total students
(A) 40
(B) 48
(C) 24
(D) 30
(E) 34
Rationale: Explanation:
Let the boys are X, then girls are 7X, total = X+7X = 8X
So it should be multiple of 8, 30 is not a multiple of 8.
Option D
Answer: (D) 30
Question: what is the smallest integer that is multiple of 8,7 and 20
(A) 141
(B) 180
(C) 130
(D) 122
(E) 280
Rationale: Correct Answer :E
It is the lcm of 8,7 and 20 which is 280
Answer: (E) 280
Question: A person is traveling at 25km/hr and reached his destiny in 5hr find the distance?
(A) 100km
(B) 95km
(C) 135km
(D) 80km
(E) 125km
Rationale: speed = 25km/hr
time = 5hr
distance = 25*5 = 125km
Answer is E
Answer: (E) 125km
Question: Shankar got 66, 83, 77, 68, 86 marks (out of 100) in English, Maths, physics, Biology and Chemistry. What are his average marks?
(A) 76
(B) 69
(C) 72
(D) 64
(E) None of these
Rationale: Explanation :
solution: 66 + 83 + 77 + 68 + 86/ 5= 76
Answer : A
Answer: (A) 76
Question: The speed of a train is 64 kmph. What is the distance covered by it in 9 minutes?
(A) 10 kmph
(B) 11 kmph
(C) 88 kmph
(D) 18 kmph
(E) 12 kmph
Rationale: 64 * 9/60
= 9.6 kmph
Answer:A
Answer: (A) 10 kmph
Question: Ron begins reading a book at 3: 30 p.m. and reads at a steady pace of 30 pages per hour. Michelle begins reading a copy of the same book at 5: 00 p.m. If Michelle started 5 pages behind the page that Ron started on and reads at an average pace of 50 pages per hour, at what time would Ron and Michelle be reading the same page?
(A) 7: 30 p.m.
(B) 7: 15 p.m.
(C) 7: 45 p.m.
(D) 8: 00 p.m.
(E) 8: 30 p.m.
Rationale: M gains 50-30=20 pages per hour on R
at 5pm R has read 45 pages and M is 45+5=50 pages behind him
time=50/20=2.5 hours
they are on the same page at 7:30pm
A
Answer: (A) 7: 30 p.m.
Question: In Country Z, the unemployment rate among construction workers dropped from 16 percent on September 1, 1992, to 9 percent on September 1, 1996. If the number of construction workers was 20 percent greater on September 1, 1996, than on September 1, 1992, what was the approximate percent change in the number of unemployed construction workers over this period?
(A)  50% decrease
(B)  30% decrease
(C)  15% decrease
(D)  30% increase
(E)  55% increase
Rationale: Country Z 1992 1996
No of construction workers 100 120
Unemployment Rate 16% 9%
Unemployed workers 16 11
% change in unemployed workers=(16-11)=5/16=~33% decrease
Closest ans=30% decrease
Ans=B
Answer: (B)  30% decrease
Question: If 378 coins consist of rupee, 50 paise and 25 paise coins, whose values are proportional to 13 :11 : 7, the number of 50 paise coins will be :
(A) 128
(B) 132
(C) 133
(D) 136
(E) None of these
Rationale: If values are proportional to 13 : 11 : 7, then the number of coins will be proportional to 13/1 : 11/0.50 : 7/0.25 ⇒ 13 : 22 : 28. Now from this the number of coins of 50 paise will be 378 × 22/63 = 132.
Answer: B
Answer: (B) 132
Question: 12 buckets of water fill a tank when the capacity of each bucket is 55 litres. How many buckets will be needed to fill the same tank, if the capacity of each bucket is 5 litres?
(A) 142
(B) 130
(C) 132
(D) 123
(E) 120
Rationale: Capacity of the tank = (12Ã— 55) litre
Number of buckets required of capacity of each bucket is 17 litre = 12Ã—55/5=12Ã—11=132
Answer is C
Answer: (C) 132
Question: A man took a loan at rate of 12% per annum simple interest. After 3 years he had to pay 3600 interest. The principal amount borrowed by him was.
(A) Rs 10000
(B) Rs 15000
(C) Rs 16000
(D) Rs 17000
(E) None of these
Rationale: Explanation:
S.I.=Pâˆ—Râˆ—T/100
=>P=S.I.âˆ—100/Râˆ—T
=>P=3600âˆ—100/12âˆ—3=Rs10000
Option A
Answer: (A) Rs 10000
Question: A train covers a certain distance at a speed of 230kmph in 4 hours. To cover the same distance in 2 2/3 hours, it must travel at a speed of
(A) 220km/hr
(B) 320km/hr
(C) 345km/hr
(D) 450km/hr
(E) 650km/hr
Rationale: Explanation:
Distance = 230Ã—4 = 920km
Required speed = (920Ã— 3/8) = 345km/hr
Answer: Option C
Answer: (C) 345km/hr
Question: What is the smallest five digit number that is divisible by 16, 36, 40, and 54?
(A) 10200
(B) 10500
(C) 10800
(D) 11000
(E) 11400
Rationale: 16 = 2^4
36 = 2^2 * 3^2
40 = 2^3 * 5
54 = 2 * 3^3
LCM = 2^4 * 3^3 * 5 = 2160
The smallest five-digit number that is a multiple of 2160 is 5*2160 = 10,800
The answer is C.
Answer: (C) 10800
Question: 15 lts are taken of from a container full of liquid A and replaced with Liquid B. Again 15 more lts of the mixture is taken and replaced with liquid B. After this process, if the container contains Liquid A and B in the ratio 9:16,What is the capacity of the container Q?
(A) A:45
(B) B:25
(C) C:37.5
(D) D:36
(E) E:42
Rationale: If you have a 37.5 liter capacity, you start with 37.5 L of A and 0 L of B.
1st Replacement
After the first replacement you have 37.5-15=22.5 L of A and 15 L of B. The key is figuring out how many liters of A and B, respectively, are contained in the next 15 liters of mixture to be removed.
The current ratio of A to total mixture is 22.5/37.5; expressed as a fraction this becomes (45/2) / (75/2), or 45/2 * 2/75. Canceling the 2s and factoring out a 5 leaves the ratio as 9/15. Note, no need to reduce further as we're trying to figure out the amount of A and B in 15 L of solution. 9/15 of A means there must be 6/15 of B.
Multiply each respective ratio by 15 to get 9 L of A and 6 L of B in the next 15L removal.
Final Replacement
The next 15L removal means 9 liters of A and 6 liters of B are removed and replaced with 15 liters of B. 22.5-9=13.5 liters of A. 15 liters of B - 6 liters + 15 more liters = 24 liters of B.
Test to the see if the final ratio = 9/16; 13.5/24 = (27/2) * (1/24) = 9/16. Choice C is correct.
Answer: (C) C:37.5
Question: How many positive integers less than 100 are multiples of a prime number?
.
(A) 91
(B) 92
(C) 94
(D) 96
(E) 98
Rationale: There are a total of 99 positive integers less than 100
and except the no. 1, every other no. is a multiple of some prime number so answer should be 98
ANswer: Option E
Answer: (E) 98
Question: An article is bought for Rs.675 and sold for Rs.945, find the gain percent?
(A) 40%
(B) 33 8/3%
(C) 33 1/3%
(D) 33 2/3%
(E) 33 1/2%
Rationale: 675 ---- 270
100 ---- ? => 40%
Answer: A
Answer: (A) 40%
Question: A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
(A) 288
(B) 240
(C) 277
(D) 127
(E) 922
Rationale: Speed = (54 * 5/18) m/sec = 15 m/sec. Length of the train = (15 x 20)m = 300 m. Let the length of the platform be x meters. Then, (x + 300)/36 = 15 ==> x + 300 = 540 ==> x = 240 m.Answer: B
Answer: (B) 240
Question: There are 10 women and 9 men in a certain club. If the club is to select a committee of 2 women and 2 men, how many different such committees are possible?
(A) 120
(B) 720
(C) 1,060
(D) 1,620
(E) 1,980
Rationale: Answer is E. Can somebody tell me what answer I may have found if I had added the 10C2 and 9C2 (45+36=81)?
I'm guessing that would've been the number of 2-member committees which had men and women separately. Is that right?
D
Answer: (D) 1,620
Question: The compound interest earned by Sunil on a certain amount at the end of two years at the rate of 4% p.a. was Rs.326.40. Find the total amount that Sunil got back at the end of two years in the form of principal plus interest earned.
(A) Rs.4326.40
(B) Rs.4236.40
(C) Rs.4136.40
(D) Rs.4316.40
(E) Rs.4136.40
Rationale: Let the sum be Rs.P
P{ [ 1 + 4/100]2 - 1 } = 326.40
P(4/100)(2 + 4/100) = 326.40 [a2 - b2 = (a - b) ( a + b)] P = 326.40 / (0.04)(2.04) = 4000 Amount =4000+326.40=4326.40 Answer : A
Answer: (A) Rs.4326.40
Question: A rabbit on a controlled diet is fed daily 300 grams of a mixture of two foods, food X and food Y. Food X contains 10% protein and food Y contains 15% protein. If the rabbit's diet provides exactly 38 grams of protein daily, how many grams of food X are in the mixture.
(A) 100
(B) 140
(C) 150
(D) 160
(E) 200
Rationale: 0.1x + 0.15y = 38
x+y = 300
x = 300-y
so 0.1(300-y) + 0.15y = 38
30-0.1y + 0.15y = 38
0.05y = 8
y = 160 grams
then x = 140 grams.
Answer: B
Answer: (B) 140
Question: A cistern which could be filled in 7 hours takes one hour more to be filled owing to a leak in its bottom. If the cistern is full in what time will the leak empty it?
(A) 76 hrs
(B) 70/3 hrs
(C) 55 hrs
(D) 90 hrs
(E) 11 hrs
Rationale: 1/7 - 1/x = 1/10
=> 70/3 hrs
Answer: B
Answer: (B) 70/3 hrs
Question: The speed of the man in still water is 40 kmph. If he can row upstream at 20 kmph, find the downstream.
(A) 40
(B) 50
(C) 55
(D) 60
(E) 65
Rationale: M = (DS + US)/2
DS=2M-US
= 2*40-20
= 60
Answer:D
Answer: (D) 60
Question: How many bricks, each measuring 25 cm x 11.25 cm x 6 cm, will be needed to build a wall of 8 m x 6 m x 22.5 cm?
(A) 6400
(B) 6410
(C) 6440
(D) 6500
(E) 6800
Rationale: Number of bricks = Volume of Wall/Volume of Bricks
=800x600x22.5/21x11.25x6= = 6400
answer :A
Answer: (A) 6400
Question: If x is equal to the sum of the even integers from 40 to 60 inclusive, and y is the number of even integers from 40 to 60 inclusive, what is the value of x+y?
(A) 550
(B) 551
(C) 560
(D) 561
(E) 572
Rationale: This is a perfect example of why you should not use formulas without understanding them properly. If you understand them, you will not make a mistake and will save time.
The formula quoted by the original poster: n(n+1) is absolutely fine. But one needs to understand that n is the number of even terms starting from the first even term. (I discuss why this is so here:
Sum of even numbers from 40 to 60 using this formula will be:
30*31 - 19*20 = 10(3*31 - 19*2) = 550
Since number of terms is 11, required sum is 561
But, I would not use this formula for this question and would do it the way many of you have done:
Average = 50 (it is the middle number), Number of terms = 11 (No formula again. Any 10 consecutive integers have 5 even and 5 odd numbers. 41 to 60 will have 10 even integers and 40 is the 11th one)
Sum = 50*11 + 11 = 561
answer is D
Answer: (D) 561
Question: What number should replace the question mark?
16, 23, 19, 19, 22, 15, 25, ?
(A) 11
(B) 12
(C) 13
(D) 14
(E) 15
Rationale: A
11
There are two alternate sequences + 3 and - 4
Answer: (A) 11
Question: A man walks at a speed of 8 km/hr and runs at a speed of 7 km/hr. How much time will the man require to cover a distance of 10 1/2 km, if he completes half of the distance, i.e., (5 1/4) km on foot and the other half by running?
(A) 1 4/2 hours
(B) 1 2/5 hours
(C) 2 1/6 hours
(D) 2 1/1 hours
(E) 2 1/2 hours
Rationale: Required time
= (5 1/4)/8 + (5 1/4)/7
= 1 2/5 hours.
Answer:B
Answer: (B) 1 2/5 hours
Question: Ravi and Ramu are partners in a business.Ravi contributes 1/6 of the capital for 16 months and Ramu received 2/3 of the profit. For how long Ramu's money was used ?
(A) 7 months
(B) 6 months
(C) 3 months
(D) 8 months
(E) 9 months
Rationale: Let the total Profit be Z.
Ramu's profit share is 2/3 of profit (i.e 2Z/3)
Ravi's profit is (Z-2Z/3) =Z/3
Hence the profit ratio is , Ravi : Ramu = Z/3 : 2Z/3 = 1:2
Let total Capital be Rs.X and Ramu has contributed for Y months.Since Ramu's profit share is 2/3, his invest share will be 2/3 in capital.
Ravi's invest for 16 months / Ramu's invest for Y months = Ravi's profit share / Ramu's profit share
i.e. (X/6 x 16) / (2X/3 x Y) = 1/2
Solving the above equation, we get Y = 8.
So Ramu's money has been used for 8 months.
Answer: D
Answer: (D) 8 months
Question: A letter lock consists of 4 rings, each ring contains 9 non-zero digits. This lock can be opened by setting four digit code with the proper combination of each of the 4 rings. Maximum how many codes can be formed to open the lock ?
(A) 4(9)
(B) 9(4)
(C) 9P4
(D) None of these
(E) Cannot be determined
Rationale: Solution: There are 9 non-zero digits to arrange themselves at 4 different position. Each letter can be arrange at different position in 9 different ways.
So, required number of ways,
= 9 *9 *9 *9
= 94.
Answer: Option B
Answer: (B) 9(4)
Question: Consider a sequence of numbers given by the expression 7 + (h - 1) * 5, where n runs from 1 to 80.What is the sum of this series ?
(A) 409
(B) 1636
(C) 16360
(D) 16000
(E) 15360
Rationale: terms in this sequence are 7,12,17----402
now since this is an a.p. with a common difference of 5. therefore its sum can be given as
h(a+l)/2----------------1)
h= total no. of terms =80
a= first term=7
l= last term=402
subsituting values in the expression 1 we have
80(7+402)/2
= 40(409)
=16360=C
Answer: (C) 16360
Question: A sum of Rs. 2704 is lent into two parts so that the interest on the first part for 8 years at 3% per annum may be equal to the interest on the second part for 3 years at 5% per annum. Find the second sum?
(A) 1672
(B) 1664
(C) 1677
(D) 1698
(E) 1679
Rationale: (x*8*3)/100 = ((2704 - x)*3*5)/100
24x/100 = 40560/100 - 15x/100
39x = 40560 => x = 1040
Second sum = 2704 â€“ 1040 = 1664
Answer:B
Answer: (B) 1664
Question: A sum of money is distributed among A,B,C,D in the proportion of 1:3:4:2. If C gets $500 more than D, what is the B's share?
(A) $450
(B) $500
(C) $750
(D) $800
(E) $840
Rationale: Let the shares of A,B,C,D are x,3x,4x,2x
4x-2x = 500
x = 250
B's share = 3x = $750
Answer is C
Answer: (C) $750
Question: A number consists of two digits. If 3/5 of 1/5 of the number is 9. Find the sum of its two digits?
(A) 33
(B) 28
(C) 13
(D) 12
(E) 11
Rationale: Explanation:
x * 3/5 * 1/5 = 9
x = 75 => 7 + 5 = 12
Answer: D
Answer: (D) 12
Question: At what rate percent per annum will sum of money double in 20 years?
(A) 1.2 %
(B) 2 %
(C) 4 %
(D) 5 %
(E) None of these
Rationale: Explanation:
Hint: If sum of money becomes (z times) in (T) years at simple interest, then rate of interest (R) can be calculated using the formula:
Rate of Interest (R) % =	100 (z – 1)/T
Here, principal amount is not given.
Hence, we can directly use the trick to calculate the rate of interest.
Rate of Interest (R) % =	100 (2 – 1)/20
Rate of Interest (R) %=5 % p.a.
ANSWER IS D
Answer: (D) 5 %
Question: If a = -0.4, which of the following is true?
(A) a < a^2 < a^3
(B) a^2 < a^3 < a
(C) a^2 < a < a^3
(D) a < a^3 < a^2
(E) a^3 < a < a^2
Rationale: a=-0.4;
a^2=0.16;
a^3=-0.064;
Answer : D
Answer: (D) a < a^3 < a^2
Question: If dy + z = d(y + z), which of the following must be true?
(A)  d = 0 and z = 0
(B)  d= 1 and y = 1
(C)  y = 1 and z = 0
(D)  d = 1 or y = 0
(E)  d = 1 or z = 0
Rationale: dy + z = dy + dz
z = dz
case 1: z not= 0, d = z/z = 1
case 2: z = 0, 0 = d0 = 0
Combining 2 cases: d = 1 or z =0
E. is the answer.
Answer: (E)  d = 1 or z = 0
Question: A certain stock exchange designates each stock with a 1, 2 or 3 letter code, where each letter is selected from the 14 letters of the alphabet. If the letters may be repeated and if the same letters used in a different order, constitute a different code, how many diff stocks is it possible to designate with these codes?
(A) 2600
(B) 2800
(C) 2500
(D) 3000
(E) 2954
Rationale: Pretty simple actually
Number of 1 letter symbols = 14
Number of 2 letter symbols = 14*14
Number of 3 letter symbols = 14*14*14
The answer is sum of the 3. = 14+14*14+14*14*14 =14(1+14+14*14)= 14*211= 2954
So the answer is E.
Answer: (E) 2954
Question: In the xy plane, the point (-2,-3) is the center of a circle. The point (-2,1) lies inside the circle and the point (4,-3) lies outside the circle. If the radius r of the circle is an integer, then r=
(A) 6
(B) 5
(C) 4
(D) 3
(E) 2
Rationale: This question might look intimidating because of its language, but once you start solving it, you will realise that the options are given to you in such a way that you reach the correct answer easily.
The radius will lie somewhere between the distance of centre from the inner point and the distance from the outer point.
Distance between centre and inner point = Distance between (-2,-3) and (-2, 1)
We can solve for the distance by using the formula for distance between two points. But that is not required here.
If one of the co-ordinates is same, then the distance between two points is simply the difference between the other coordinate.
In this case, Distance = 1 - (-3) = 4
Distance between centre and utter point = Distance between (-2, -3) and (4, -3) = 4 - (-2) = 6
The radius has to be between 4 and 6
On looking at the options, only 5 satisfies
Correct Option: B
Answer: (B) 5
Question: One copy machine can make 15 copies a minute, and a second copy machine makes 10 copies a minute. If the two copiers work together, how long would it take them to make 1,000 copies?
(A) 20 minutes
(B) 30 minutes
(C) 40 minutes
(D) 50 minutes
(E) 60 minutes
Rationale: Total work done by both machines in a minute = 15 + 10 = 25 copies
Total number of copies required = 1000
Time = 1000/25 = 40 mins
Answer C
Answer: (C) 40 minutes
Question: If 5 people contributed a total of $20.00 toward a gift and each of them contributed at least $3.00, then the maximum possible amount any one person could have contributed is
(A)  $1.00
(B)  $1.25
(C)  $5.00
(D)  $8.00
(E)  $20.00
Rationale: D for me
4 people with 3$ each -> maximum = 8
Answer: (D)  $8.00
Question: A retailer bought a shirt at wholesale and marked it up 80% to its initial price of $27. By how many more dollars does he need to increase the price to achieve a 100% markup?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: Let x be the wholesale price.
Then 1.8x= 27 and x = 27/1.8 = 15.
To achieve a 100% markup, the price needs to be $30.
The retailer needs to increase the price by $3 more.
The answer is C.
Answer: (C) 3
Question: A number is said to be prime saturated if the product of all the different positive prime factors of n is less than the square root of n. What is the greatest two digit prime saturated integer ?
(A) 99
(B) 98
(C) 97
(D) 96
(E) 95
Rationale: A prime factors are 3 and 11. 33<sqrt(99)? no
B prime factors are 2 and 7. 14<sqrt(98)? no
C prime number. its sqrt is never greater than itself
D A prime factors are 2 and 6. 6<sqrt(96)? yes
E prime factors are 5 and 19. 45<sqrt(95)? no
ANSWER:D
Answer: (D) 96
Question: A man can row his boat with the stream at 26 km/h and against the stream in 4 km/h. The man's rate is?
(A) 1 kmph
(B) 7 kmph
(C) 98 kmph
(D) 11 kmph
(E) 4 kmph
Rationale: DS = 26
US = 4
S = ?
S = (26 - 4)/2 = 11 kmph
Answer: D
Answer: (D) 11 kmph