mathewhe/aqua_rat huggingface dataset:
Question: If 3 persons can do 3 times of a particular work in 3 days, then, 7 persons can do 7 times of that work in
(A) 2 days
(B) 3 days
(C) 5 days
(D) 7 days
(E) 9 days
Rationale: That is, 1 person can do one time of the work in 3 days.
Therefore, 7 persons can do 7 times work in the same 3 days itself.
B)
Answer: (B) 3 days
Question: A committee is to be formed by randomly choosing 4 people from 8 candidates. If Alice and Bob are candidates, what is the probability that Alice will be selected but Bob will not?
(A) 1/3
(B) 2/5
(C) 3/5
(D) 1/7
(E) 2/7
Rationale: The total number of ways to form a committee is 8C4=70.
The number of committees which include Alice but not Bob is 6C3=20.
The probability that Alice is selected but Bob is not selected is 20/70=2/7.
The answer is E.
Answer: (E) 2/7
Question: Liam is pulled over for speeding just as he is arriving at work.He explains to the police officer that he could not afford to be late today, and has arrived at work only four minutes before he is to start. The officer explains that if Liam had driven 5mph slower for his whole commute, he would have arrived at work exactly on time. If Liam's commute is 10 miles long,how fast was he actually driving?(Assume that Liam drove at a constant speed for the duration of his commute.)
(A) 50 mph
(B) 45 mph
(C) 48 mph
(D) 30 mph
(E) 60 mph
Rationale: Let t be the number of hours he would need to reach office on time.
when he is driving with over speed, he reached office 4 min earlier! so the equation for this is s(t - 4/60) = 30
where s is the speed and 30 is the distance.
if he decreases his speed by 5mph then he would have reached his office on time: (s-5)t = 30
if you solve above equations, you will arrive at t = 2/3 hr and s = 30mph
therefore answer is D
Answer: (D) 30 mph
Question: If m = 3^n, what is the greatest value of n for which m is a factor of 25!
(A) 8
(B) 10
(C) 12
(D) 14
(E) 16
Rationale: We should find the highest power of 3 in 25!: 25/3+25/3^2=8+2=10 (take only the quotient into account).. So the highest power of 3 in 25! is 10.
Answer: B.
Answer: (B) 10
Question: A bookshop had science and art books in the ratio of 2:5. By the end of the week, 20% of both type of books were sold and 2240 books were unsold. How many art books were there at the starting?
(A) 800
(B) 1200
(C) 1405
(D) 1540
(E) 2000
Rationale: science books sold = 2x × 0.2 = 0.4x
science books unsold = 2x – 0.4x = 1.6x
art books sold = 5x × 0.2 = x
art books unsold = 5x – x = 4x
total books unsold = 1.6x + 4x = 5.6x
5.6x = 2240
x = 400
2x science = 800
and 5x art books = 2000
E
Answer: (E) 2000
Question: Find the average of first 10 multiples of 7
(A) 35.5
(B) 37.5
(C) 38.5
(D) 40.5
(E) None of these
Rationale: Explanation:
=7(1+2+3+...+10)10
=7(10(10+1))10×2
=7(110)10×2=38.5
Answer: Option C
Answer: (C) 38.5
Question: Calculate the L.C.M of 5/6, 4/ 7, 9/10, 8/9 is :
(A) 560
(B) 364
(C) 320
(D) 330
(E) 360
Rationale: Required L.C.M =L.C.M. of 5, 4, 9, 8/H.C.F. of 6, 7, 10, 9 =360/1=360
Answer is E
Answer: (E) 360
Question: The average age of a husband, wife and their child 3 years ago was 27 years and that of wife and the child 5 years ago was 20 years. The present age of the husband is:
(A) 19 years
(B) 17 years
(C) 25 years
(D) 15 years
(E) 12 years
Rationale: Sum of the present ages of husband, wife and child
= (23 * 2 + 5 * 2) = 57 years.
Required average
= 57/3 = 19 years.
Answer: A
Answer: (A) 19 years
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) 277
(B) 240
(C) 278
(D) 2667
(E) 122
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: Three pipes of same capacity A,B,C can fill a tank in 18 hours. If there are only two pipes B and A of same capacity, the tank can be filled in?
(A) 16
(B) 19
(C) 27
(D) 24
(E) 29
Rationale: The part of the tank filled by three pipes in one hour
= 1/6
=> The part of the tank filled by two pipes in 1 hour
= 2/3 * 1/18= 1/27.
The tank can be filled in 27 hours.
Answer:C
Answer: (C) 27
Question: A, B and C start swimming in a pool simultaneously from the same end. To complete 10 laps, A takes 10 minutes, B takes 8 minutes and C takes 2 minutes. What is the ratio of speeds A:B:C?
(A) 3:4:5
(B) 4: 5:20
(C) 5:4:3
(D) 4:6:5
(E) 12:15:25
Rationale: The slowest one is A, then comes B and the fastest one is C. So, the the ratio of speeds A:B:C must be in ascending order. Eliminate options C, D, and E.
A's speed (distance)/(time) = 10/10 = 1 lap per minute = 4 laps in 4 minute;
B's speed (distance)/(time) = 10/8 = 5/4 lap per minute = 5 laps in 4 minutes;
C's speed (distance)/(time) = 10/2 = 5 lap per minute = 20 laps in 4 minutes/
Therefore, the the ratio of speeds A:B:C is 4: 5:20.
Answer: B.
Answer: (B) 4: 5:20
Question: Solve(0.76 × 0.76 × 0.76 − 0.008)/(0.76 × 0.76 + 0.76 × 0.2 + 0.04)
(A) 0.56
(B) 0.57
(C) 0.6
(D) 0.76
(E) 0.87
Rationale: Option 'A'
Answer: (A) 0.56
Question: If x < y < z and y-x > 7, where x is an even integer and y and z are odd integers, what is the least possible value of z - x?
(A) 6
(B) 7
(C) 11
(D) 8
(E) 10
Rationale: We have:
1) x<y<z
2) y-x>5
3) x=2k (x is an even number)
4) y=2n+1 (y is an odd number)
5) z=2p+1 (z is an odd number)
6) z-x=? least value
z-x=2p+1-2k=2p-2k+1=2(p-k)+1 - that means that z-x must be an ODD number. We can eliminate answer choices A, C and E
we are asked to find the least value, so we have to pick the least numbers
since y is odd and x is even, y-x must be odd. since y-x>7 the least value for y-x must be 11, the least value for x must be 2, and, thus, the least possible value for y must be 11 (y-2=9, y=11)
2<11<z, since z is odd, the least possible value for z is 13
z-x=13-2=11
Answer C
Answer: (C) 11
Question: Find the rate % of C.I and S.I on Rs. 1000 for 2 years if the difference between C.I and S.I is given to be 22.50.
(A) 15%.
(B) 20%
(C) 25%
(D) 30%
(E) 35%
Rationale: Difference between C.I and S.I =P(R/100)^2 1000(R/100)^2=22.50. ie)( R/100)^2=22.50/1000. R^2 =225 R =15%. Answer : A
Answer: (A) 15%.
Question: If in a certain code "RANGE" is coded as 12345 and "RANDOM" is coded as 123678. Then the code for the word
"GONE" would be
(A) 1234
(B) 2367
(C) 3547
(D) 5382
(E) 4735
Rationale: G-4
O-7
N-3
E-5
so for mango the code is 4735
ANSWER:E
Answer: (E) 4735
Question: A farmer spent $36 on feed for chickens and goats. He spent 40% money on chicken feed, which he bought at a 20% discount off the full price, and spent the rest on goat feed, which he bought at full price. If the farmer had paid full price for both the chicken feed and the goat feed, what amount would he have spent on the chicken feed and goat feed combined?
(A) $37.80
(B) $38.50
(C) $39.20
(D) $39.60
(E) $40.60
Rationale: A farmer spent 40% money on chicken feed, so he spent 0.4*$36=$14.4 on chicken feed, thus he spent the remaining 36-14.4=$21.6 on goat feed.
Now, since he bought chicken feed at a 20% discount then the original price of it was x*0.8=$14.4 --> x=$18
Therefore if the farmer had paid full price for both the chicken feed and the goat feed, then he would he have spent 18+21.6=$39.6.
Answer: D.
Answer: (D) $39.60
Question: When R is divided by W, the quotient is Q and the remainder is E. Which of the following expressions is equal to E?
(A) QW + R
(B) RW - Q
(C) Q - RW
(D) -QW + R
(E) Q/R
Rationale: R/W = Q + E/W
R -QW = E
Amswer: D
Answer: (D) -QW + R
Question: A train running at the speed of 60 km/hr crosses a pole in 9 seconds. Find the length of the train?
(A) 150
(B) 8827
(C) 166
(D) 199
(E) 121
Rationale: Speed = 60*(5/18) m/sec = 50/3 m/sec
Length of Train (Distance) = Speed * Time
(50/3) * 9 = 150 meter
Answer: A
Answer: (A) 150
Question: For positive integers k and n, the k-power remainder of n is defined as r in the following equation:
n = k^w + r, where w is the largest integer such that r is not negative. For instance, the 3-power remainder of 13 is 4, since 13 = 3^2 + 4. In terms of k and w, what is the largest possible value of r that satisfies the given conditions?
(A) (k – 1)k^w – 1
(B) k^w – 1
(C) (k + 1)k^w – 1
(D) k^(w+1) – 1
(E) (k + 1)k^(w+1) – 1
Rationale: n = k^w + r, where w is the largest integer such that r is not negative
This means k^w <= n, and k^(w+1) > n
So n lies between k^w and k^(w+1)
Now, r = n - k^w, which means r is the distance between n and k^w
This distance is maximised at the highest possible value of n, which can be just below k^(w+1)
So n = k^(w+1) - 1, as n is an integer
Therefore, highest value of r = n - k^w = k^(w+1) - 1 - k^w = (k - 1)k^w - 1
A is the correct
Answer: (A) (k – 1)k^w – 1
Question: If n = 2×3×5×7, then which of the following statements must be true?
I. n2 is divisible by 60
II. n + 19 is divisible by 19
III. is even n+4 / 2 = even
IV n is divisible by 35
(A) I only
(B) b- II only
(C) III only
(D) none and IV only
(E) e None
Rationale: n = 2×3×5×7= 210
I. n is not divisible by 60
II. n + 19 is not divisible by 19
III. is even n+4 / 2 = odd 107
IV n is divisible by 35
D
Answer: (D) none and IV only
Question: A bat is bought for Rs.400 and sold at a gain of 20% find its selling price
(A) Rs.500/-
(B) Rs.480/-
(C) Rs.430/-
(D) Rs.490/-
(E) Rs.500/-
Rationale: 100 % ------> 400 (100 * 4 = 400)
120 % ------> 480 (120 * 4 = 480)
Selling price = Rs.480/-
B
Answer: (B) Rs.480/-
Question: A candy company sells premium chocolate at $5 per pound and regular chocolate at $4 per pound in increment of whole pound only.If Barrett buys a pack of candies which costs him $40, how many pounds of premium chocolates are in the box?
(A) [A] 1
(B) [B] 2
(C) [C] 3
(D) [D] 4
(E) [E] 5
Rationale: This question is a bit of Special equations with a single set of unique values.
the Equation stands : 5X + 4Y = 31
Subtract multiple of 5 from 31 and check whether the remaining total is divisible by 4
31 - 5 = 26 -> Not divisible by 4
31 - 10 = 21 -> Not divisible by 4
31 - 15 =16 -> Divisible by 4
31 - 20 =11 -> Not divisible by 4
31 - 25 =6 -> Not divisible by 4
31 - 30 =1 -> Not divisible by 4
Any multiple of 5 hereon will give a negative value for regular chocolates bought and hence, inadmissible
Thus Amount spent on regular chocolate= $16
Amount spent on Premium chocolate= $15
Price per premium chocolate = $5
No. Of boxes of premium chocolate bought = 20 / 5 = 4
Correct Option : D
Answer: (D) [D] 4
Question: A juice manufacturer organized taste-testing sessions featuring four brands of orange juice, A, B, C and D. All customers who participated told the organizer which variety they thought was the most similar to freshly-squeezed orange juice. 61% preferred brand A and exactly half as many preferred brand B. Only 60 chose brand C. Which of the following could be the number of customers who preferred brand D?
(A)  1
(B)  8
(C)  14
(D)  20
(E)  27
Rationale: I get D, but I'm not sure that my method is sound.
You have A + B + C + D = total testers. Stating the variety they think is most similar to freshly squeezed orange juice means each person should get 1 vote.
x = total number of testers
A + B + C + D
.61x + (.5)(.61x) + 65 + D = x
.61x + .305x + 65 + D = x
I took total testers = 1000 because that gives me nice numbers to deal with. Also, if I use 200 total testers, that gives me A = 122, B = 61, C = 65...that's over 200 without considering D.
x = 400
A = 244, B = 122, C = 65..also over 400
x = 600
A = 366, B = 183 C = 65....also over 600
x = 800
A = 488, B = 244, C = 65...D = 3...not an option on the list.
x = 1000
A = 610 B = 305 C = 65 D = 27....the first time I get an answer that is an option in the question.
E
Answer: (E)  27
Question: A palindrome is a number that reads the same front-to-back as it does back-to-front (e.g. 202, 575, 1991, etc.) p is the smallest integer greater than 500 that is both a prime and a palindrome. What is the sum of the digits of p?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: Given that p is smallest integer greater than 200 - assume there is a 3-digit that satisfies the above conditions. Let the number be xyx ; question asks us the values of 2x+y
We can straight away cross out options A) and D) - sum of digits 3 or 6 implies it is divisible by 3 ---> we know that p is a prime number
Coming to option B) 2x + y = 4 --> only x = 2 and y = 0 satisfy this equation ( x> 2 will never give sum of digits = 4) ; but 202 is divisible by 2 ; we know that p is a prime number
Similarly option C) 2x+y = 5 --> only x = 2 and y = 1 satisfy this equation ( x> 2 will never give sum of digits = 5) ; but 212 is divisible by 2 ; we know that p is a prime number
Therefore answer option should be E ---> can be verified by taking 2x+y = 7 ---> x = 3 and y = 1 ; gives 313
B
Answer: (B) 4
Question: Baseball's World Series matches 2 teams against each other in a best-of-seven series. The first team to win four games wins the series and no subsequent games are played. If you have no special information about either of the teams, what is the probability L that the World Series will consist of fewer than 7 games?
(A)  12.5%
(B)  25%
(C)  31.25%
(D)  68.75%
(E)  75%
Rationale: Your explanation is very close toManhattan GMAT's official answer - it's quite uncanny:
"There are many other ways this could happen. Using the permutation formula, there are 6!/(3!)(3!) = 20 ways for the two teams to split the first 6 games (3 wins for each).
There are then 2 possible outcomes to break the tie in Game 7. Thus, there are a total of 202 = 40 ways for the World Series to last the full 7 games.
The probability that any one of these 40 ways occurs can be calculated from the fact that the probability of a team winning a game equals the probability of a team losing a game = 1/2.
Given that 7 distinct events must happen in any 7 game series, and that each of these events has a probability of 1/2, the probability that any one particular 7 game series occurs is.
Since there are 40 possible different 7 game series, the probability that the World Series will last exactly 7 games is: (1/2)^7 = 1/128
40*1/128 = 40/128 = 31.25%
Thus the probability L=that the World Series will last less than 7 games is 100% - 31.25% = 68.75%.
The correct answer is D."
Answer: (D)  68.75%
Question: A group of medical interns at Bohemus Medical School want to go on dates. There are 3 girls and 3 guys. Assuming girls go on dates with guys, how many possible ways can these 6 medical interns date each other?
(A) A)2
(B) B)3
(C) C)4
(D) D)5
(E) E)6
Rationale: 1st girl can go with 3 guys
2nd girl can go with remaining 2
3rd girl can go with remaining 1
so the total ways are 3!= 6
E should be the answer
Answer: (E) E)6
Question: A certain bakery baked a batch of 550 cookies one day. Of those, 320 contained nuts, 230 contained chocolate chips, and 85 contained neither nuts nor chocolate chips. What is the fewest possible number of cookies with both chocolate chips and nuts that would need to be added to that batch so that cookies with both nuts and chocolate chips represented more than 3/5 of all the cookies in the batch?
(A) 166
(B) 275
(C) 413
(D) 438
(E) 613
Rationale: Cookies which have both nuts and chocolate chips = 85
Let fewest possible number of cookies with both chocolate chips and nuts that would need to be added to that
batch so that cookies with both nuts and chocolate chips represented more than 3/5 of all the cookies in the batch = x
(85+x)/(550+x) = 6/10
=>850 + 10x = 3300 + 6x
=> 4x = 2450
=> x = 612.5
Therefore x = 613
Answer E
Answer: (E) 613
Question: Difference between two numbers is 5, six times of the smaller lacks by 6 from the four times of the greater. Find the numbers?
(A) 12, 9
(B) 10, 5
(C) 12, 7
(D) 11, 6
(E) 12, 6
Rationale: x – y = 5
4x – 6y = 6
x = 12 y = 7
ANSWER:C
Answer: (C) 12, 7
Question: After a business trip to London, Michele has enough time to visit three European cities before returning home. If she has narrowed her list to six cities that she'd like to visit - Paris, Barcelona, Rome, Munich, Oslo, and Stockholm - but does not want to visit both Oslo and Stockholm on the same trip, how many different sequences of three cities does she have to choose from?
(A) 36
(B) 48
(C) 72
(D) 96
(E) 120
Rationale: Sequence of cities she can visit without any restrictions= 6*5*4= 120
Sequence of cities she can visit if she visits both Oslo and Stockholm on the same trip= 3*2 *1 *4 (after choosing Oslo and Stockholm, she is left with 4 cities to choose from)= 24
Sequence of cities to choose with restrictions= 120-24= 96
D is the answer
Answer: (D) 96
Question: A man in a train notices that he can count 21 telephone posts in one minute. If they are known to be 50 metres apart, at what speed is the train travelling?
(A) 61 km/hr
(B) 56 km/hr
(C) 63 km/hr
(D) 60 km/hr
(E) 70 km/hr
Rationale: 21 telephone posts in 1 min
No of gaps b/w 21 posts = 20
adjacent post = 50 m
20*50 = 1000 m in 1 min
dist = 1000 m = 1 km
time = 1 min = 1/60 hr
speed = 1/(1/60) = 60 km/hr
ANSWER D
Answer: (D) 60 km/hr
Question: The price of 10 chairs is equal to that of 4 tables. The price of 15 chairs and 2 tables together is Rs. 4000. The total price of 12 chairs and 3 tables is:
(A) Rs. 3700
(B) Rs. 3800
(C) Rs. 3900
(D) Rs. 4000
(E) Rs. 4200
Rationale: Let the cost of a chair and that of a table be Rs. x and Rs. y respectively.
Then, 10x = 4y or y = 5 x.
2
15x + 2y = 4000
15x + 2 x 5 x = 4000
2
20x = 4000
x = 200.
So, y = 5 x 200 = 500.
2
Hence, the cost of 12 chairs and 3 tables = 12x + 3y
= Rs. (2400 + 1500)
= Rs. 3900.
C)
Answer: (C) Rs. 3900
Question: At a constant Rate of flow, it takes 60 minutes to fill a swimming pool if a large hose is used and 90 minutes if a small hose is Used. At these constant rates, how many minutes will it take to fill the pool when both hoses are used simultaneously?
(A) 20
(B) 25
(C) 28
(D) 36
(E) 33
Rationale: time taken to fill the pool by Large Hose =30 minutes =L or 1/L=1/60 similarly 1/S=1/90
simultaneously it will take 1/L+1/S=1/60+1/90=5/180=36 minutes
Answer : D
Answer: (D) 36
Question: The sale price sarees listed for Rs.298 after successive discount is 12% and 15% is?
(A) 321
(B) 223
(C) 245
(D) 265
(E) 162
Rationale: Explanation:
298*(88/100)*(85/100) = 223
Answer: B
Answer: (B) 223
Question: A milk man has 15 liters of milk. If he mixes 5 liters of water, which is freely available, in 20 liters of pure milk.If the cost of pure milk is Rs.18 per liter,then the profit of the milkman, when he sells all the mixture at cost price is:
(A) 20%
(B) 25%
(C) 33.33%
(D) 18%
(E) None of these
Rationale: Explanation:
when the water is freely available and all the water is sold at the price of the milk, then the water gives the profit on the cost of 20 liters of milk.
Therefore, profit percentage = 20 %. Answer: A
Answer: (A) 20%
Question: 45% of major airline companies equip their planes with wireless internet access. 70% of major airlines offer passengers free on-board snacks. What is the greatest possible percentage of major airline companies that offer both wireless internet and free on-board snacks?
(A) 25%
(B) 35%
(C) 45%
(D) 55%
(E) 65%
Rationale: To maximize the percentage of companies offering both, let's assume that all 45% of companies which offer wireless internet also offer snacks.
The answer is C.
Answer: (C) 45%
Question: How much interest will $10,000 earn in 9 months at an annual rate of 6%?
(A) $250
(B) $350
(C) $450
(D) $550
(E) $650
Rationale: Soln:-
9 months = 3/4 of year;
6% = 6/100=3/50;
$10,000(principal)*3/50(interest rate)*3/4(time)=$450.
ANSWER:C
Answer: (C) $450
Question: A salad bowl of 4 ingredients is chosen from 3 types of lettuce and 4 types of tomatos. The salad must have at least 1 type of lettuce and at least 2 types of tomatos. How many ways can this salad be made?
(A) 106
(B) 30
(C) 16
(D) 18
(E) 12
Rationale: Solution: We have two possibilities 1L 3T or 2L 2T
(3C1)(4C3)+(3C2)(4C2)=30
B) 30
Answer: (B) 30
Question: Difference of two numbers is 1620. If 7.5% of the number is 12.5% of the other number , find the number ?
(A) 2660, 1000
(B) 3660, 2000
(C) 3000, 4160
(D) 2430, 4050
(E) 4660, 3000
Rationale: Let the numbers be x and y. Then, 7.5 % of x =12.5% of y
X = 125*y/75 = 5*y/3.
Now, x-y =1620
5*y/3 –y =1620
2*y/3= 1620
y =[ (1620*3)/2] =2430.
One number = 2430, Second number =5*y/3 =4050.
Answer D.
Answer: (D) 2430, 4050
Question: A group of men decided to do a work in 6 days, but 4 of them became absent. If the rest of the group did the work in 12 days, Find the original number of men?
(A) 15
(B) 6
(C) 40
(D) 10
(E) 8
Rationale: Original number of men = 4*12 / (12-6) = 8
Answer is E
Answer: (E) 8
Question: Eesha bought 18 sharpeners for Rs.100. She paid 1 rupee more for each white sharpener than for each brown sharpener. What is the price of a white sharpener and how many white sharpener did she buy ?
(A) s.6, 19
(B) s.6, 10 white sharpener
(C) s.6, 16
(D) s.6, 11
(E) s.6, 12
Rationale: Explanation: Just check the options. If she bought 10 white sharpeners at Rs.6 per piece, She has spent Rs.60 already. And with the remaining Rs.40, she bought 8 brown sharpeners at 40/8 = Rs.5 which is Rs.1 less than White sharpener.
Sol: B
Answer: (B) s.6, 10 white sharpener
Question: A cow and horse are bought for Rs.2,00,000. The cow is sold at a profit of 20% and the horse is sold a t a loss of 10%. The overall gain is Rs.4000, the Cost price of cow?
(A) 2 percent
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: Ans: Overall profit = 4000200000×100=2%4000200000×100 =2%
By applying alligation rule, we get
Answer:A
Answer: (A) 2 percent
Question: Two stations A and B are 245 km apart on a straight line. One train starts from A at 7 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet?
(A) 9
(B) 10
(C) 11
(D) 12
(E) 1
Rationale: Suppose they meet x hours after 7 a.m.
Distance covered by A in x hours = 20x km.
Distance covered by B in (x - 1) hours = 25(x - 1) km.
Therefore 20x + 25(x - 1) = 245
45x = 270
x = 6.
So, they meet at 1 p.m.
Answer: Option E
Answer: (E) 1
Question: How many 4 digit numbers are there, if it is known that the first digit is even, the second is odd, the third is prime, the fourth (units digit) is divisible by 3?
(A) 20
(B) 150
(C) 225
(D) 300
(E) 320
Rationale: 4 options for the first digit: 2, 4, 6, 8;
5 options for the second digit: 1, 3, 5, 7, 9;
4 options for the third digit: 2, 3, 5, 7;
4 options for the fourth digit: 0, 3, 6, 9.
Four digit # possible without the restriction (about the digit 2): 4*5*4*4=320
Answer: E.
Answer: (E) 320
Question: A batch of cookies was divided amomg 4 tins: 2/3 of all the cookies were placed in either the blue or the green tin, and the rest were placed in the red tin. If 1/4 of all the cookies were placed in the blue tin, what fraction of the cookies that were placed in the other tins were placed in the green tin
(A) 15/2
(B) 9/4
(C) 5/9
(D) 7/5
(E) 5/8
Rationale: This will help reduce the number of variables you have to deal with:
G + B = 2/3
R = 1/4
B = 1/4
We can solve for G which is 5/12
What fraction (let it equal X) of the cookies that were placed in the other tins were placed in the green tin?
So..
X*(G+R)=G
X*(5/12 + 1/4) = 5/12
X = 5/8
ANSWER: E
Answer: (E) 5/8
Question: A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. What is the total distance traveled by the man?
(A) 5.72
(B) 5.29
(C) 5.76
(D) 5.39
(E) 5.29
Rationale: M = 6
S = 1.2
DS = 7.2
US = 4.8
x/7.2 + x/4.8 = 1
x = 2.88
D = 2.88 * 2
=5.76
Answer:C
Answer: (C) 5.76
Question: For every integer n ≥ 3, the function g(n) is defined as the product of all the odd integers from 1 to n, inclusive. What is the value of g(101) – g(99)?
(A) 0
(B) 98
(C) 99
(D) 100
(E) 90
Rationale: g(101) = 1*3*5*7*9*...*99*101
g(99) = 1*3*5*7*9*...*99
g(101) - g(99) = 1*3*5*7*9*...*99*101 - 1*3*5*7*9*...*99 = 1*3*5*7*9*...*99*(101 - 1) = 1*3*5*7*9*...*99*100
hence:D
Answer: (D) 100