mathewhe/aqua_rat huggingface dataset:
Question: Suppose you flip a fair coin three times. What is the probability that, in three flips, you get at least one head?
(A) 15/8
(B) 7/8
(C) 13/8
(D) 3/8
(E) 1/8
Rationale: Best way of solving an at least 1 type of question is to compute 1 - probability of flipping 0 heads
probability of flipping either a head or a tail = 1/2
probability of flipping 3 tails in a row (1/2)^3
probability of flipping at least 1 head = 1 - (1/2)^3 = 7/8
Answer : B
Answer: (B) 7/8
Question: At what time between 4 and 5 o'clock will the hands of a watch point in opposite directions?
(A) (54 + 6/11) past 9
(B) (54 + 6/11) past 1
(C) (54 + 6/11) past 2
(D) (54 + 6/11) past 4
(E) (54 + 6/11) past 7
Rationale: 4 o'clock, the hands of the watch are 20 min. spaces apart.
To be in opposite directions, they must be 30 min. spaces apart.
Minute hand will have to gain 50 min. spaces.
55 min. spaces are gained in 60 min
50 min. spaces are gained in min. or
Required time = min. past 4.
Answer: D
Answer: (D) (54 + 6/11) past 4
Question: In a certain random experiment, exactly one of the outcomes A, B, and C will occur. In each random experiment, the probability that outcome A will occur is 1/3 , and the probability that outcome B will occur is 1/3. What is the probability that when the random experiment is conducted 6 independent times, each of outcomes A, B, and C will occur twice?
(A) 5/243
(B) 1/12
(C) 10/81
(D) 1/6
(E) 16/81
Rationale: Given that P(A) = P(B) = P(C) = 1/3.
P(AABBCC) = (13)^6∗6!2!2!2!=1081 we multiply by 6!/(2!2!2!) because AABBCC scenario can occur in several ways: AABBCC, AABCBC, AACBBC, ... (the number of permutations of 6 letters AABBCC is 6!(2!2!2!)).
Answer: C.
Answer: (C) 10/81
Question: Lisa and Robert have taken the same number of photos on their school trip. Lisa has taken 3 times as many photos as Claire and Robert has taken 20 more photos than Claire. How many photos has Claire taken?
(A) 6
(B) 8
(C) 10
(D) 12
(E) 14
Rationale: L = R
L = 3C
R = C + 20
3C = C + 20
C = 10
The answer is C.
Answer: (C) 10
Question: A 290 meter long train running at the speed of 120 kmph crosses another train running in the opposite direction at the speed of 80 kmph in 9 seconds.What is the lenght of other train.
(A) 210m
(B) 220m
(C) 230m
(D) 240m
(E) 250m
Rationale: Relative speeds=(120+80)km/hr
=200km/hr=(200*5/18)m/s=(500/9)m/s
let length of train be xm
x+290/9=500/9
x=210
Ans is 210m
ANSWER:A
Answer: (A) 210m
Question: A person sells a book for Rs. 11. He gains as many percent as its cost price in rupees. What is the cost price?
(A) Rs. 19
(B) Rs. 12
(C) Rs. 10
(D) Rs. 11
(E) Rs. 14
Rationale: ANSWER: C
Answer: (C) Rs. 10
Question: How many multiples of 2 are there between 101 and 999 ?
(A) 250
(B) 440
(C) 510
(D) 575
(E) 449
Rationale: 2 multiples are 102,104,106,---------,994,996,998
It should be mentioned whether 1 and 89 are inclusive.
the answer is (998-102)/2+1=449
Answer is E
Answer: (E) 449
Question: The ratio between c and y is 7/9; c and y are increased by 4, what is the ratio between the new values of c and y?
(A) 7/9
(B) 14/9
(C) 7/18
(D) 11/13
(E) It Cannot Be Determined
Rationale: Ratio = 7k/9k = 7/9, 14/18, etc.
c and y are increased by 4 --> (7k + 4)/(9k + 4)
New ratio can be 11/13, 18/22, etc.
Answer: E
Answer: (E) It Cannot Be Determined
Question: In a race with 11 competitors, the first-place finisher receives a gold medal, the second-place finisher receives a silver medal, and the third-place finisher receives a bronze medal. If there are no ties, in how many different ways may these three medals be awarded?
(A) 35
(B) 120
(C) 720
(D) 990
(E) 604,800
Rationale: Well in this case since there are 3 positions and they can be taken by 3 persons only ,so order matters over here .For gold there are 11 choices ,for silver 10 remain (one who got gold cannot be given silver) and for bronze 9 choices remain.
So total possibilities=11*10*9=990
Correct answer D=990
Answer: (D) 990
Question: The averge score of a cricketer for ten matches is 45 runs. If the average for the first six matches is 48. Then find the average for the last four matches?
(A) 43.25
(B) 43
(C) 38
(D) 40.5
(E) 36
Rationale: sum of last 4 matches = ((10 × 45) – (6 × 48)= 162
Average =
162/4
= 40.5
ANSWER:D
Answer: (D) 40.5
Question: The dividend is 208, the quotient is 8 and the remainder is 2.
What is the divisor?
(A) 22
(B) 24
(C) 26
(D) 28
(E) 30
Rationale: D = d * Q + R
208 = d * 8 + 2
208/8 = d + 2
26 = d + 2
26-2 = d
24 = d
Answer: B
Answer: (B) 24
Question: A gambler has won 40% of his 20 poker games for the week so far. If, all of a sudden, his luck changes and he begins winning 80% of the time, how many more games must he play to end up winning 60% of all his games for the week?
(A) 20
(B) 25
(C) 30
(D) 35
(E) 40
Rationale: Let x be the number of additional games the gambler needs to play.
0.4(20) + 0.8x = 0.6(x+20)
0.2x = 4
x = 20
The answer is A.
Answer: (A) 20
Question: The area of the floor of a room is 20 m2 that of a longer wall 15 m2 and of the shorter wall 12 m2, find the edge of the new cube?
(A) 40
(B) 50
(C) 60
(D) 70
(E) 80
Rationale: lb = 20 ; lh = 15 ; fh = 12
(lbh)2 = 20 * 15 * 12 => lbh = 60 m3
Answer: Option C
Answer: (C) 60
Question: If nn is a positive integer and (n+1)(n+3)(n+1)(n+3) is odd, then (n+2)(n+4)(n+2)(n+4) must be a multiple of which one of the following?
(A) 1
(B) 4
(C) 6
(D) 8
(E) 9
Rationale: (n+1)(n+3)(n+1)(n+3) is odd only when both (n+1)(n+1) and (n+3)(n+3) are odd. This is possible only when nn is even.
Hence, n=2mn=2m, where mm is a positive integer. Then,
(n+2)(n+4)=(2m+2)(2m+4)=2(m+1)2(m+2)=4(m+1)(m+2)(n+2)(n+4)=(2m+2)(2m+4)=2(m+1)2(m+2)=4(m+1)(m+2)
=4 * (product of two consecutive positive integers, one which must be even)=4 * (product of two consecutive positive integers, one which must be even) =4 * (an even number), and this equals a number that is at least a multiple of 8=4 * (an even number), and this equals a number that is at least a multiple of 8
Hence, the answer is (D).
Answer: (D) 8
Question: Find the fourth proportion to 4,8,12
(A) 6
(B) 12
(C) 18
(D) 24
(E) 8
Rationale: Explanation:
4:8 :: 12:x
=> 4/8= 12/x
=> x = 12*8/4
=> x = 24
Answer:D
Answer: (D) 24
Question: Find the sum of first 20 multiples of 12.
(A) 2520
(B) 3878
(C) 2778
(D) 27
(E) 911
Rationale: Sum of first 20 multiples of 12 are = (12×1) + (12×2) + (12×3) + . . . . . . + (12×19) + (12×20). = 12 (1+2+3+ . . . . . + 20)
Use the formula:
n(n+1) 2
⇒
12×(20×21) 2
=2520.
Answer:A
Answer: (A) 2520
Question: The cost of the paint is rs.40 per kg. if 1kg of paint covers 20 sq.ft, how much will it cost to paint outside of a cube having 30 feet each side
(A) Rs.962
(B) Rs.672
(C) Rs.546
(D) Rs.10800
(E) None of these
Rationale: Explanation:
surface area of a cube= 6 x 30^2 = 5400 sq.ft
quantity of paint required=(5400/20)=270 kg
cost of painting= 40 x 270 = Rs.10800
Answer: D
Answer: (D) Rs.10800
Question: An express train travelled at an average speed of 100 km/hr, stopping for 3 minutes after every 75 km. How long did it take to reach its destination 600 km from the starting point?
(A) 5 hrs 20 min
(B) 6 hrs 21 min
(C) 6 hrs 24 min
(D) 6 hrs 30 min
(E) None
Rationale: Sol.
Time taken to cover 600 km = (600 / 100) hrs = 6 hrs.
Number of stoppages = 600 / 75 - 1 = 8 -1 = 7.
Total time of stoppages = (3x7) min = 21 min.
Hence, total time taken = 6 hrs 21 min.
Answer B
Answer: (B) 6 hrs 21 min
Question: Betty leaves her home and walks toward Dave's house. Two hours later, Dave leaves his home and walks toward Betty's house. The distance between their homes is 36 kilometers, Betty's walking speed is 4 km/h, and Dave's walking speed is 3 km/h. How many kilometers will Betty walk before she meets Dave?
(A) 18
(B) 20
(C) 22
(D) 24
(E) 25
Rationale: Betty walks 8 km in the first two hours so there are 28 km remaining.
When Dave starts walking, they complete a total of 7 km per hour.
They will meet four hours after Dave starts walking.
Since Betty walks for 6 hours, she walks 24 km.
The answer is D.
Answer: (D) 24
Question: James has a total of 560 balls. 140 balls are yellow, 250 balls are blue, and 170 balls are red. What percentage of the balls are yellow ?
(A) 45 %
(B) 30 %
(C) 25 %
(D) 55 %
(E) 75 %
Rationale: Explanation :
Yellow Percentage = (140/560 x 100)%
= 25%
Answer : C
Answer: (C) 25 %
Question: nd the area of trapezium whose parallel sides are 20 cm and 18 cm long, and the distance between them is 14 cm?
(A) 235cm2
(B) 260cm2
(C) 266cm2
(D) 270cm2
(E) 280cm2
Rationale: Area of a trapezium = 1/2 (sum of parallel sides) * (perpendicular distance between them)
= 1/2 (20 + 18) * (14)
= 266 cm2
Answer:C
Answer: (C) 266cm2
Question: Daniel went to the store 5 times last month. He buys 8 tickets and 14 bottle caps each time he goes to the store. How many tickets did Daniel buy last month?
(A) 25
(B) 14
(C) 40
(D) 33
(E) 11
Rationale: 8*5=40.Answer is C.
Answer: (C) 40
Question: A man entered a store and spent one-half of the money that was in his pocket. When he came out he found that he had just as many cents as he had dollars when he went in and half as many dollars as he had cents when he went in. How much money did he have on him when he entered?
(A) $95.98
(B) $77.98
(C) $99.98
(D) $65.98
(E) $76.98
Rationale: C
$99.98
The man must have entered the store with $99.98 in his pocket.
Answer: (C) $99.98
Question: A shop sells bicycles and tricycles. In total there are 7 cycles (cycles include both bicycles and tricycles) and 19 wheels. Determine how many of each there are, if a bicycle has two wheels and a tricycle has three wheels.
(A) b=2,t=3
(B) b=5,t=3
(C) b=6,t=2
(D) b=2,t=5
(E) b=3,t=4
Rationale: Let b be the number of bicycles and let t be the number of tricycles.
Set up the equations
b+t=7............(1)
2b+3t=19............(2)
Rearrange equation (1) and substitute into equation (2)
t=7-b
2b+21-3b=19
-b=-2
b=2
Calculate the number of tricycles t
t=7−b
=7−2
=5
There are 5 tricycles and 2 bicycles.
Answer is D.
Answer: (D) b=2,t=5
Question: What is the lowest positive integer that is divisible by each of the odd integers between 9 and 15 inclusive?
(A) 3×17×19×21
(B) 5×17×19×23
(C) 7×15×17×19
(D) 15*11*13
(E) 15×17×19×21
Rationale: We should find the LCM of 9= 3*3,11,13 and 15 = 3*5 --> LCM = 15*11*13
Answer: D.
Answer: (D) 15*11*13
Question: In how many ways can the letters of the word CAREER be arranged?
(A) 180
(B) 2500
(C) 2000
(D) 2520
(E) 3420
Rationale: CAREER has 6 words, but E and R are repeated two times. Thus ways = 6! / 2!*2! = 180 ways
A
Answer: (A) 180
Question: The sum of the squares of the first 15 positive integers (1^2 + 2^2 + 3^2 + . . . + 15^2) is equal to 1250. What is the sum of the squares of the second 15 positive integers (16^2 + 17^2 + 18^2 + . . . + 30^2) ?
(A)  2480
(B)  3490
(C)  6785
(D)  8225
(E)  9255
Rationale: You'll never need a formula for the sums of squares on the actual GMAT. You don't need to use that formula here, though it's not all that straightforward to solve without one. Two different approaches:
16^2 + 17^2 + 18^2 + ... + 30^2 = (15 + 1)^2 + (15 + 2)^2 + (15 + 3)^2 + ... + (15 + 15)^2
Now we can expand each square; they are all in the (x + y)^2 = x^2 + 2xy + y^2 pattern.
= (15^2 + 2*15 + 1^2) + (15^2 + 4*15 + 2^2) + (15^2 + 6*15 + 3^2) + ... + (15^2 + 30*15 + 15^2)
Now we have fifteen 15^2 terms, so adding these gives 15*15^2 = 15^3 = 3375. We also have the entire sum 1^2 + 2^2 + ... + 15^2, which we know is equal to 1240. Finally adding the middle terms, we have:
2*15 + 4*15 + 6*15 + ... + 30*15 = 15(2 + 4 + 6 + .... + 30) = 15*2*(1 + 2 + 3 + ... + 15) = 15*2*8*15 = 3600
So the sum must be 3375 + 1240 + 3600 = 8215
Alternatively, we can use a different factoring pattern. We want to find the value of 30^2 + 29^2 + ... + 17^2 + 16^2. Well if we subtract 15^2 + 14^2 + .... + 2^2 + 1^2 from this, the answer will be 1240 less than what we want to find. So if we can find the value of
30^2 + 29^2 + ... + 17^2 + 16^2 - (15^2 + 14^2 + .... + 2^2 + 1^2)
then we can add 1240 to get the answer. Now grouping the terms above to get differences of squares, we have
= (30^2 - 15^2) + (29^2 - 14^2) + ... + (16^2 - 1^2)
and factoring each of these using x^2 - y^2 = (x + y)(x - y), we have
= 45*15 + 43*15 + 41*15 + ... + 17*15 = 15(45 + 43 + 41 + ... + 17)
In brackets we have an equally spaced sum with fifteen terms, which we can evaluate using the familiar formula. So the above equals
15*15*62/2 = 6975
and adding back the 1250, we get the answer of 8225. (ANS D)
Answer: (D)  8225
Question: A letter lock consists of three rings each marked with six different letters. The number of distinct unsuccessful attempts to open the lock is at the most -.
(A) 216
(B) 243
(C) 215
(D) 729
(E) 728
Rationale: Since each ring consists of six different letters, the total number of attempts possible with the three rings is = 6 * 6 * 6 = 216. Of these attempts, one of them is a successful attempt.
Maximum number of unsuccessful attempts = 216 - 1 = 215.
ANSWER:C
Answer: (C) 215
Question: A baker filled with a measuring cup with 3/4 cup water. He poured 1/2 of the water into the batter, and then spilled 2/8 of the water on the floor. How much water will the baker needed to add what is left in the cup to have 50% more than what he started with?
(A) 1/8 cup
(B) 3/8 cup
(C) 1/4 cup
(D) 1/2 cup
(E) 8/8 cup
Rationale: 3/4 is the original water in cup .half in batter.So left is 3/8 out which 2/8 is spilled out.So again left with 1/8.
so 50% more than what he started was = 3/4+1/2*(3/4)=9/8
Amount of water needed to add = 9/8 - 1/8=8/8
ANSWER:E
Answer: (E) 8/8 cup
Question: A large tanker can be filled by two pipes A and B in 60 and 40 minutes respectively. How many minutes will it take to fill the tanker from empty state if B is used for half the time and A and B fill it together for the other half?
(A) 17 min
(B) 18 min
(C) 15 min
(D) 30 min
(E) 20 min
Rationale: Part filled by (A + B) in 1 minute = (1/60 + 1/40) = 1/24
Suppose the tank is filled in x minutes.
Then, x/2(1/24 + 1/40) = 1
x/2 * 1/15 = 1 => x = 30 min.
Answer:D
Answer: (D) 30 min
Question: The length of rectangle is thrice its breadth and its perimeter is 40 m, find the area of the rectangle?
(A) 432
(B) 212
(C) 75
(D) 992
(E) 212
Rationale: 2(3x + x) = 40
l = 15 b = 5
lb = 15 * 5 = 75
Answer:C
Answer: (C) 75
Question: Rs.2600 is divided so that 4 times the first share, thrice the 2nd share and twice the third share amount to the same. What is the value of the third share?
(A) s.1200
(B) s.1542
(C) s.1528
(D) s.1540
(E) s.1549
Rationale: A+B+C = 2600
4A = 3B = 2C = x
A:B:C = 1/4:1/3:1/2 = 3:4:6
6/13 * 2600 = Rs.1200
Answer: A
Answer: (A) s.1200
Question: Find the least number which when divided by 5,6,7,8 leaves a remainder 3 but when divided by 9 leaves no remainder
(A) 9632
(B) 7896
(C) 8741
(D) 1683
(E) 8523
Rationale: L.C.M Of 5,6,7,8=840
required number is of the form of 840K+3
least value of k for which (840k+3)is divided by 9 is k =2
required number=(840*2+3)=1683
Answer(D)
Answer: (D) 1683
Question: A certain company charges $6 per package to ship packages weighing less than 2 pounds each. For a package weighing 2 pounds or more, the company charges an initial fee of $6 plus $2 per pound. If the company charged $32 to ship a certain package, which of the following was the weight of the package, in pounds?
(A) 9
(B) 11
(C) 13
(D) 15
(E) 17
Rationale: Let the weight of the package be X.
2X + 6= 32
X = 13
The answer is C.
Answer: (C) 13
Question: A boat can travel with a speed of 24 km/hr in still water. If the speed of the stream is 4 km/hr, find the time taken by the boat to go 140 km downstream
(A) 3 hours
(B) 4 hours
(C) 5 hours
(D) 6 hours
(E) 7 hours
Rationale: Explanation:
Speed of the boat in still water = 24 km/hr
speed of the stream = 4 km/hr
Speed downstream = (22+5) = 28 km/hr
Distance travelled downstream = 140 km
Time taken = distance/speed = 140/28 = 5 hours
Answer: Option C
Answer: (C) 5 hours
Question: The length of a rectangular plot is thrice its breadth. If the area of the rectangular plot is 1323 sq m, then what is the breadth of the rectangular plot?
(A) 11
(B) 17
(C) 18
(D) 21
(E) 1322
Rationale: Let the breadth of the plot be b m.
Length of the plot = 3 b m
(3b)(b) = 1323
3b2 = 1323
b2 = 441 = 21 (b > 0)
b = 21 m.
Answer: D
Answer: (D) 21
Question: If v=4p where p is a prime number greater than 2, how many different positive even divisors does v have, including v?
(A) two
(B) three
(C) four
(D) six
(E) eight
Rationale: v=2, 2, p (p is in the prime factorization since were told it is a prime number in the question)
2
4 (because of 2*2)
2p (because of 2 * p)
4p (because of 2 * 2 * p)=C
Answer: (C) four
Question: Sum of the squares of three numbers is 138 and the sum of their products taken two at a time is 131. Find the sum?
(A) 20
(B) 22
(C) 25
(D) 26
(E) 29
Rationale: (a + b + c)2 = a2 + b2 + c2 + 2(ab +bc + ca) = 138 + 2* 131
a + b + c = √400 = 20
A
Answer: (A) 20
Question: If 8 men and 2 boys working together, can do four times as much work per hour as a man and a boy together. Find the ratio of the work done by a man and that of a boy for a given time?
(A) 3:2
(B) 2:1
(C) 3:3
(D) 1:2
(E) 6:1
Rationale: 8M + 2B = 4(1M + 1B)
8M + 2B = 4M + 4B
4M = 2B
The required ratio of work done by a man and a boy = 2:4=1:2
D
Answer: (D) 1:2
Question: If the following is true, can you find the value of (4 + 9)?
7 + 7 = 2
8 + 8 = 4
8 + 5 = 1
6 + 9 = 3
10 + 11 = 9
(A) 3
(B) 2
(C) 1
(D) 4
(E) 5
Rationale: Solution:
1
Explanation:
4 + 9 = 1
The trick to solve is to assume the first number as the time in AM and the second number is the number of hours you have to add to it. You'll find the time in PM when you do that.
For example
7 AM + 7 hours = 14:00 or 2 PM
4 AM + 9 hours = 13:00 or 1 PM.
Answer C
Answer: (C) 1
Question: While working alone at their respective constant rates, server J uploads 480 files in 4 hours and server Y uploads 480 files in 8 hours. If all files uploaded by these servers are the same size, how long would it take the two servers, working at the same time and at their respective constant rates, to process a total of 480 files?
(A)  2 hr
(B)  2hr 20 min
(C)  2hr 40 min
(D)  5 hr 40 min
(E)  6hr
Rationale: Server J processes 480/4 files per hour = 120 per hour
Server Y processes 180/8 files per hour = 60 per hour
Total files processed per hour when J and Y work together = 120+60 per hour = 180 files per hour
480/180 = 2 2/3 hours=C
Answer: (C)  2hr 40 min
Question: If the perimeter of square region Z and the perimeter of rectangular region R are equal and the sides of R are in the ratio 2:3 then the ratio of the area of R to the area of Z
(A) 25:16
(B) 24:25
(C) 5:6
(D) 4:5
(E) 4:9
Rationale: We know Perimeter of a square (Pz) = 4*side
Perimeter of a rectangle (Pr) = 2(length+breath)
Let us assume 40 to be the perimeter of the square (since we know each side of a square is equal and the perimeter is divisible by 4, also take in to account the length and breadth of the rectangle is in the ration 2k:3k = 5k; we can assume such a number)
Therefore,
Pz = Pr = 40
Area of the square = 100 sq. units
We know 2(length+breadth) = 40
i.e. length + breadth = 20 (or 5k = 20 given that l:b (or b:l) = 2:3)
Therefore length = 8, breath = 12
Area of the rectangle = 8*12 = 96 sq. units
Question asked = Area of the rectangle : Area of the square = 96:100 ==> 24:25=B
Answer: (B) 24:25
Question: A lady bought four books namely A,B,C,D to distribute her 6 children. How many ways she can distribute books?
(A) 6^3
(B) 6^4
(C) 6^5
(D) 6^6
(E) 6^2
Rationale: 6*6*6*6
6^4
ANSWER:B
Answer: (B) 6^4
Question: A starts business with Rs. 3500 and after 5 months, B joins with A as his partner. After a year, the profit is divided in the ratio 2 : 3. What is B's contribution in the capital?
(A) 7000
(B) 7320
(C) 8000
(D) 9000
(E) 9200
Rationale: Let B's capital be Rs. x.
Then,(3500 / 12)/7x	=	2/3
14x = 126000
x = 9000.
answer :D
Answer: (D) 9000
Question: The amount of water (in ml) that should be added to reduce 21 ml. Lotion, containing 50% alcohol, to a lotion containing 30% alcohol, is?
(A) 8 ml
(B) 5 ml
(C) 14.5 ml
(D) 6 ml
(E) 1 ml
Rationale: 10.5 10.5
30% 70%
30% ----- 10.5
70% ------? => 24.5 - 10.5 = 14.5 ml
Answer:C
Answer: (C) 14.5 ml
Question: A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If three marbles are drawn what is the probability that one is yellow and two are red?
(A) 12/428
(B) 12/420
(C) 12/455
(D) 12/429
(E) 12/413
Rationale: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles.
When three marbles are drawn, the probability that one is yellow and two are red
= (2C1)(4C2)/15C3
= (2 * 4 * 3 * 3 * 2)/(1 * 2 * 15 * 14 * 13)
= 12/455
Answer:C
Answer: (C) 12/455
Question: Sum of ages of two friends is 30 while difference is 2 then their ages are
(A) 15 years, 17 years
(B) 16 years, 14 years
(C) 24 years, 1 years
(D) 18 years, 16 years
(E) None
Rationale: 16,14
ANSWER:B
Answer: (B) 16 years, 14 years
Question: In an electric circuit, two resistors with resistances x and y are connected in parallel. If R is the combined resistance of these two resistors, then the reciprocal of R is equal to the sum of the reciprocals of x and y. What is R if x is 4 Ohms and y is 6 Ohms?
(A) 5/12
(B) 7/12
(C) 12/5
(D) 7/5
(E) 11/5
Rationale: 1/R = 1/x + 1/y
1/R = 1/4+1/6 = 5/12
R = 12/5
The answer is C.
Answer: (C) 12/5
Question: Lawrence is interested in dividing his backyard into equal pens for his dogs. Unfortunately, it does not divide equally. It turns out that in order for the yard to divide equally, Lawrence has to buy an additional six square feet of land and sell three of his dogs.. Which of the following can describe the number of square feet of the initial yard and the initial number of dogs (in the order square feet, dogs)?
(A) 45; 8.
(B) 20; 7.
(C) 30; 9.
(D) 80; 12.
(E) 35; 7
Rationale: Option C) Initially 9 dogs then reduced to 6 dogs; and Initially 30 square feet of yard increased to 36 square feet of yard fits the requirement.
36 / 6 = 6 square feet of yard per dog
Answer: (C) 30; 9.
Question: QUANT 4-PACK SERIES Problem Solving Pack 4 Question 2 For every positive integer n...
For every positive integer n that is greater than 1, the function d(n) is defined to be the sum of all of the odd integers from 1 to n, inclusive. The d(n) could have any of the following units digits except…?
(A) 1
(B) 2
(C) 4
(D) 6
(E) 9
Rationale: For every positive integer n that is greater than 1, the function d(n) is defined to be the sum of all of the odd integers from 1 to n, inclusive. The d(n) could have any of the following units digits except…?
Used brute force on this one to calculate. Not sure if there is a quicker way.
1+3=4 C is out
1+3+....15= 81 A is out
1+3+5+7=16 D is out
1+3+5=9 E i out
Answer: B
Answer: (B) 2
Question: Amar takes as much time in running 18 meters as a car takes in covering 48 meters. What will be the distance covered by Amar during the time the car covers 1.6 km?
(A) 700 m
(B) 500 m
(C) 670 m
(D) 600 m
(E) 640 m
Rationale: Distance covered by Amar
= 18/4.8 (1.6km)
= 3/8(1600) = 600 m
Answer: D
Answer: (D) 600 m
Question: A train moves with a speed of 216 kmph. Its speed in metres per second is
(A) 10.8
(B) 18
(C) 30
(D) 38.8
(E) 60
Rationale: Solution
Speed	= 216 Kmph
= (216 x 5/18)m/sec
= 60 m/sec.
Answer E
Answer: (E) 60
Question: A train sets off at 2 p.m. at the speed of 60 kmph. Another train starts at 3:30 p.m. in the same direction at the rate of 75 kmph. At what time the trains will meet?
(A) 9.37 p.m
(B) 9.20 p.m
(C) 9.30 p.m
(D) 9.38 p.m
(E) 9.10 p.m
Rationale: D = 60 * 1 Â½ = 90 km
RS = 75 â€“ 60 = 15
T = 90/15 = 6 h
3.30 + 6 h = 9.30 p.m.
Answer: C
Answer: (C) 9.30 p.m
Question: If the average costs of three colors of 20,40,60 chocolates respectively is 10,15,20 what is the average costs of all the chocolates?
(A) 12.22
(B) 13.33
(C) 14.44
(D) 15.55
(E) 16.66
Rationale: Average costs of group 1 =10
chocolates in group 1 = 20
Total costs of group 1 = 10*20
Average costs of group 2 = 15
chocolates in group 2 = 40
Total costs of group 2 = 15*40
Average costs of group 3 = 20
chocolates in group 3 = 60
Total costs of group 3 = 20*60
Total chocolates = 20+40+60 = 120
Average costs of all the chocolates
=((10*20)+(15×40)+(20*60))/120
=50/3
=16.66
Answer is E.
Answer: (E) 16.66