mathewhe/aqua_rat huggingface dataset:
Question: When n liters of fuel was added to a tank that was already 2/3 full, the tank was filled to 7/9 of its capacity. In terms of n, what is the capacity of the tank, in liters?
(A) 10/9 n
(B) 4/3 n
(C) 3/2 n
(D) 9/4 n
(E) 9n
Rationale: E is the answer.
To solve this problem, draw diagram or use algebra. I'm more comfortable with algebra.
Given
- tank was already 2/3 full.
- When n ltr added, it became 7/9
So 2/3 + n = 7/9
n = 7/9 - 6/9
n = 1/9
capacity of the tank is full fraction . i.e. 1 i.e. 9/9
so the question is 9/9 is how much times n
= 9/9 = 1 = xn
so x = 9/1
and total = 9/1n=9n
Answer: (E) 9n
Question: A box contains 13 apples, 12 of which are red. An apple is drawn from the box and its color is noted before it is eaten. This is done a total of n times, and the probability that a red apple is drawn each time is less than 0.5. What is the smallest possible value of n?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: P(choosing a red apple 7 times in a row) = 12/13*11/12*10/11*9/10*8/9*7/8*6/7 = 6/13 < 0.5
The answer is E.
Answer: (E) 7
Question: 96 is divided into two parts in such a way that seventh part of first and ninth part of second are equal. Find the smallest part?
(A) 88
(B) 66
(C) 42
(D) 11
(E) 43
Rationale: x/7 = y/9 => x:y = 7:9
7/16 * 96 = 42
Answer: C
Answer: (C) 42
Question: The diagonals of a rhombus are 12 cm and 10 cm. Find its area?
(A) 158
(B) 129
(C) 150
(D) 123
(E) 60
Rationale: 1/2 * 12 * 10 = 60
Answer:E
Answer: (E) 60
Question: The length of the bridge, which a train 160 meters long and travelling at 45 km/hr can cross in 30 seconds, is?
(A) 266
(B) 288
(C) 245
(D) 215
(E) 232
Rationale: Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time = 30 sec. Let the length of bridge be x meters. Then, (160 + X)/30 = 25/2 ==> 2(160 + X) = 750 ==> X
= 215 m.
Answer:D
Answer: (D) 215
Question: How many trailing zeros will be there after the rightmost non-zero digit in the value of 25! (factorial 25)?
(A) 25
(B) 8
(C) 6
(D) 5
(E) 2
Rationale: Explanatory Answer
25! means factorial 25 whose value = 25 * 24 * 23 * 22 *....* 1
When a number that has 5 as its factor is multiplied by an even number, it results in a trailing zero.
(Product of 5 and 2 is 10 and any number when multiplied with 10 or a power of 10 will have one or as many zeroes as the power of 10 with which it has been multiplied)
In 25!, the following numbers have 5 as their factor: 5, 10, 15, 20, and 25.
25 is the square of 5 and hence it has two 5s in it.
In toto, it is equivalent of having six 5s.
There are at least 6 even numbers in 25!
Hence, the number 25! will have 6 trailing zeroes in it.
Choice C
Answer: (C) 6
Question: A no.when divided by 142 gives a remainder 110, what remainder will be obtainedby dividingthe same no.14?
(A) 16
(B) 17
(C) 18
(D) 19
(E) 20
Rationale: 142 + 110 = 252/14 = 18 (Remainder)
C
Answer: (C) 18
Question: In a 100 m race between Rose and Diane, Rose lost to Diane by 0.75 m. If Diane was given a 7 m head start , how many meters more will it take before Rose overtakes Diane?
(A) 12.91m
(B) 11.91m
(C) 12.5m
(D) 10.91m
(E) 13.91m
Rationale: Distance Rose ran before completion of race---100 m-0.75m=99.25m
Distance gained on Diane over 99.25m---7m-0.75m=6.25
then Rose gains 99.25/6.25m = 1m on Kelly every 15.88 meters.
Therefore 15.88 divided by 0.75 of 1 meter.
ANSWER: B. 11.91m
Answer: (B) 11.91m
Question: The blood group of 200people is distributed as follows: 50 have A group, 65have B group, 70have O blood type and 15have type AB group. If a person from this group isselected at random, what is the probability that this person has O group type?
(A) 0.35
(B) 0.5
(C) 1
(D) 1.23
(E) 1.25
Rationale: We construct a table of frequencies for the the blood groups as follows
group frequency
a 50
B 65
O 70
AB 15
We use the empirical formula of the probability
Frequency for O blood
P(E)= ________________________________________________
Total frequencies
= 70 / 200 = 0.35
A
Answer: (A) 0.35
Question: 45 persons can repair a road in 12 days, working 5 hours a day. In how many days will 30 persons, working 6 hours a day, complete the work?
(A) 10
(B) 15
(C) 13
(D) 18
(E) 19
Rationale: Let the required number of days be x.
Less persons, More days (Indirect Proportion)
More working hours per day, Less days (Indirect Proportion)
Persons 30 : 45 :: 12 : x
Working hours/day 6 : 5
30 x 6 x x = 45 x 5 x 12
x = (45 x 5 x 12)/(30 x 6)
x = 15
ANSWER B
Answer: (B) 15
Question: A and B invests Rs.3500 and Rs.4000 respectively in a business. If A doubles his capital after 6 months. In what ratio should A and B divide that year's profit?
(A) 21:5
(B) 21:16
(C) 21:2
(D) 9:9
(E) 21:11
Rationale: (3.5*6 + 7*6): (4*12)
63:48 =>
21:16
Answer:B
Answer: (B) 21:16
Question: P,Q and R together earn Rs.1710 in 9 days. P and R can earn Rs.600 in 5 days. Q and R in 7 days can earn Rs.910. How much amount does R can earn per day?
(A) s.40
(B) s.60
(C) s.90
(D) s.100
(E) s.120
Rationale: Explanation :
Amount Earned by P,Q and R in 1 day = 1710/9 = 190 ---(1)
Amount Earned by P and R in 1 day = 600/5 = 120	---(2)
Amount Earned by Q and R in 1 day = 910/7 = 130	---(3)
(2)+(3)-(1) => Amount Earned by P , Q and 2R in 1 day
- Amount Earned by P,Q and R in 1 day = 120+130-190 = 60
=>Amount Earned by R in 1 day = 60
Answer : Option B
Answer: (B) s.60
Question: If 45-[28-{37-(15-*)}]= 55, then * is equal to:
(A) -29
(B) -19
(C) 16
(D) 29
(E) 39
Rationale: 45-[28-{37-(15-*)}]= 55 => 45-[28-{37-15+*}]=55
45-[28-37+15-*]=55 => 45[43-37-*]=55
45-[6-*]=55 => 45-6+*=55
39+*=55 => *=55-39
= 16
ANSWER:C
Answer: (C) 16
Question: A factory has a fixed cost of $40,000 a month, and a cost of $2.5 for every item produced. If the selling price of a single item is $5, what is the number of items must be sold monthly for the factory to cover its cost exactly?
(A) 9,000
(B) 14,000
(C) 16,000
(D) 22,500
(E) 27,000
Rationale: selling price - Cost price = 2.5 so per unit profit =2.5
cost to recover =40000
no of items required = 40000/2.5 = 16000
Ans C
Answer: (C) 16,000
Question: What will be the difference in simple and compound interest on 6000 after three years at the rate of 10 percent per annum?
(A) 160
(B) 186
(C) 62
(D) 20
(E) None of these
Rationale: For 3 years:
Diff.=Sum×(rate)2(300+rate)/(100)3
= 6000×10×10×310/100×100×100 = 186
Answer B
Answer: (B) 186
Question: X and Y are both integers. If X/Y = 59.40, then what is the sum of all the possible two digit remainders of X/Y?
(A) 450
(B) 616
(C) 672
(D) 900
(E) 1024
Rationale: Remainder = 0.40 --> 40/100 --> Can be written as (40/4) / (100/4) = 10/25
So remainders can be 10, 20, 30, 40, ..... 90.
We need the sum of only 2 digit remainders --> 10 + 20 + 30 + 40 + 50 + 60 + 70+ 80 + 90 =450
Answer: A
Answer: (A) 450
Question: A retailer buys a radio for Rs 232. His overhead expenses are Rs 15. He sellis the radio for Rs 300. The profit percent of the retailer is
(A) 10%
(B) 50%
(C) 21.4%
(D) 52%
(E) None of these
Rationale: Explanation:
cost price = (232 + 15) = 247 sell price = 300
gain = (53/247)*100 = 21.4%. Answer: C
Answer: (C) 21.4%
Question: Aman started a business investing Rs. 65,000. Rakhi joined him after six months with an amount of Rs. 1,05,000 and Sagar joined them with Rs. 1.4 lakhs after another six months. The amount of profit earned should be distributed in what ratio among Aman, Rakhi and Sagar respectively, 3 years after Aman started the business?
(A) 10:105:112
(B) 78:105:112
(C) 72:105:112
(D) 74:105:112
(E) 16:105:112
Rationale: Explanation:
Aman : Rakhi : Sagar = (65000 * 36) : (105000 * 30) : (140000 * 24)
= 78:105:112
Answer: B
Answer: (B) 78:105:112
Question: Find the fourth proportional to 33.6 , 41.2 and 48.9?
(A) 59.96
(B) 56.15
(C) 52.39
(D) 58.96
(E) 57
Rationale: Formula= Fourth proportional =(b x c)/a
a=33.6 , b=41.2 and c=48.9
(41.2 x 48.9)/33.6=59.96
A
Answer: (A) 59.96
Question: Calculate the share of Y , if Rs. 2690 is divided among X, Y and Z in the ratio 5 : 7 : 9?
(A) 890.7
(B) 826.7
(C) 895.7
(D) 896.7
(E) 816.7
Rationale: 5 + 7 + 9 =21
2690/21=128.1
Y's share =7*128.1
=896.7
ANSWER:D
Answer: (D) 896.7
Question: The rate of increase of the price of sugar is observed to be three percent more than the inflation rate expressed in percentage. The price of sugar, on January 1, 1994, is Rs. 25 per kg. The inflation rate for the years 1994 and 1995 are expected to be 12% each. The expected price of sugar on January 1, 1996 would be
(A) 33.06
(B) 34.1
(C) 34.2
(D) 24.6
(E) None of these
Rationale: Explanation :
Increase in the price of sugar = (12+3)= 15%
Hence, price of the sugar on Jan 1, 1996
=> (25 * 115 * 115)/( 100 * 100 ) = Rs 33.06.
Answer : A
Answer: (A) 33.06
Question: The ratio between the sale price and the cost price of an article is 6:4. What is the ratio between the profit and the cost price of that article?
(A) 23
(B) 1:2
(C) 2:5
(D) 3:5
(E) 25
Rationale: C.P. = Rs. 4x and S.P. = Rs. 6x.
Then, Gain = Rs. 2x
Required ratio = 2x : 4x = 1:2
B
Answer: (B) 1:2
Question: 40 men can catch 200 sharks in 20 days working 6 hours a day. In how many days 25 men can catch 300 sharks working 4 hours a day?
(A) 30
(B) 34
(C) 24
(D) 20
(E) 50
Rationale: We have, M1D1H1/W1 = M2D2H2/W2
40*20*6/200 = 25*D2*4/300
D2= 40*20*6*300/200*25*4 = 24
ANSWER:C
Answer: (C) 24
Question: What is the CP of Rs 100 stock at 7 discount, with 1/5% brokerage?
(A) 93.9
(B) 96.3
(C) 93.2
(D) 96.7
(E) 96.21
Rationale: Explanation:
Use the formula,
CP= 100 â€“ discount + brokerage%
CP= 100-7+1/5
93.2
Thus the CP is Rs 93.2.
ANSWER: C
Answer: (C) 93.2
Question: For a fundraising dinner, a florist is asked to create flower arrangements for 8 tables. Each table can have one of the two types of bouquets available, one with a single type of flower or one with three different types of flowers. If the florist wants to make each table unique, what is the least number of types of flowers he needs?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
Rationale: Looking for (n + nC3) = 8
2 types of flower arrangements: some with 1 flower and some with 3 different flowers.
Therefore, total number of arrangements we could make from n different types of flowers = (n + nC3).
Since 4C3 = 4 (nC(n-1) always equals n combinations i.e. nC(n-1) = n),	(n + nC3) = (4 + 4C3) = (4 + 4) = 8
Aim to get 8 distinct floral arrangements, 4 different types of flowers is the answer.
Answer: A
Answer: (A) 4
Question: When N is divided by T, the quotient is A and the remainder is V. Which of the following expressions is equal to N?
(A) ST
(B) S + V
(C) ST + A
(D) T(S+V)
(E) T(S – V)
Rationale: Using the rule dividend = Quotient * divisor + remainder =>ST + A C is correct
Answer: (C) ST + A
Question: If the original mass of an element, in grams, is a whole number and the element has decayed by exactly 93 percent in some time period, which of the following could be the final mass of that element?
(A) 27 grams
(B) 30 grams
(C) 29 grams
(D) 31 grams
(E) 35 grams
Rationale: Let original mass be 100
The final mass of that element will be 7
So whatever option we have it will be divisible by 7
Check for the options the one that doesn't produce non terminating decimal is our answer
A. 27 grams
27/7 = 3.857...
B. 30 grams
28/7 = 4.285...
C. 29 grams
29/7 = 4.142.......
D. 31 grams
31/7 = 4.428.....
E. 35 grams
35/7 = 5
Hence our answer will be (E)
Answer: (E) 35 grams
Question: 2 hours after train A leaves Lucknow a train B leaves the same stationtraveling in the same direction at an average speed of 20 km/hr. After traveling 6 hrsthe train B overtakes the train A. What is the average speed of the train A?
(A) 15 km/hr
(B) 16 km/hr
(C) 17 km/hr
(D) 18 km/hr
(E) None of these
Rationale: Explanation :
Total distance covered by B=20*6=120kmTotal time taken by A to cover same distance=2+6=8 hrsaverage speed of A=120/8=15 km/hr
Answer : A
Answer: (A) 15 km/hr
Question: If X:Y is 1:2 and Y:Z is 2:5 then X:Z is equal to
(A) 2:5
(B) 3:5
(C) 1:5
(D) 4:5
(E) 1:3
Rationale: The two ratios given are having the same number 2 for Y in both the ratios.
Hence- X:Y = 1:2 Y:Z = 2:5
=> X:Z = 1:5
Answer C
Answer: (C) 1:5
Question: man buys an article for 10% less than its value and sells it for 10% more than its value. His gain or loss percent is?
(A) 12
(B) 76
(C) 26
(D) 20
(E) 12
Rationale: Let the article be worth Rs. x.
C.P. 90% of Rs. x = Rs. 9x/10
S.P. = 110% of Rs. x = Rs. 11x/10
Gain = (11x/10 - 9x/10) = Rs. x/5
Gain % = x/5 * 10/9x * 100 = 22 2/9 % > 20%
Answer: D
Answer: (D) 20
Question: When Jessica withdrew $200 from her bank account, her account balance decreased by 2/5. If she deposits an amount equal to 1/3 of the remaining balance, what will be the final balance in her bank account?
(A) 300
(B) 375
(C) 400
(D) 500
(E) 575
Rationale: As per the question 200=2a/5
thus- a which is the total amount =500
The amount thus left =300
She then deposited 1/3 of 300=100
total amount in her account =400
Answer C
Answer: (C) 400
Question: The sum of all consecutive odd integers from −27 to 37, inclusive, is
(A) 110
(B) 135
(C) 150
(D) 165
(E) 235
Rationale: The sum of the odd numbers from -27 to +27 is 0.
Let's add the remaining numbers.
29+31+33+35+37 = 5(33) = 165
The answer is D.
Answer: (D) 165
Question: A cistern has a leak which would empty the cistern in 20 minutes. A tap is turned on which admits 4 liters a minute into the cistern, and it is emptied in 24 minutes. How many liters does the cistern hold?
(A) 480
(B) 289
(C) 279
(D) 276
(E) 911
Rationale: 1/x - 1/20 = -1/24
x = 120
120 * 4 = 480
Answer:A
Answer: (A) 480
Question: In the quadrilateral PQRS d=7 cm, h1=4.2 cm and
h2=2.1 cm. Find the area
(A) 21
(B) 22
(C) 23
(D) 24
(E) 25
Rationale: area of quad.=1/2*any diagonal*(sum of 2 perpendiculars which is drawn on that diagona)
so 1/2*7*(4.2+2.1)=22.05
ANSWER:B
Answer: (B) 22
Question: There are 200 cats in Cat-City. Out of the 200, 70 are street cats and the rest are domestic cats. 110 cats are gray, 50 out of the gray cats are NOT domestic ones. How many domestic cats are there which are not gray in Cat-City?
(A) 90.
(B) 70.
(C) 50.
(D) 40.
(E) 25.
Rationale: STREET-CAT DOMESTIC-Cat
70 130
(50gray+20other) 60gray+70other
Answer:B
Answer: (B) 70.
Question: Bhaman travelled for 15 hours. He covered the first half of the distance at 40 kmph and remaining half of the distance at 10 kmph. Find the distance travelled by Bhaman?
(A) 240
(B) 230
(C) 260
(D) 220
(E) 340
Rationale: Let the distance travelled be x km.
Total time = (x/2)/40 + (x/2)/10 = 15 => x/80 + x/20 = 15 => (x + 4x)/80 = 15
=> x = 240 km
Answer:A
Answer: (A) 240
Question: A group of students decided to collect as many paise from each member of group as is the number of members. If the total collection amounts to Rs. 3025., the number of the member is the group is:
(A) 55
(B) 67
(C) 77
(D) 87
(E) 97
Rationale: Money collected = (30.25 x 100) paise = 3025 paise.
Number of members =Square root of 3025 = 55.
Answer: Option A
Answer: (A) 55
Question: What ratio must a shopkeeper mix Peas and Soybean of Rs.16 and Rs. 25/kg, As to obtain a mixture of Rs.21?
(A) 10 : 7
(B) 9 : 8
(C) 4 : 5
(D) 13 : 11
(E) 14 : 8
Rationale: Correct option: (C)
Use rule of alligation, to determine the ratio
The required ratio of Soybean and Peas = 4 : 5
Answer: (C) 4 : 5
Question: A rectangular window is twice as long as it is wide. If its perimeter is 20 feet, then what are its dimensions in feet?
(A) 3/2 by 7/2
(B) 5/3 by 10/3
(C) 2 by 4
(D) 3 by 6
(E) 10/3 by 20/3
Rationale: Let x be the width of the window. Then the length is 2x.
x+2x+x+2x = 20
6x = 20
x = 20/6 = 10/3
The width is 10/3 and the length is 20/3.
The answer is E.
Answer: (E) 10/3 by 20/3
Question: Dick and Jane each saved $2,000 in 1989. In 1990 Dick saved 10 percent more than in 1989, and together he and Jane saved a total of $4,000. Approximately what percent less did Jane save in 1990 than in 1989?
(A) 10%
(B) 20%
(C) 25%
(D) 30%
(E) 35%
Rationale: 1990
Dick saved = $ 2200
Jane saved = $ 1800 (jane saved $200 less than she did the prior year)
Jane saved approximately $200/2000$ (10%) less in 1990
Answer: A
Answer: (A) 10%
Question: A train runs at the speed of 72 kmph and crosses a 250 m long platform in 26 seconds. What is the length of the train?
(A) 300 m
(B) 270 m
(C) 200 m
(D) 250 m
(E) 260 m
Rationale: speed = 72*5/18 = 20 m/sec
t = 26 sec
length => x
x+250 = 520
x= 270
ANSWER B
Answer: (B) 270 m
Question: X can lay railway track between two station in 16; Y can do the same work in 20 days,both are working together for 2 days after Y left the job then how many days X requires to complete the remaining work ? Total number of days taken to complete the whole work?
(A) 7 Days and 9 days
(B) 5.89 Days and 7.89 days
(C) 8.26 Days and 10.26 days
(D) 7.75 Days and 9.75 days
(E) 9 Days and 11 days
Rationale: First take LCM of (16,20) = 160; Total work = 160; X's one day work = 160/16 =10; Y's one day work =160/20 = 8; One day work of both X+Y= 10+8 = 18; Total work completed in 2 days = 18*2=36; remaining work is = 160 - 36 =124; remaining work completed by X in = 124/16= 7.75 days.Total number of days taken to complete the whole work = 2+7.75 = 9.75 days.
Answer =D
Answer: (D) 7.75 Days and 9.75 days
Question: In a certain growth fund, 3/5 of the investment capital is invested in stocks, and of that portion, 1/3 is invested in preferred stocks. If the mutual fund has $845,000 invested in preferred stocks, what is the total amount of money invested in the fund?
(A) $1,974,000
(B) $2,538,000
(C) $3,264,000
(D) $3,826,000
(E) $4,225,000
Rationale: Portion invested in preferred stock = 3/5 * 1/3 = 1/5
1/5 of fund = 845---
Fund = 5 * 845---
Here, we can avoid the math and simply look at 5 * 5 -> 25. Only option E has 25 in it.
Answer (E).
Answer: (E) $4,225,000
Question: By selling an article at Rs.600, a profit of 25% is made. Find its cost price?
(A) 228
(B) 200
(C) 279
(D) 480
(E) 221
Rationale: SP = 600
CP = (SP)*[100/(100+P)]
= 600 * [100/(100+25)]
= 600 * [100/125] = Rs.480.Answer:D
Answer: (D) 480
Question: If two sides of a triangle have lengths 4 and 7, which of the following could be the perimeter of the triangle?
I. 9
II. 15
III. 19
(A) None
(B) I only
(C) II only
(D) II and III only
(E) I, II, and III
Rationale: Let x be the length of the third side.
7-4 < x < 7+4
3 < x < 11
14 < perimeter < 22
The answer is D.
Answer: (D) II and III only
Question: A can run a kilometer race in 4 1/2 min while B can run same race in 5 min. How many meters start can A give B in a kilometer race, so that the race mat end in a dead heat?
(A) 188m
(B) 278m
(C) 887m
(D) 100m
(E) 776m
Rationale: A can give B (5 min - 4 1/2 min) = 30 sec start.
The distance covered by B in 5 min = 1000 m.
Distance covered in 30 sec = (1000 * 30)/300 = 100 m.
A can give B 100m start.
Answer: D
Answer: (D) 100m
Question: Two trains start simultaneously from opposite ends of a 140-km route and travel toward each other on parallel tracks. Train X, traveling at a constant rate, completes the 140-km trip in 4 hours. Train Y, travelling at a constant rate, completes the 140-km trip in 3 hours. How many kilometers had Train X traveled when it met Train Y?
(A) 60
(B) 64
(C) 68
(D) 72
(E) 76
Rationale: If the two trains cover a total distance D, then Train X travels (3/7)*D while Train Y travels (4/7)*D. If the trains travel 140 km to the meeting point, then Train X travels (3/7)*140 = 60 km.
The answer is A.
Answer: (A) 60
Question: The area of a circle is subtracted from its diameter, and the circumference is then added to this total, the result is 0. What is the radius of the circle?
(A) 2*pi
(B) pi
(C) 1
(D) 2
(E) 3
Rationale: The equation is; diameter - Area + Circumference = d - A + C = d - pi * r^2 + 2 * pi * r = 2r - pi * r(r + 2).
By plugging in the answers we can test the answers quickly; then, 2 is the only possible answer.
Answer: D
Answer: (D) 2
Question: Bullock likes to keep a spare tyre in his car every time. On a certain day, he travels 1, 30,000 km and just to make the most of all the tyres, he changes the tyres between his journey such that each tyre runs the same distance.
What is the distance traveled by each tyre?
(A) 104,000
(B) 60,000
(C) 80,000
(D) 90,000
(E) 10,000
Rationale: The distance traveled by each tyre:
4/5 * 1, 30, 000km = 104,000 km. A
Answer: (A) 104,000
Question: On a certain day, mangrov farm harvested 4267 apples. If mangrov distributes his apples evenly across 7 different retail shops, how many apples would remain with him.
Options:
(A) 1 apple
(B) 2 apple
(C) 3 apple
(D) 4 apple
(E) 5 apple
Rationale: This is equivalent to finding the first number that is divisible by 7 that occurs before 4267.
In order to divide the sum in 7 parts, the amount must be divisible by 7
Divisibility rule of 7: The sum of the digits must be divisible by 7
Sum of digits of 4267 = 19 and 7 is divisible by 7.
Hence, we need to remove 5 to this number for it to be divisible by 7
Correct Option:E
Answer: (E) 5 apple
Question: In a group of ducks and cows, the total number of legs are 34 more than twice the no. of heads. Find the total no.of buffaloes.
(A) 11
(B) 12
(C) 14
(D) 17
(E) 18
Rationale: Let the number of buffaloes be x and the number of ducks be y
=> 4x + 2y = 2 (x + y) + 34
=> 2x = 34 => x = 17
D
Answer: (D) 17
Question: A shop owner sells 15mtr of cloth and gains SP of 10 mtrs. Find the gain %?
(A) 30%
(B) 40%
(C) 50%
(D) 100%
(E) 200%
Rationale: Here, selling price of 10 m cloth is obtained as profit.
Profit of 10 m cloth = (S.P. of 15 m cloth) – (C.P. of 15 m cloth)
Selling price of 5 m cloth = Selling Price of 15 m of cloth
Let cost of each metre be Rs. 100.
Therefore, cost price of 5 m cloth = Rs. 500 and S.P. of 5 m cloth = Rs. Rs. 1500
Profit% = 1000/500 × 100 = 200%
Profit of 200% was made by the merchant.
E
Answer: (E) 200%
Question: The positive number x is q percent greater than the positive number b, which is p percent less than x itself. If a is increased by p percent, and the result is then decreased by q percent to produce a positive number c, which of the following could be true?
I. c > x
II. c = x
III. c < x
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) II and III only
Rationale: Let q = 10% then p = 100/11 %
let b = 100 then x = 110
after increasing x by p and decreasing by q we get c= 108
therefore c<x
C it is answer
Answer: (C) III only
Question: A certain company had a total annual expenditure of 2.55∗10^7 on employee salaries last year. If the company employed 425 people, what was the average employee salary?
(A) $60,000
(B) $25,000
(C) $35,000
(D) $40,000
(E) $45,000
Rationale: Given: Total annual expenditure of 2.55∗10^7 on employee salaries
Total employees = 425
Observe that 425*6 = 2550
Therefore try to bring the numerator in terms of 2550
Average salary = (2550*10^4) /425 = 6*10^4 = 60,000
Option A
Answer: (A) $60,000
Question: In a class of students, the ratio of girls to boys is 1:2. If 3 more girls joined the class, the ratio would be 3:4. How many students are in the class?
(A) 16
(B) 18
(C) 20
(D) 22
(E) 24
Rationale: Let x be the number of students in the class.
(1/3)*x=(3/7)(x+3)-3
7x=9x+27-63
2x=36
x=18
The answer is B.
Answer: (B) 18
Question: A fair coin is tossed 3 times. What is the probability of getting at least 2 heads?
(A) 3/4
(B) 3/2
(C) 1/4
(D) 1/2
(E) 1/5
Rationale: Let's find the probability of 2 heads , 3 heads
P(HHH)=((1/2)^3=1/8.
P(HHT)=(3!/2!)*(1/2)^3=3/8
Total Probablity = 1/8 + 3/8
=1/2
Answer(D)
Answer: (D) 1/2
Question: Which one of the following is the sum of the numbers 1, 3, 5, 7, 9â€¦. up to nth number?
(A) N2 + 1
(B) N2 - 1
(C) N(N + 1)/2
(D) N2
(E) N(N + 1)
Rationale: Explanation:
N2
Answer: D
Answer: (D) N2
Question: A car costs a dealer Rs.50,000.Dealer raised price by Rs.10,000 and then deducted 4% of new price.
What is the profit/loss %?
(A) 14
(B) 15
(C) 15.2%
(D) 16
(E) 17.2%
Rationale: Ans: Let P be the percentage of price raised=(10000/500000) * 100 =20%
Discount %=4%
profit %=(20-4- 20*4/100 ) =15.2%
Answer C
Answer: (C) 15.2%
Question: If 'c' is a positive integer exactly divisible by 6 or 5 but not divisible by 12.What could possibly be the value of 'c' ?
(A) 30
(B) 60
(C) 120
(D) 24
(E) 72
Rationale: 60 and 120 are both divisible by 6 and 5 but also by 12. so they are not the right answer.
24 and 72 are both clearly not divisible by 5(not correct)
30 is both divisible by 6 and 5 but not by 12.
answer : (A) 30
Answer: (A) 30