mathewhe/aqua_rat huggingface dataset:
Question: 10 t-shirts are available to choose. 5 of them are printed, and 5 of them are plain t-shirts. If 3 t-shirts are to be selected at random from the 10, what is the probability that at least one of them is a printed t-shirt.
(A) 1/12
(B) 7/12
(C) 5/12
(D) 11/12
(E) 13/12
Rationale: You have 10 t-shirts. You need to choose 3 of them. You can do this in 10C3 = 10*9*8/3*2*1 = 120 ways.
You have 5 plain t-shirts. You can choose 3 out of them in 5C3 = 5*4/2 = 10 ways.
So you have total 120 ways of picking 3 t-shirts out of 10. In 10 of those ways, you pick all plain t-shirts. So what happens in the rest of the 110 ways? In those, you must be picking up at least one printed t-shirt.
So probability of picking at least one printed t-shirt = 110/120 = 11/12
Answer is D
Answer: (D) 11/12
Question: All the milk in container A which was filled to its brim was poured into two containers B and C. The quantity of milk in container B was 62.5% less than the capacity of container A. If 152 liters was now transferred from C to B, then both the containers would have equal quantities of milk. What was the initial quantity of milk in container A?
(A) 1216
(B) 1723
(C) 1129
(D) 2613
(E) 1372
Rationale: A
B has 62.5% or (5/8) of the milk in A. Therefore, let the quantity of milk in container A(initially) be 8k.
Quantity of milk in B = 8k - 5k = 3k.
Quantity of milk in container C = 8k - 3k = 5k
Container: A B C
Quantity of milk: 8k 3k 5k
It is given that if 152 liters was transferred from container C to container B, then both the containers would have equal quantities of milk.
5k - 152 = 3k + 152 => 2k = 304 => k = 152
The initial quantity of milk in A = 8k = 8 * 152 = 1216 liters.
Answer: (A) 1216
Question: A walks at 10 kmph and 4 hours after his start, B cycles after him at 20 kmph. How far from the start does B catch up with A?
(A) 100km
(B) 150km
(C) 80km
(D) 120km
(E) 200km
Rationale: Suppose after x km from the start B catches up with A. Then, the difference in the time taken by A to cover x km and that taken by B to cover x km is 4 hours.
x/10 - x/20 = 4
x = 80 km
Answer is C
Answer: (C) 80km
Question: Albert and Bob are painting rooms at constant, but different rates. Albert takes 1 hour longer than Bob to paint n rooms. Working side by side, they can paint a total of 3n/6 rooms in 4/3 hours. How many hours would it take Albert to paint 3n rooms by himself?
(A) 7
(B) 9
(C) 11
(D) D.13
(E) 18
Rationale: rate of bob to paint n rooms is n/T(bob)
rate of Albert to paint n rooms is n/T(albert).
albert paints the room 1 hour slower than bob, so T (albert) = T(bob) -1
Together they paint the 3n/5 rooms in 4/3 hours. Rate is equal to work over time
Therefore
n/x + n/x-1 = (3n/5)/(4/3) =
n/x + n/x-1 = 9n/20. Fastest way for me is to think how would make the denominator 20. 4*5 = 20 and it fits x and x-1 or you can solve the quadratic
4n/20 + 5n/20 = 9n/20. Therefore you know it takes Albert 5 hours to paint n room, since Albert's rate is n/5.
6*3 = 3n
18 = 3n.
Answer is E
Answer: (E) 18
Question: A clock loses a minute every three hours for 4 days and gains 1% in the subsequent 6 days. If it was set right on Thursday at 11 AM, what will be the time at the end of 10 days?
(A) 11:54:24 AM
(B) 11:56:24 AM
(C) 12:16:40 PM
(D) 11:54:40 AM
(E) 12:06:36 PM
Rationale: Clock loses: 1 minute in 3 hours = 8 minutes in 24 hours = 32 minutes in 4 days.
Clock gains: 1% in the subsequent 6 days = 1% in 6*24*60 minutes = 86.40 minute in 6 days;
Net gain in 10 days = 86.40 - 32 = 54.4 minutes.
11AM + 54.4 minutes = 11:54 and 4/10th of a minute or 24 seconds.
Answer: A
Answer: (A) 11:54:24 AM
Question: A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?
(A) 40
(B) 56
(C) 41
(D) 42
(E) 34
Rationale: Speed = 45 * 5/18 = 25/2 m/sec
Total distance covered = 360 + 140 = 500 m
Required time = 500 * 2/25 = 40 sec
Answer: Option A
Answer: (A) 40
Question: If the average marks of three batches of 40, 50 and 60 students respectively is 45, 55, 65, what is the average marks of all the students?
(A) 56.33
(B) 34.89
(C) 23.67
(D) 54.65
(E) 43.98
Rationale: Average marks of batch1 = 45
Students in batch1 = 40
Total marks of batch1 = 40*45
Average marks of batch2 = 55
Students in batch2 = 50
Total marks of batch2 = 50 × 55
Average marks of batch3 = 65
Students in batch3 = 60
Total marks of batch3 = 65 × 60
Total students = 40 + 60 + 50 = 150
Average marks of all the students
=((40*45)+(50×55)+(65×60))/150
=169/3
=56.333
Answer is A.
Answer: (A) 56.33
Question: a, b are positive integers. The remainder of a to be divided by 5 is 2 and the remainder of b to be divided by 7 is 3.
Which is possible to be the remainder of a*b to be divided by 48
(A) a) 2
(B) b) 6
(C) c) 8
(D) d) 12
(E) e) 20
Rationale: Two ways to do it...
a=5x+2..
b=7y+3..
1) convenient way..
Take x and y as 0, and you will get a*b as 2*3=6
Answer : B
Answer: (B) b) 6
Question: What is the length of a bridge (in meters), which a train 156 meters long and travelling at 45 km/h can cross in 40 seconds?
(A) 308
(B) 320
(C) 332
(D) 344
(E) 356
Rationale: speed = 45 km/h = 45000 m / 3600 s = 25/2 m/s
In 40 seconds, the train can travel 25/2 * 40 = 500 meters
500 = length of train + length of bridge
length of bridge = 500 - 156 = 344 meters
The answer is D.
Answer: (D) 344
Question: 10 groups have applied for funding from the rec board. After dividing the budget equally among the 10, the rec board finds that there are 4 dollars left over, as funding allocations must be in whole numbers of dollars.
The next semester, the rec board has 4 times as much money to allocate to the 10 groups. How much money will be left over this semester?
(A) 2
(B) 4
(C) 6
(D) 8
(E) 0
Rationale: We can put m=10*k+4.
So 4*m=40*k+16 ---> 40*k+16 = 10*(4*m+1) +6 ---> The remainder is 6.
The answer is, therefore, (C).
Answer: (C) 6
Question: Increasing the original price of a certain item by 15 percent and then increasing the new price by 25 percent is equivalent to increasing the original price by what percent?
(A) 31.25
(B) 37.5
(C) 50.0
(D) 52.5
(E) 43.75
Rationale: We're told that the original price of an item is increased by 15% and then THAT price is increased by 25%....
IF....
Starting value = $100
+ 15% = 100 + .15(100) = 115
+ 25% = 115 + .25(115) = 115 + 28.75 = 143.75
The question asks how the final price relates to the original price. This is essentially about Percentage Change, which means we should use the Percentage Change Formula:
Percentage Change = (New - Old)/Old = Difference/Original
Doing either calculation will yield the same result:
43.75/100 = 43.75%
Final Answer:
E
Answer: (E) 43.75
Question: Two employees X and Y are paid a total of Rs. 700 per week by their employer. If X is paid 120 percent of the sum paid to Y, how much is Y paid per week?
(A) s.200.18
(B) s.240.18
(C) s.290.18
(D) s.300.18
(E) s.318.18
Rationale: Let the amount paid to X per week = x
and the amount paid to Y per week = y
Then x + y = 700
But x = 120% of y = 120y/100 = 12y/10
∴12y/10 + y = 700
⇒ y[12/10 + 1] = 700
⇒ 22y/10 = 700
⇒ 22y = 7000
⇒ y =7000/22 = Rs.318.18
E)
Answer: (E) s.318.18
Question: Sum of the squares of three numbers is 467 and the sum of their products taken two at a time is 131. Find the sum?
(A) 20
(B) 27
(C) 25
(D) 27
(E) 29
Rationale: (a + b + c)2 = a2 + b2 + c2 + 2(ab +bc + ca) = 467 + 2* 131
a + b + c = √729 = 27
B
Answer: (B) 27
Question: A train 140 m long is running at 60 kmph. In how much time wiU it pass a platform 260 m long?
(A) 21sec
(B) 22sec
(C) 23sec
(D) 24sec
(E) 26sec
Rationale: s=d/t
d=140+260=400m
s=60*5/18 m/sec=50/3 m/sec
t=400/(50/3)=1200/50=24sec
ANSWER:D
Answer: (D) 24sec
Question: Tabby is training for a triathlon. She swims at a speed of 1 mile per hour. She runs at a speed of 6 miles per hour. She wants to figure out her average speed for these two events. What is the correct answer for her?
(A) 8 mph
(B) 5.25 mph
(C) 3.5 mph
(D) 4 mph
(E) 0.5 mph
Rationale: (1 mph +6 mph)/2 = 3.5 mph
Correct option is: C
Answer: (C) 3.5 mph
Question: A charity is raising Â£1000 for disabled children. If it spends Â£20 for every Â£100 raised, how much money do they need to raise to reach the goal?
(A) A - 1200
(B) A - 1200
(C) A - 1200
(D) D - 12
(E) 155
Rationale: His overall steps are +6
take 100 - 6
take 94/6 to lowest divisible number - 90/6
This means that it will take 15 "overall" actions to reach the 90th centimeter. -15*18 steps added later
Set steps at 90. walk 10 steps. fall off - add 10 to total
15*18 + 10 = 280 steps in total
Double checking, 6*15 = 90, meaning that it took 15 forwards and backwards to reach.
It is dangerous to oversimplify so take context. For each average steps, adding 12 each time will ensure that it is a valid process that will not resulting in falling off the meter stick. At 15 overall, he falls off. but at 14, 6*14 = 84, adding 12 we get 96 which does not result in him falling off. It is completely safe to say 15 overall steps do not result in falling off.
From there, take 10 steps an on the 11th, not counted, he falls off since he was at 90.
All that's left is to count the total steps.
each overall step has 18 steps, 12 forward and 6 backward
18*15 = 270
then add the final steps 270 +10 = 280
Answer: C
Answer: (C) A - 1200
Question: There are three persons A, B and C when the age of A is added to half of the age of B, the result is equal to C's age. One-third of the age of 'B' is equal to one-fourth of the age of 'C'. If one-fifth of A's age is added to half of B's age, the result is equal to half of C's age. Then what is the age of 'B' ?
(A) 16 yrs
(B) 20 yrs
(C) 24 yrs
(D) 30 yrs
(E) 35 yrs
Rationale: Explanation :
A + B/2 = C .......(i)
B/3 = C/4 ........(ii)
A/5 + B/2 = C/2 ........(iii)
Solving these three eqns, A = 20, B = 24 and C = 32
Answer : Option C
Answer: (C) 24 yrs
Question: On average, activated yeast cells divide once every 120 minutes; that is, each individual cell divides into two individual cells over that time span. Given that a certain yeast colony consisted of 310,000 cells two hours ago, approximately how many cells will be populating the colony eight hours from now?
(A) 4,960,000
(B) 6,860,000
(C) 9,920,000
(D) 11,720,000
(E) 14,960,000
Rationale: 310,000 × 2 × 2×2×2×2 = 310,000 × 32 = C
Answer: (C) 9,920,000
Question: A train covered a distance at a uniform speed .if the train had been 6 km/hr faster it would have been 4 hour less than schedule time and if the train were slower by 6 km/hr it would have been 6 hrs more.find the distance.
(A) 720 km
(B) 820 km
(C) 920 km
(D) 620 km
(E) 780 km
Rationale: Let t be the usual time taken by the train to cover the distance
Let d be the distance, s be the usual speed
Usual time taken => d/s = t => d=ts
d/(s+6) = t-4
ts/(s+6) = t-4
ts = ts+6t-4s-24
6t - 4s - 24 = 0 --> (1)
d/(s-6) = t+6
ts = ts-6t+6s-36
-6t + 6s - 36=0 --->(2)
Solving (1) nd (2), v get
s = 30 km/h
t = 24 hrs
d = t * s
d = 30 * 24 = 720 km
ANSWER:A
Answer: (A) 720 km
Question: The speed of a boat in still water is 40kmph and the speed of the current is 20kmph. Find the speed downstream and upstream?
(A) 40, 68 kmph
(B) 40, 30 kmph
(C) 90, 60 kmph
(D) 40, 60 kmph
(E) 60, 20 kmph
Rationale: Speed downstream = 40 + 20 = 60 kmph
Speed upstream = 40 - 20 = 20 kmph
Answer: E
Answer: (E) 60, 20 kmph
Question: The Pinedale bus line travels at an average speed of 60 km/h, and has stops every 5 minutes along its route. Yahya wants to go from his house to the Pinedale Mall, which is 5 stops away. How far away, in kilometers, is Pinedale Mall away from Yahya's house?
(A) 25 km
(B) 30 km
(C) 40 km
(D) 50 km
(E) 60 km
Rationale: Number of stops in an hour: 60/5 = 12
Distance between stops: 60/12 = 5 km
Distance between Yahya's house and Pinedale Mall: 5 x 5 = 25 km
IMO, correct answer is "A."
Answer: (A) 25 km
Question: Three table runners have a combined area of 220 square inches. By overlapping the runners to cover 80% of a table of area 175 square inches, the area that is covered by exactly two layers of runner is 24 square inches. What is the area of the table that is covered with three layers of runner?
(A)  18 square inches
(B)  20 square inches
(C)  24 square inches
(D)  28 square inches
(E)  30 square inches
Rationale: Total = a + b + c - (sum of EXACTLY 2-group overlaps) - 2*(all three) + Neither
80%*175 = 220 - 24 - 2*(all three) + 0
2*(all three) = 220 - 24 - 140
all three = 28
Answer: D
Answer: (D)  28 square inches
Question: In 10 years, A will be twice as old as B was 10 years ago. If A is now 4 years older than B the present age of B is
(A) 37
(B) 38
(C) 39
(D) 34
(E) 41
Rationale: let present age of A be a and B be b
a+10 = 2*(b-10)
=> 2b-a = 30 ......(i)
a = b+4
=>2b-b-4 = 30
b=34
so the present age of b is 34 years
ANSWER:D
Answer: (D) 34
Question: Jimâ€™s Taxi Service charges an initial fee of $2.25 at the beginning of a trip and an additional charge of $0.4 for each 2/5 of a mile traveled. What is the total charge for a trip of 3.6 miles?
(A) $3.15
(B) $4.45
(C) $4.80
(D) $5.05
(E) $5.85
Rationale: Let the fixed charge of Jimâ€™s Taxi Service = 2.25 $
and charge per 2/5 mile(.4 mile) = .4$
Total charge for a trip of 3.6 miles = 2.25 + (3.6/.4) * .4
= 2.25 + 9*.4
= 5.85 $
Answer E
Answer: (E) $5.85
Question: The average weight of a class of 24 students is 35 kg. If the weight of the teacher be included, the average rises by 400 g. The weight of the teacher is :
(A) 45
(B) 46
(C) 47
(D) 48
(E) 49
Rationale: Weight of the teacher = (35.4 x 25 - 35 x 24) kg = 45 kg. Answer : A
Answer: (A) 45
Question: The number N is H,284, where H represents the ten's digit. If N is divisible by 6, what is the value of H?
(A) 1
(B) 2
(C) 3
(D) 5
(E) 8
Rationale: If the number is divisible by 6, then the sum of the digits must also be divisible by both 3 and 2. Only 1 yields such a number.
Answer: A
Answer: (A) 1
Question: How many keystrokes are needed to type numbers from 8 to 180?
(A) 360
(B) 180
(C) 325
(D) 425
(E) None of these
Rationale: Explanatory Answer
While typing numbers from 8 to 180, there are 2 single digit numbers: 8 and 9.
Each of these numbers requires one keystroke.
That is 2 key strokes.
There are 90 two-digit numbers: from 10 to 99.
Each of these numbers requires 2 keystrokes.
Therefore, 180 keystrokes to type the 2-digit numbers.
There are 81 three-digit numbers: from 100 to 180.
Each of these numbers requires 3 keystrokes.
Therefore, 243 keystrokes to type the 3-digit numbers.
Totally, therefore, one requires 2 + 180 + 243 = 425 keystrokes.
Choice D is the correct answer.
Answer: (D) 425
Question: Peter purchased 30 kg of rice at the rate of $11.50 per kg and 20 kg of rice at the rate of 14.25 per kg. He mixed the two and sold the mixture. Approximately what price per kg should be sell the mixture to make 30% profit?
(A) 17.2
(B) 15.3
(C) 16.3
(D) 19.3
(E) 10.12
Rationale: C
16.30
C.P. of 50 kg rice = (30 * 11.50 + 20 * 14.25) = $630.
S.P. of 50 kg rice = 130% of $630 = 130/100 * 630 = $819.
S.P. per kg = 819/50 = $16.38 = 16.30.
Answer: (C) 16.3
Question: How long does a train 100 m long traveling at 54 kmph takes to cross a station of 250 m in length?
(A) 22 sec
(B) 20 sec
(C) 15 sec
(D) 23 sec
(E) 16 sec
Rationale: D = 100 + 245 = 345 m
S = 54* 5/18 = 15
T = 345 * 1/15 = 23 sec
ANSWER:D
Answer: (D) 23 sec
Question: River A and River B have a combined length of 650 miles and River B is 250 miles shorter than river A. How many miles long in river B?
(A) 100
(B) 200
(C) 300
(D) 400
(E) not be determined
Rationale: Total length of River A and River B is 650 miles.
Let X be the length of River A.
River B is 250 miles shorter than River A.
x+x-250=650
2x=650+250
x=450
Length of River A=450 miles.
Length of River B=450-250
=200 miles
Answer is option B
Answer: (B) 200
Question: Three 6 faced dice are thrown together. The probability that all the three show the same number on them is
(A) 1/37
(B) 1/36
(C) 1/28
(D) 1/29
(E) 1/23
Rationale: It all 3 numbers have to be same basically we want triplets. 111, 222, 333, 444, 555 and 666. Those are six in number. Further the three dice can fall in 6 * 6 * 6
= 216 ways.
Hence the probability is 6/216
= 1/36
Answer: B
Answer: (B) 1/36
Question: Jackson has $313,193 dollars in his investment accounts. What is the least amount of money (in whole number of dollars) that he must remove from his account if he wants to split this money evenly among nine new investors?
(A) $1
(B) $2
(C) $3
(D) $4
(E) $5
Rationale: In order to divide the sum in 9 parts, the amount must also be divisible by 9
Divisibility rule of 9: The sum of the digits must be divisible by 9
Sum of digits of 313,193 = 20 and 18 is divisible by 9.
Hence we need to subtract 2 to this number for it to be divisible by 9
Correct Option: B
Answer: (B) $2
Question: The angles of a triangle are in the ratio 2: 3 : 4. Find the measurement of the 3 angles of triangle.
(A) 75°
(B) 25°
(C) 40°
(D) 80°
(E) 20°
Rationale: If the ratio of the three angles is 2:3:4, then the measures of these angles can be written as 2x, 3x and 4x. Also the sum of the three interior angles of a triangle is equal to 180°. Hence
2x + 3x + 4x = 180
Solve for x
9x = 180
x = 20
The measures of the three angles are
2x =2 x 2=40°
3x = 3 × 20 = 60°
4x = 4 × 20 = 80°
D
Answer: (D) 80°
Question: Two numbers are respectively 20% and 25% more than a third number. The percentage that is first of the second is?
(A) 86%
(B) 98%
(C) 96%
(D) 06%
(E) 92%
Rationale: I II III
120 125 100
125----------120
100-----------? => 96%
Answer:C
Answer: (C) 96%
Question: The price of a new SUV is $50,000 and you have $10,000 cash to make a down-payment. You will be able to finance the remainder of the balance over 60 months. Regarding the principle only, what percent of the original price of the SUV will you pay monthly?
(A)  1/2 %
(B)  1 %
(C)  1 1/3 %
(D)  2 %
(E)  3 %
Rationale: A certain percentage of questions in the Quant section of the GMAT are just 'math questions' - you'll use a formula, do some calculations and you'll have the answer. This is one of those types of questions. You still have to write everything down and stay organized, but the work involved is relatively straight-forward.
Original price = $50,000.
Down-payment is $10,000, which is 20% of $50,000. ($10,000/ $50,000 x 100).
80% of original price remains. (100% - 20%)
80% to be paid over 60 months.
What percent of original price will be paid monthly? (80% ÷ 60 = 1 1/3 %)
C
Answer: (C)  1 1/3 %
Question: Shipment ------No. of Defective Chips/shipment---Total Chips in shipment
S2 -------------- 5 ------------------------ ----------------------12000
S3 -------------- 6 ----------------------------------------------- 18000
S4 -------------- 4 ----------------------------------------------- 16000
A computer chip manufacturer expects the ratio of the number of defective chips to be total number of chips in all future shipments equal to the corresponding ratio for shipmemts S1,S2,S3 and S4 comined as shown in the table above. What is the expected number Q of defective chips in a shipment of 60000 chips?
(A) 14
(B) 20
(C) 22
(D) 24
(E) 25
Rationale: I agree with your solution = 20. But the question is:
There are different combination to get 60,000 chips. For example: 1*S3 + 2*S4 + 2*S2. In this way, we ship 60,000 chips with only 6 + 4*2 + 2*2 = 18 defective chips, better than the average of 20.
The question is to find the expected number Q of defective chips, i guess it assume the minimum #, therefore it might not be 20.
Answer: (B) 20
Question: Miguel is 41 years old. He is 3 years older than twice his son’s age. Find the age of his son.
(A) 11years
(B) 12years
(C) 13years
(D) 18years
(E) 19years
Rationale: sons age=x
41-2x=3
x=19years
ANSWER:E
Answer: (E) 19years
Question: The area of a rectangular plot is 20 times its breadth. If the difference between the length and the breadth is 10 metres, what is its breadth?
(A) 10 metres
(B) 5 metres
(C) 7.5 metres
(D) Data inadequate
(E) None of these
Rationale: L × B = 20 × B
∴ L = 20 m
and L – B = 10
∴ B = 20 – 10 = 10 m
Answer A
Answer: (A) 10 metres
Question: Q' = 3Q - 3, what is the value of (7')' ?
(A)  6
(B)  106
(C)  206
(D)  306
(E)  406
Rationale: (7')'=(3*7-3)'=18'=18*18-18=306
Answer D
Answer: (D)  306
Question: In a park there are two ponds with both brown ducks and green ducks. In the smaller pond there are 45 ducks and in the larger pond there are 55 ducks. If 20% of the ducks in the smaller pond are green and 40% of the ducks in the larger pond are green, then what percentage of ducks are green?
(A) 25%
(B) 27%
(C) 29%
(D) 31%
(E) 33%
Rationale: Number of ducks in small pond = 45
green ducks in small pond = 20 % of 45 = 9 ducks
Number of ducks in large pond = 55
green ducks in large pond = 40 % of 55 = 22 ducks
Total number of ducks = 45 + 55 = 100
total number of green ducks = 9 + 22 = 31 ducks
percentage of green ducks = 31/100 * 100 = 31%
Answer: D
Answer: (D) 31%
Question: People were sitting in a circle.7th one is direct opposite to 18th one..Then how many were there in that group?
(A) 21
(B) 22
(C) 23
(D) 24
(E) 20
Rationale: 7 th one is exactly opposite represents half of circle. with 7 and 18 total members are 12
for remaing half=12*2-2(7th and 18th(already taken))=22
ANSWER:B
Answer: (B) 22
Question: If 3^x = 2, then 3^(4x+3) =
(A) 429
(B) 454
(C) 432
(D) 438
(E) 108
Rationale: 3^x=2
3^4x=2^4
3^4x=16
3^(4x+3)
=3^4x*3^3
=16*27
=432
Answer: C
Answer: (C) 432
Question: A perfect square is defined as the square of an integer and a perfect cube is defined as the cube of an integer. How many positive integers n are there such that n is less than 20,000 and at the same time n is a perfect square and a perfect cube?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: If n is a perfect square and a perfect cube, then n = a^6 for some integer a.
The numbers are 1^6=1, 2^6=64, 3^6= 729, 4^6=4096, 5^6=15,625.
The answer is C.
Answer: (C) 5
Question: There are 35 students in a hostel. If the no. of students increases by 7, the expenses of the mess increase by Rs.42/day while the average expenditure per head diminishes by Rs1. Find the original expenditure of the mess?
(A) 38
(B) 40
(C) 42
(D) 45
(E) 80
Rationale: Suppose the average join the mess , total expenditure = 35x + 42
Now, the average expenditure = (35x + 42)/ (35 + 7) = x – 1
or, 35x + 42 = 42x – 42
or, x = 12
Thus the original expenditure of the mess = 35 x 12 = Rs. 42
C
Answer: (C) 42
Question: A certain fraction has the same ratio to 1/36, as 4/7 does to 5/9. What is this certain fraction?
(A) 1/35
(B) 1/42
(C) 1/49
(D) 1/56
(E) 1/63
Rationale: x / (1/36) = (4/7) / (5/9)
x = 4*9*1 / 36*7*5 = 1/35
The answer is A.
Answer: (A) 1/35
Question: A man has some hens and cows. If the number of heads be 50 and the number of feet equals 144, then the number of hens will be
(A) 22
(B) 24
(C) 26
(D) 20
(E) 28
Rationale: Explanation :
Let number of hens = h and number of cows = c
number of heads = 50
=> h + c = 48 ---(Equation 1)
number of feet = 144
=> 2h + 4c = 144
=> h + 2c = 72 ---(Equation 2)
(Equation 2) - (Equation 1) gives
2c - c = 72 - 50=> c = 22
Substituting the value of c in Equation 1, we get
h + 22 = 50
=> h = 50 - 22 = 28
i.e., number of hens = 28
Answer : E
Answer: (E) 28
Question: 34, 45, 56, 67,78, _ ?
(A) 33
(B) 82
(C) 99
(D) 89
(E) 27
Rationale: ANSWER: D
Answer: (D) 89
Question: Raman mixed 24 kg of butter at Rs. 150 per kg with 36 kg butter at the rate of Rs. 125 per kg. At what price per kg should he sell the mixture to make a profit of 40% in the transaction?
(A) Rs.689
(B) Rs.179
(C) Rs.189
(D) Rs.187
(E) Rs.119
Rationale: CP per kg of mixture = [24(150) + 36(125)]/(24 + 36)
= Rs. 135
SP = CP[(100 + profit%)/100]
= 135 * [(100 + 40)/100]
= Rs.189.
Answer:C
Answer: (C) Rs.189