mathewhe/aqua_rat huggingface dataset:
Question: Assisants are needed to prepare for preparation. Each helper can make either 2 large cakes or 35 small cakes/hour. The kitchen is available for 3hours and 20 large cakes and 700small cakes are needed. How many helpers are required?
(A) 9
(B) 10
(C) 13
(D) 16
(E) 18
Rationale: 20 large cakes will require the equivalent of 10 helpers working for one hour. 700 small cakes will require the equivalent of 20 helpers working for one hour. This means if only one hour were available we would need 30 helpers. But since three hours are available we can use 10 helpers.
B
Answer: (B) 10
Question: A man buys two articles for Rs.1980 each and he gains 10% on the first and loses 10% on the next. Find his total gain or loss percent?
(A) 9%loss
(B) 8%loss
(C) 3%loss
(D) 2%loss
(E) 1%loss
Rationale: (30*30)/100
= 9%loss
Answer: A
Answer: (A) 9%loss
Question: If the cost of x metres of wire is d rupees, then what is the cost of y metres of wire at the same rate?
(A) Rs.(xy/d)
(B) Rs.(yd/x)
(C) Rs.(y/d)
(D) Rs.(xd)
(E) Rs.(x/d)
Rationale: Cost of x metres = Rs. d.
Cost of 1 metre = Rs.	d/x
Cost of y metres = Rs.(d/x)* y= Rs.(yd/x)
Answer is B.
Answer: (B) Rs.(yd/x)
Question: 1370 , 1320 , 1070 , -180 ?
(A) -6440
(B) -6680
(C) -6480
(D) -5480
(E) -4480
Rationale: 1370-1320=50 -->50*5=250
1320-250=1070-->250*5=1250
1070-1250=-180-->1250*5=6250
-180-6250=-6430......so ans:-6480
ANSWER:C
Answer: (C) -6480
Question: Golu started from his house towards North. After covering a distance of 8 km. he turned towards left and covered a distance of 6 km. What is the shortest distance now from his house?
(A) 10 km.
(B) 16 km.
(C) 14 km
(D) 2 km.
(E) 4 km.
Rationale: C-------------B
!
!
!
!
!
A
AB=8 Km BC=6Km
AC=sqrtof(8^2+6^2)
AC=10KM
ANSWER:A
Answer: (A) 10 km.
Question: A goods train runs at the speed of 72 km/hr and crosses a 250 m long platform in 26 sec. What is the length of the goods train?
(A) 49 sec
(B) 50 sec
(C) 48 sec
(D) 43 sec
(E) 32 sec
Rationale: D = 540 + 180 = 720
S = 54 * 5/18 = 15 mps
T = 720/15 = 48 sec
Answer:C
Answer: (C) 48 sec
Question: If the speed of a man is 45 km per hour, then what is the distance traveled by him in 30 seconds ?
(A) 275m
(B) 360m
(C) 375 m
(D) 420 m
(E) 440 m
Rationale: The distance traveled in 30 sec = 45*(5/18) *30 =375m
ANSWER:C
Answer: (C) 375 m
Question: A car travelling 5/7th of its actual speed covers 42 km in 1 hr 40 min 48 sec. what is the actual speed of the car?
(A) 22
(B) 35
(C) 27
(D) 10
(E) 18
Rationale: Explanation:
Let the Actual Speed = x
It is travelling with 5/7 of its actual speed = 5x/7.
Converting the time into seconds = 3600 + 2400 + 48 seconds.
Covers a distance with speed = 42/(3600 + 2400 + 48)
= 424048424048 × 3600 = 25 kph
Given 5x75x7 = 25 kph
So Actual Speed = 25 × (7/5) = 35 kph
Answer:B
Answer: (B) 35
Question: In how many different ways can pennies (1 cent), nickels (5 cents), dimes (10 cents), and quarters (25 cents) be combined for a total of $1.05 (105 cents), if at least one coin of at least three types of coins must be included?
(A) 78
(B) 103
(C) 118
(D) 131
(E) 221
Rationale: This question is similar to determining the number of ways using one of each type of coin, but allows the exclusion of one type.
I. Case I = Four Quarters (100 cents)
Subcase 1= 4 Q, 1 D (110 cents) not allowed as this exceeds $1.05.
Subcase 2= 4 Q, 0 D (100 cents) not allowed since it does not allow for both nickels and pennies.
Case I does not allow any ways.
II. Case II = Three Quarters (75 cents)
This allows for two, one, or zero dimes. Three dimes would bring us up to $1.05, and we wouldn't have room for any pennies or nickels.
Subcase 1 = 3 Q, 2 D (95 cents)
1) one nickel (N) and 5 pennies (P)
2) 2 N and 0 P
3) 0 N and 10 P
Subcase 2 = 3 Q, 1 D (85 cents)
4) 4 N and 0 P
5) 3 N and 5 P
6) 2 N and 10 P
7) 1 N and 15 P
8) 0 N and 20 P
Subcase 3 = 3 Q, 0 D (75 cents)
(5 ways) we could have 1-5 nickels
Case II allows for a total of 13 ways.
III. Case III = Two Quarters (50 cents)
This allows for 0-5 dimes.
Subcase 1 = 2 Q, 5 D (100 cents)
(2 ways) we could have 0-1 nickel
Subcase 2 = 2 Q, 4 D (90 cents)
(4 ways) we could have 0-3 nickels
Subcase 3 = 2 Q, 3 D (80 cents)
(6 ways) we could have 0-5 nickels
Subcase 4 = 2 Q, 2 D (70 cents)
(8 ways) we could have 0-7 nickels
Subcase 5 = 2 Q, 1 D (60 cents)
(10 ways) we could have 0-9 nickels
Subcase 6 = 2 Q, 0 D (50 cents)
(10 ways) we could have 1-10 nickels
Case III allows for a total of 40 ways
IV. Case IV = One Quarter (25 cents)
This allows for 0-7 dimes
Subcase 1 = 1 Q, 7 D (95 cents)
(3 ways) we could have 0-2 nickels
Subcase 2 = 1 Q, 6 D (85 cents)
(5 ways) we could have 0-4 nickels
Subcase 3 = 1 Q, 5 D (75 cents)
(7 ways) we could have 0-6 nickels
Subcase 4 = 1 Q, 4 D (65 cents)
(9 ways) we could have 0-8 nickels
Subcase 5 = 1 Q, 3 D (55 cents)
(11 ways) we could have 0-10 nickels
Subcase 6 = 1 Q, 2 D (45 cents)
(13 ways) we could have 0-12 nickels
Subcase 7 = 1 Q, 1 D (35 cents)
(15 ways) we could have 0-14 nickels
Subcase 8 = 1 Q, 0 D (25 cents)
(15 ways) we could have 1-15 nickels
Case IV allows for a total of 78 ways.
IV. Case V = Zero Quarters (0 cents)
This allows for 1-9 dimes
Subcase 1 = 0 Q, 9 D (90 cents)
(2 ways) we could have 1-2 nickels
Subcase 2 = 0 Q, 8 D (80 cents)
(4 ways) we could have 1-4 nickels
Subcase 3 = 0 Q, 7 D (70 cents)
(6 ways) we could have 1-6 nickels
Subcase 4 = 0 Q, 6 D (60 cents)
(8 ways) we could have 1-8 nickels
Subcase 5 = 0 Q, 5 D (50 cents)
(10 ways) we could have 1-10 nickels
Subcase 6 = 0 Q, 4 D (40 cents)
(12 ways) we could have 1-12 nickels
Subcase 7 = 0 Q, 3 D (30 cents)
(14 ways) we could have 1-14 nickels
Subcase 8 = 0 Q, 2 D (20 cents)
(16 ways) we could have 1-16 nickels
Subcase 9 = 0 Q, 1 D (10 cents)
(18 ways) we could have 1-18 nickels
Case V allows for a total of 90 ways.There's no other case, because we have to have at least one quarter or one dime. The total over the cases equals
Total = 0 + 13 + 40 + 78 + 90 =221 ways.
OA =(E)
Answer: (E) 221
Question: What is the sum of all digits for the number 10^28 - 44?
(A) 233
(B) 245
(C) 257
(D) 270
(E) 285
Rationale: 10^28 is a 29-digit number: 1 followed by 28 zeros.
10^28 - 44 is a 28-digit number: 26 9's and 56 at the end.
The sum of the digits is 26*9+5+6=245.
The answer is B.
Answer: (B) 245
Question: 8 men and 2 boys working together can do four times as much work as a man and a boy. Working capacity of man and boy is in the ratio
(A) 1:2
(B) 1:3
(C) 2:1
(D) 2:3
(E) None of these
Rationale: Explanation:
Let 1 man 1 day work = x
1 boy 1 day work = y
then 8x + 2y = 4(x+y)
=> 4x = 2y
=> x/y = 2/4
=> x:y = 1:2
Option A
Answer: (A) 1:2
Question: 4 mat-weavers can weave 4 mats in 4 days. At the same rate, how many mats would be woven by 14 mat-weavers in 14 days?
(A) 25
(B) 19
(C) 39
(D) 61
(E) 49
Rationale: Let the required number of bottles be x.
More weavers, More mats (Direct Proportion)
More days, More mats (Direct Proportion)
Wavers	4	:	14 :: 4 : x
Days	4:14
4 * 4 * x = 14 * 14 * 4
x =	(14 * 14 * 4)/(4 x 4)
x = 49.
Answer is E.
Answer: (E) 49
Question: If y ≠ 3 and 2a/y is a prime integer greater than 2, which of the following must be true?
I. xa= y
II. y = 1
III. a and y are prime integers.
(A)  None
(B)  I only
(C)  II only
(D)  III only
(E)  I and II
Rationale: Note that we are asked which of the following MUST be true, not COULD be true. For such kind of questions if you can prove that a statement is NOT true for one particular set of numbers, it will mean that this statement is not always true and hence not a correct answer.
So we should try to make the listed statements not true for some x and y (which satisfy y≠3 and 2x/y=prime>2).
I. a = y --> not necessarily true: a=3 and y=2 (2a/y=3=prime>2);
II. y=1 --> not necessarily true: a=3 and y=2 (2a/y=3=prime>2);
III. a and y are prime integers --> not necessarily true: a=10 and y=4 (2a/y=5=prime>2).
Answer: A.
Answer: (A)  None
Question: The ratio of two numbers is 3 : 4 and their H.C.F. is 3. Their L.C.M. is
(A) 48
(B) 22
(C) 56
(D) 27
(E) 36
Rationale: Explanation:
Let the numbers be 3x and 4x. Then, their H.C.F. = x. So, x = 3.
So, the numbers 9 and 12.
L.C.M. of 9 and 12 = 36.
Answer: Option E
Answer: (E) 36
Question: A girl sitting in a train which is travelling at 40 kmph observes that a goods train travelling in a opposite direction, takes 12 seconds to pass him. If the goods train is 1120 m long, find its speed.
(A) 295
(B) 296
(C) 297
(D) 298
(E) 299
Rationale: Relative speed = (1120/12)m/s = (1120/12)*(18/5) = 336 kmph
speed of goods train = 336-40 = 296 kmph
Answer is B
Answer: (B) 296
Question: There are 32 students in a class. Nine of those students are women. What percent are men? (round to the nearest tenth)
(A) 70.9%
(B) 71.9%
(C) 72.9%
(D) 73.9%
(E) 74.9%
Rationale: Total 100% 32
Men 23
Women 9
32-9=23
x/100=23/32
Multiply the opposites:
100 x 23 = 2300
Divide by the remaining number:
71.87/2300.00
32
71.9%(rounded to nearest tenth)
correct answer B
Answer: (B) 71.9%
Question: There are 20 states in a certain country and every pair of them is connected by a road way. How many road ways are there?
(A) 22
(B) 277
(C) 288
(D) 266
(E) 2A1
Rationale: Answer:A
Answer: (A) 22
Question: At what time between 5 and 6 o' clock are the hands of a 3 minutes apart ?
(A) 24min
(B) 14min
(C) 74min
(D) 54min
(E) 44min
Rationale: In this type of problems the formuae is
(5*x+ or - t)*12/11
Here x is replaced by the first interval of given time. Here x is 5.
t is spaces apart
Case 1 : (5*x + t) * 12/11
(5*5 + 3) * 12/11
28 * 12/11 = 336/11= min
therefore the hands will be 3 min apart at 31 5/11 min past 5.
Case 2 : (5*x - t) * 12/11
(5*5 -3 ) * 12/11
22 *12/11 = 24 min
therefore the hands will be 3 min apart at 24 min past 5
Answer: A
Answer: (A) 24min
Question: If (x + 1)(x + 3) = x^2 + x, what is a possible value of x?
(A)  2
(B)  3
(C)  -1/3
(D)  -3
(E)  -1
Rationale: Rearranging the given expression:
(x + 1)(x + 3) = x^2 + x
i.e. x^2 + 4x + 3 = x^2 + x
i.e. 3x = -3
i.e. x = -3/3 = -1
Answer: Option E
Had it been a difficult expression to solve further, then we could have used options to check which one satisfies the expression after solving it as further as possible.
Answer: (E)  -1
Question: In how many ways can 4 black and 4 white chess pieces be arranged in a row such that they occupy alternate places? Assume that the pieces are distinct.
(A) 144
(B) 24
(C) 576
(D) 48
(E) 16
Rationale: 4 black chess pieces can be arranged in 4! ways and 4 white pieces can be arranged in 4! ways.
W_W_W_W
Number of ways = 4!*4! = 24 * 24 = 576
Answer C
Answer: (C) 576
Question: The average of six numbers is X and the average of three of these is Y.If the average of the remaining three is z, then
(A) x = y + z
(B) 2x = y + z
(C) x = 2y + z
(D) x = y + 2z
(E) None of these
Rationale: Explanation:
X =((3y+3z)/6)
or
2X= y + z
Option B
Answer: (B) 2x = y + z
Question: The ratio of a compound, by weight, consisting only of substances x, y, and z is 4:6:10,
respectively. Due to a dramatic increase in the surrounding temperature, the composition of the
compound is changed such that the ratio of x to y is halved and the ratio of x to z is tripled. In the
changed compound, if the total weight is 406 lbs, how much does substance x weigh?
(A) 68
(B) 76
(C) 84
(D) 92
(E) 110
Rationale: x:y=4:6
if the ratio is halevd then x:y=2:6
The old ratio of x to z was 4:10. If this ratio is tripled, then the new ratio of x to z is 12:10.
x:y=2:6=12:36 ( multiplied the ration with 6/6 to have a common co eff x in both the rations x:y and x:z)
so x:y:z= 12:36:10
and we know x + y + z = 406 lbs
from the ratio of x ,y and z we have x=12k y=36k z=10K
put it in the equation we have 12k+36k+10k=406
k=7
Hence x=12(7)=84
Ans C
Answer: (C) 84
Question: Adam and Beth each drove from Smallville to Crown City by different routes. Adam drove an an average speed of 40 miles per hour and completed the trip in 30 minutes. Beth's route was 5 miles longer, and it took her 20 minutes more than Adam to complete the trip. How many miles per hour was Beth's average speed on this trip?
(A) 24
(B) 30
(C) 48
(D) 54
(E) 75
Rationale: Speed = Distance/Time
Distance for Adam = Speed * Time = 40 * 1/2 = 20 miles
Distance for Beth = Distance for Adam+5 = 20+5 = 25 miles
Time taken by Beth = Time taken by Adam + (1/3 hour) = 1/2+1/3 = 5/6
Speed of Beth = D/T = 25/(5/6) = 25*6/5 = 30 miles per hour
Hence, B is the answer.
Answer: (B) 30
Question: The number of new words that can be formed by rearranging the letters of the word 'garden' is?
(A) 720
(B) 721
(C) 719
(D) 700
(E) 721
Rationale: Number of words which can be formed
= 6! - 1 = 720 - 1
= 719.
Answer:C
Answer: (C) 719
Question: In an election, candidate Smith won 52% of the total vote in Counties A and E. He won 61% of the vote in County A. If the ratio of people who voted in County A to County E is 3:1, what percent of the vote did candidate Smith win in County E ?
(A) A.25%
(B) B.27%
(C) C.34%
(D) D.43%
(E) E.49%
Rationale: (61%)*3x + (y%)*x = (52%)*4x
y = 25% of County E
hence answer is A.
Answer: (A) A.25%
Question: Find the invalid no.from the following series 15 46 63 71 75 77 78
(A) 32
(B) 35
(C) 46
(D) 49
(E) 67
Rationale: In this question, if you start from the beginning, firstly the difference is 31, then the difference is 17, then the difference is 8. So there is no logic. If you start backwards,you can see that firstly, 1 is added, then 2 is added, then 4 is added, then 8,16 and 32 should have been added. So you have got the right clue. So 15 + 32 the first number should be 47 and afterwards, the series becomes + 16, + 8, + 4and so on.
46
C
Answer: (C) 46
Question: A goods train runs at a speed of 72 kmph and crosses a 240 m long platform in 26 seconds.What is the length of the goods train?
(A) 230 m
(B) 240 m
(C) 260 m
(D) 270 m
(E) 280 m
Rationale: s=240+x/t
72*5/18=240+x/26
x=280
ANSWER:E
Answer: (E) 280 m
Question: A train traveled 580 miles in 2 hours 20 minutes. What was the averge speed of train in miles per hour?
(A) 270 miles / hour
(B) 280 miles / hour
(C) 290 miles / hour
(D) 300 miles / hour
(E) 310 miles / hour
Rationale: We first convert the time of 2 hours 20 minutes in minutes
2 hours 20 minutes = 2* 60 + 20= 140 minutes
Average speed S is given by distance / time. Hence
S = 580 miles / 140 minutes = 4.83 miles / minute
= 290 miles / hour
correct answer C
Answer: (C) 290 miles / hour
Question: When each of the opposite sides of a square is increasedby 8cm then ratio of sides of the rectangle thus formed is 5:3. What is the area of the original square?
(A) 123
(B) 132
(C) 154
(D) 144
(E) 175
Rationale: Sol. (x+8)/x = 5/3
X = 12
Required area = 12*12 = 144
D
Answer: (D) 144
Question: The smallest value of n, for which 2n is not a prime number, is
(A) 2,3,4
(B) 1,3,5
(C) 2,5,6
(D) 4,8,9
(E) 12,14,16
Rationale: (2Ã—1) = 2.
(2Ã—2) = 4.
(2Ã—3) = 6.
(2Ã—4) = 8.
which is not prime , n=2,3,4.
ANSWER:A
Answer: (A) 2,3,4
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) 1
(D) 2
(E) none of these
Rationale: Explanation:
Average of 20 numbers = 0.
Sum of 20 numbers = (0 * 20) = 0.
It is quite possible that 19 of these numbers may be positive and if their sum is a, then 20th number is (- a). Answer: A
Answer: (A) 0
Question: In a shop, 40% socks are white and rest are black. 60% socks are made of cotton and rest are made of wool. 25% white socks are made of cotton and 20 of the black socks are made of wool. How many black socks are made of cotton?
(A) 100
(B) 80
(C) 60
(D) 50
(E) 25
Rationale: 40% is white -> wht = 0.4x
Blk = 0.6 x
also 60% socks are made of cotton - > ct = 0.6x
wl = 0.4x
we know 25% of the white socks is cotton --> 1/4 (0.4x) = 0.1x = wh-ct
=> 0.3x = wh-wl
total wool is 0.4x => black wool socks = 0.4 x (total) - 0.3 x (wh-wl) = 0.1x given as 20
=> total number of socks = 200
= > total black socks = .6x = 120
total cotton black socks = 120 - 20 (bl-wl) = 100 hence A
Answer: (A) 100
Question: How many years will it take John’s investment to double at a simple interest rate of 4% per annum.
(A) 20
(B) 30
(C) 15
(D) 25
(E) 19
Rationale: P = (P*4*R)/100
100P = P*4*R
100 = 4R
Therefore R = 25
D = 25 Years
Answer: (D) 25
Question: A bus from city M is traveling to city N at a constant speed while another bus is making the same journey in the opposite direction at the same constant speed. They meet in point P after driving for 2 hours. The following day the buses do the return trip at the same constant speed. One bus is delayed 24 minutes and the other leaves 36 minutes earlier. If they meet 24 miles from point P, what is the distance E between the two cities?
(A) 48
(B) 72
(C) 96
(D) 120
(E) 192
Rationale: Hmmm I did this question a while ago and got it wrong so trying again
Rate x time = distance.
For the initial trip lets the distance E to the midpoint be represented by P.
EQN1: R x 2 = P
For the second trip we know one bus left late and one left early. Together this is just a tricky way of saying one bus left an hour after the other. We know the total trip takes 4 hours (since getting to P is 2 hours). The second trip can be represented by:
Since the trip takes 4 hours if a bus leaves one hour early, the reminaining 3 hours are split between the two buses, ie. 1 + 3/2 = 2.5
EQN2: R x 2.5 = P + 24
EQN2-EQN1 : 0.5R=24
R=48
So the distance is rate x time = 48 x 4 = 192.
ANS = E
Answer: (E) 192
Question: A 300 meter long train crosses a platform in 33 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform?
(A) 250
(B) 266
(C) 230
(D) 288
(E) 271
Rationale: Speed = [300 / 18] m/sec = 50/3 m/sec.
Let the length of the platform be x meters.
Then, x + 300 / 33 = 50/3
3(x + 300) = 1650 è x = 250m.
Answer: A
Answer: (A) 250
Question: A palindrome is a number that reads the same forward and backward, such as 242. How many odd three-digit numbers are palindromes?
(A) 40
(B) 400
(C) 50
(D) 5,000
(E) 100,000
Rationale: 3rd digit 1,3,5,7,9
2nd digit 0 through 9
i.e 10*5 = 50 numbers
first digit is going to be same as 3rd . so it would still be 50 numbers.
Answer is C.
Answer: (C) 50
Question: Two men Amar and Bhavan have the ratio of their monthly incomes as 6:5. The ratio of their monthly expenditures is 3:2. If Bhavan saves one-fourth of his income, find the ratio of their monthly savings?
(A) 3:19
(B) 3:10
(C) 3:12
(D) 3:11
(E) 3:22
Rationale: Let the monthly incomes of Amar and Bhavan be 6x and 5x respectively.
Let the monthly expenditures of Amar and Bhavan be 3y and 2y respectively.
Savings of Bhavan every month = 1/4 (5x)
=(his income) - (his expenditure) = 5x - 2y
=> 5x = 20x - 8y => y = 15x/8
Ratio of savings of Amar and Bhavan
= 6x - 3y : 1/4 (5x) = 6x - 3(15x/8) : 5x/4
= 3x/8 : 5x/4 => 3:10
Answer:B
Answer: (B) 3:10
Question: Three 6 faced dice are thrown together. The probability that exactly two dice show the same number on them is -.
(A) 5/12
(B) 4/13
(C) 5/17
(D) 3/12
(E) 8/9
Rationale: Using question number 11 and 12, we get the probability as
1 - (1/36 + 5/9) = 5/12
ANSWER A
Answer: (A) 5/12
Question: 16* 16 * 16 * 16 * 16 = 4^ ?
(A) 8
(B) 6
(C) 10
(D) 4
(E) 3
Rationale: 4^2 * 4^2 * 4^2 * 4^2 * 4^2 = 4^(2 +2+2+2+2) = 4^10
Answer : 10
Option : C
Answer: (C) 10
Question: In a division sum, the divisor is ten times the quotient and five times the remainder. If the remainder is 52, the dividend is:
(A) 6832
(B) 6814
(C) 6816
(D) 6812
(E) 6810
Rationale: Divisor = (5 * 52) = 260
= 10 * Quotient = Divisor
=> Quotient = 260/10 = 26
Dividend = (Divisor * Quotient) + Remainder
Dividend = (260 * 26) + 52 = 6812.
D
Answer: (D) 6812
Question: There are 20 poles with a constant distance between each pole. A car takes 25 second to reach the 12th pole. How much will it take to reach the last pole.
(A) 43.1543
(B) 43.1818
(C) 43.45128
(D) 43.41288
(E) 43.41222
Rationale: Assuming the car starts at the first pole.
To reach the 12th pole, the car need to travel 11 poles (the first pole doesn't count, as the car is already there).
11 poles 25 seconds
1 pole (25/11) seconds
To reach the last (20th) pole, the car needs to travel 19 poles.
19 pole 19 x (25/11) seconds
= 43.1818 seconds
Answer:B
Answer: (B) 43.1818
Question: For an employee to qualify for early retirement at a certain company, the sum of the employee’s age and years of service must be at least 65, If Sue was K years old when she was hired by the company, what is the minimum age at which she could possibly qualify for early retirement.
(A) K+35
(B) 2K+35
(C) (70+K)/2
(D) (65+K)/2
(E) 2(70-K)
Rationale: Say Sue was hired when she was already 65 years old (k=65), then she could retire right away, at the age of 65. Now, plug k=65 in the answer choices and see which yields 65. Only C fits.
Answer: D.
Answer: (D) (65+K)/2
Question: 2 no's are respectively 40% & 60% more than 3rdnumber. Find the ration of two numbers ?
(A) 3 : 4
(B) 4 : 5
(C) 7 : 8
(D) 8 : 9
(E) 8 : 11
Rationale: Step 1: Let the third number is A
Then first number is 140% of A = 140 x A / 100 = 7A / 5 and second number is 160% of B = 160 x B / 100 = 8B /5.
Step 2: now ratio of first and second number is 7A / 5 : 8B / 5 = 35A : 40B = 7 : 8.
C
Answer: (C) 7 : 8
Question: An alloy of copper and aluminum has 40% copper. An alloy of Copper and Zinc has Copper and Zinc in the ratio 2:7. These two alloys are mixed in such a way that in the overall alloy, there is more aluminum than Zinc, and copper constitutes x% of this alloy. What is the range of values x can take?
(A) 30% ≤ x ≤ 40%
(B) 32.5% ≤ x ≤ 40%
(C) 32.5% ≤ x ≤ 42%
(D) 33.33% ≤ x ≤ 40%
(E) 33.33 % ≤ x ≤ 42%
Rationale: The maximum aluminium you can have is when you mix copper and aluminium alloy (say alloy A) with infinitesimally small amount of copper and zinc alloy (alloy B). In that case, you will have almost 40% of copper in the mix (because alloy A has 40% of copper). So x% < 40%.
Minimum case:
60% of alloy A > (7/9) of alloy B
A/B > 35/27
If the two alloys are mixed in this ratio, the copper concentration will be:
Using weighted average:
Cavg = (2/5 * 35 + 2/9 * 27)/(35 + 27)
Cavg = (14 + 6)/62= 20/62 = 32.26% (rounded to 2 decimal places)
So x% > 32.26%
Answer: 32.26 < x < 40
ANSWER:A
Answer: (A) 30% ≤ x ≤ 40%
Question: For four days of work, a clerk had daily earnings of $180, $170, $180, and $180 respectively. In which of the following intervals does the standard deviation of the daily earnings lie?
(A) Between $10 and $100
(B) Between $10 and $50
(C) Between $50 and $75
(D) Between $50 and $100
(E) Between $0 and $10
Rationale: The standard deviation is between 0 and 10.
The reason is that none of the numbers in the set is further away from the mean than 10(or rather Abs(170-(180*3+170)/4)). I am not fully sure how to calculate the standard deviation(I simply remember that there were some formula for calculating the average of the squared distances from the mean for all items in the set from statistics classes - variation), but I believe this will suffice for any GMAT question related to standard deviation.
Answer : E
Answer: (E) Between $0 and $10
Question: In a single throw of a die, what is the probability of getting a number greater than 2?
(A) 1/2
(B) 2/5
(C) 1/3
(D) 2/7
(E) 2/3
Rationale: S = {1,2,3,4,5,6}
E = {3,4,5,6}
Probability = 4/6 = 2/3
Answer is E
Answer: (E) 2/3
Question: 10 men can complete a work in 7 days and 10 children take 14 days to complete the work. How many days will 5 men and 10 children take to complete the work?
(A) 4
(B) 7
(C) 3
(D) 5
(E) nONE
Rationale: 1 man's 1 day's work = 1
70
1 child's 1 day's work = 1
140
(5 men + 10 children)'s day's work = 5 + 10 = 1 + 1 = 1
70 140 14 14 7
5 men and 10 children will complete the work in 7 days.
Correct Answer is B
Answer: (B) 7
Question: A man can row a boat at 20 kmph in still water. If the speed of the stream is 6 kmph, what is the time taken to row a distance of 60 km downstream?
(A) 20/6 hours
(B) 27/2 hours
(C) 30 hours
(D) 30/13 hours
(E) 20/13 hours
Rationale: Speed downstream = 20 + 6 = 26 kmph.
Time required to cover 60 km downstream = d/s = 60/26 = 30/13 hours
ANSWER:D
Answer: (D) 30/13 hours