mathewhe/aqua_rat huggingface dataset:
Question: Tracey sold her house for 40 percent more than the amount that she bought it for. If she has to pay a brokerage fee of 5 percent of the selling price of the home, and then has to pay 40 percent of the leftover profit in taxes, what is the net after-tax percent profit Tracey makes on the sale?
(A) 12%
(B) 14.4%
(C) 16%
(D) 19.8%
(E) 21%
Rationale: Lets assume Cost price is 100. Then the selling price will be 1.4*100= 140.
5% brokerage fee= 5% of 140 = 7
After brokerage amount left is 140-7=133.
Next, taxes are 40% of left over profit which is 40% of (133-100)=40% of 33 which is 19.8.
Hence answer is D.
Answer: (D) 19.8%
Question: If the ratio of the roots of the equation 16x2+px-32=0 is equal to that of the roots 8x2+rx-16=0, then:
(A) 2r=p
(B) r=p
(C) 2p=r
(D) 3p=2r
(E) None
Rationale: 16x2+px-32=0 for this eqn... roots are R1=-p/16 R2=2
8x2+rx-16=0 for this eqn... roots are R3=-r/8 R4=2
As per Question, p/-32=r/-16
=> 2r=p
ANSWER:A
Answer: (A) 2r=p
Question: A train crosses a platform of 150 m in 15 sec, same train crosses another platform of length 250 m in 20 sec. then find the length of the train?
(A) 150m
(B) 170m
(C) 180m
(D) 158m
(E) 350m
Rationale: Length of the train be ‘X’
X + 150/15 = X + 250/20
4X + 600 = 3X + 750
X = 150m
Answer: A
Answer: (A) 150m
Question: There are 13 hearts in a full deck of 52 cards. In a certain game, you pick a card from a standard deck of 52 cards. If the card is a heart, you win. If the card is not a heart, the person replaces the card to the deck, reshuffles, and draws again. The person keeps repeating that process until he picks a heart, and the point is to measure how many draws it took before the person picked a heart and, thereby, won. What is the probability that one will pick the first heart on the third draw or later?
(A) 1/2
(B) 9/16
(C) 11/16
(D) 13/16
(E) 15/16
Rationale: Here, we're told that 13 of the 52 cards are "hearts" - this is 1/4 of the deck. We're also told that after drawing a card, the card is PUT BACK in to the deck (so there will always be 52 cards to draw from).
To draw a heart for the first time on the 3rd draw (or later), the FIRST TWO draws MUST NOT be hearts....
Probability of NOT drawing a heart on the first draw = 3/4
Probability of NOT drawing a heart on the second draw = 3/4
(3/4)(3/4) = 9/16
From this point, you will eventually draw a heart (which is what the question is asking for), so the probability is 9/16.
ANSWER:B
Answer: (B) 9/16
Question: The value of {(.87)3 + (.13)3 + .87 × .39}0.5 is:
(A) 0.6
(B) 1
(C) 0
(D) 3
(E) 4
Rationale: (a^3 + b^3)=(a+b)(a^2-ab+b^2)
so, (a^2-ab+3ab+b^2) ^0.5 , here a+b=1
(0.87+0.13)^2*0.5
=1
ANSWER:B
Answer: (B) 1
Question: The difference between simple and compound interests on a certain sum for 2 years at 4% per annum is Rs.50. The sum is
(A) Rs.20,400
(B) Rs.25,000
(C) Rs.31,250
(D) Rs.38,000
(E) Rs.48,000
Rationale: difference between 2yr CI and SI is given by PR^2 ..
PR^2= 50
P*R/100*R/100=50
P*4/100*4/100 =50
P=(50*100*100)/4*4
P= 31,250
ANSWER:C
Answer: (C) Rs.31,250
Question: The sum of two consecutive even integers is 26. What are the two numbers?
(A) 14
(B) 15
(C) 16
(D) 17
(E) 18
Rationale: Solution
Let 2n be the first even integer and let 2n + 2 be the second integer
2n + 2n + 2 = 26
4n + 2 = 26
4n + 2 - 2 = 26 - 2
4n = 24
n = 6
So the first even integer is 2n = 2 × 6 = 12 and the second is 12 + 2 = 14
Answer A
Answer: (A) 14
Question: How many batteries will remain unboxed if in a factory that manufactures batteries 2 types of boxes are used to store batteries. the bigger box can store 25 batteries while the smaller box can store 18 batteries. The total number of batteries to be stored is 217.
(A) 0
(B) 1
(C) 2
(D) 7
(E) 5
Rationale: Total batteries to be stored 218
The big box can store 25
small box can store 18
storing 217 batteries in big box 218/25 =8 r 18
store remainder in small box 18/18=1 r 0
least number of batteries that will be left unboxed=0
Answer: A
Answer: (A) 0
Question: A packet of 10 electronic components is known to include 3 defectives. If 4 components are randomly chosen and tested, what is the probability of finding among them not more than one defective component.
(A) 0.6517
(B) 0.868
(C) 0.4483
(D) None of these
(E) Cannot be determined
Rationale: Explanation :
Here, the trials are independent , since the probability of defective component in any trial is not affected by the occurrence or non-occurrence of a defective component in any other trial. So, it is a case of binomial distribution.
No. of trials = n = 4.
Occurrence of a defective component is a success.
Then, the probability of success = p = 3/10.
the probability of failure = 1- p = 7/10.
Components not more than one defective one means x ≤ 1 i.e x = 0.
Using the formula,
P(x) = ncxPx(1-P)n-x.
Since,
=> P(x ≤ 1) = P(x = 0) or P(x = 1)
= P(0) + P(1) .
= 4c0(3/10)0 x (7/10)4 + 4c1(3/10)1x (7/10)3 .
= (7/10)4 + 4 x (3/10) x (7/10)3.
= 0.6517
Hence, the required probability is 0.6517.
Answer : A
Answer: (A) 0.6517
Question: The average age of a husband and a wife is 23 years when they were married five years ago but now the average age of the husband, wife and child is 22 years(the child was born during the interval). What is the present age of the child?
(A) 6
(B) 5
(C) 10
(D) 4
(E) 2
Rationale: 28 * 2 = 56
22 * 3 = 66
-----------
10 years.Answer: C
Answer: (C) 10
Question: The area of a parallelogram is 200sq m and its altitude is twice the corresponding base. Then the length of the base is?
(A) 8
(B) 9
(C) 7
(D) 10
(E) 5
Rationale: 2x * x = 200 => x= 10
Answer: D
Answer: (D) 10
Question: The sum of three integers is 19. The largest integer is 3 times the middle integer, and the smallest integer is 9 less than the largest integer. What is the product of the three integers?
(A) 132
(B) 144
(C) 156
(D) 168
(E) 180
Rationale: Let x be the middle integer. Then the largest is 3x and the smallest is 3x - 9.
3x - 9 + x + 3x = 19
x = 4
The three integers are 3, 4, and 12.
The product is 3*4*12 = 144
The answer is B.
Answer: (B) 144
Question: Which is the smallest fraction:
(A) 11/13
(B) 9/11
(C) 5/4
(D) 5/7
(E) 6/7
Rationale: 11/13=.846
9/11=.818
5/4=1.25
5/7=.714
So smallest is 5/7
ANSWER:D
Answer: (D) 5/7
Question: What is the length of the diagonal of a square whose area is 4 times of another square with diagonal as 5v2 cm?
(A) 20v2
(B) 10
(C) 10v2
(D) 20
(E) 25
Rationale: SOLUTION : 10v2
Area of square = 1/2 * (length of diagonal)2
Area of square 1 = * (5v2)2 = 25
Area of square 2 = 4*25 = 100
Length of diagonal of square 2 = v2 * area = v2 * 100 = v200 = 10v2 cm
ANSWER IS C
Answer: (C) 10v2
Question: The largest four digit number which is a perfect cube, is:
(A) 7000
(B) 8000
(C) 9261
(D) 9999
(E) None of these
Rationale: Explanation:
21*21*21 = 9261
Option C
Answer: (C) 9261
Question: A large box contains 15 small boxes and each small box contains 25 chocolate bars. How many chocolate bars are in the large box?
(A) A)220
(B) B)490
(C) C)375
(D) D)450
(E) E)690
Rationale: the only thing you have to do is a simple multiply
we have:
15*25
=375
correct answer is:
C) 375
Answer: (C) C)375
Question: A person distributed 15% of his income to his 3 children each. He deposited 30% of his income to his wife's account. He donated 10% of remaining amount to an orphan house.Finally he has $40000. Find his total income?
(A) A)266666.7
(B) B)562000
(C) C)800000
(D) D)500000
(E) E)652000
Rationale: 3 children got = 3*15% = 45%
wife got = 30%
orphan house = 10%
total = 45+30+10 = 85%
remaining = 100-85 = 15%
15% = 40000
100% = 40000*100/15 = $266666.7
Answer is A
Answer: (A) A)266666.7
Question: In a maths test, students were asked to find 5/16 of a certain number. One of the students by mistake found 5/6th of that number and his answer was 100 more than the correct answer. Find the number.
(A) 192
(B) 280
(C) 384
(D) 400
(E) 500
Rationale: Explanation:
Let the number be x.
5*x/6 = 5*x/16 + 100
25*x/48 = 100
x = 192
ANSWER A
Answer: (A) 192
Question: One day Eesha started 30 min late from home and reached her office 50 min late while driving 25% slower than her usual speed. How much time in min does eesha usually take to reach her office from home?
(A) 22
(B) 60
(C) 99
(D) 17
(E) 18
Rationale: We know that Speed is inversely proportional to time
While she drives 25% slower means she drove at 3434(S)
We know that D = S x T
When speed became 3434(S) then Time taken should be 4343(T)
i.e, She has taken 4343(T) - T extra to cover the distance.
Extra Time = T3T3 = 20 min (as 20 min late due to slow driving)
Actual time T = 60 Minutes
Answer:B
Answer: (B) 60
Question: A dealer originally bought 70 identical batteries at a total cost of q dollars. If each battery was sold at 50 percent above the original cost per battery, then, in terms of q, for how many dollars was each battery sold?
(A) 3q/140
(B) 3q/2
(C) 105q
(D) q/70
(E) 105/q
Rationale: The cost of each battery was q/70.
Each battery was sold for 1.5q/70 = 3q/140.
The answer is A.
Answer: (A) 3q/140
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) 30/18
(B) 30/29
(C) 30/12
(D) 30/13
(E) 30/82
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
Question: X can finish a work in 18 days. Y can finish the same work in 15 days. Yworked for 5 days and left the job. how many days does X alone need to finish the remaining work?
(A) 12
(B) 5
(C) 6
(D) 8
(E) 9
Rationale: Work done by X in 1 day = 1/18
Work done by Y in 1 day = 1/15
Work done by Y in 5 days = 5/15 = 1/3
Remaining work = 1 – 1/3 = 2/3
Number of days in which X can finish the remaining work = (2/3) / (1/18) = 12
A
Answer: (A) 12
Question: A tank can supply water to a village for 30 days. If a leak at the bottom of the tank drains out 15 liters per day, the supply lasts for 20 days only. For how many days will the supply last if the leak drains out 20 liters per day?
(A) 12
(B) 14
(C) 15
(D) 16
(E) 18
Rationale: Losing 15 liters per day results in a loss of 300 liters in 20 days. So, those 300 liters were for 10 days, making daily consumption of the village 30 liters per day. Thus the capacity of the tank is 30*30 = 900 liters.
Losing 20 liters plus 30 liters gives 50 liters per day. At this rate the supply will last 900/50 = 18 days.
The answer is E.
Answer: (E) 18
Question: If the least common addition of two prime numbers x and y is 10, where x > y, then the value of 2x + y is
(A) 7
(B) 9
(C) 14
(D) 17
(E) 21
Rationale: (x+y) = 10 and both x an y are prime.
The only values of x and y can be 7 and 3 (x = 7 and y = 3)
2x + y = 2*7 + 3 = 17
Correct Option: D
Answer: (D) 17
Question: Two trains, each 100 m long, moving in opposite directions, cross other in 15 sec. If one is moving twice as fast the other, then the speed of the faster train is?
(A) 76 km/hr
(B) 66 km/hr
(C) 60 km/hr
(D) 67 km/hr
(E) 32 km/hr
Rationale: Let the speed of the slower train be x m/sec.
Then, speed of the train = 2x m/sec.
Relative speed = ( x + 2x) = 3x m/sec.
(100 + 100)/15 = 3x => x = 40/9.
So, speed of the faster train = 80/9 = 80/9 * 18/5 = 32 km/hr.
Answer:E
Answer: (E) 32 km/hr
Question: The area of the floor of a class room is 10 m2 that of a longer wall 15 m2 and of the shorter wall 6 m2, find the edge of the new cube?
(A) 50 m3
(B) 30 m2
(C) 60 m3
(D) 40 m3
(E) 900 m3
Rationale: lb = 10 ; lh = 15 ; fh = 6
(lbh)2 = 10 * 15 * 6 => lbh = 30 m3
ANSWER:B
Answer: (B) 30 m2
Question: If x is an integer and 1 ≤ x ≤ 100, what is the probability that x(x + 1) is a multiple of 12 and 9?
(A) 1/25
(B) 1/20
(C) 2/25
(D) 11/100
(E) 1
Rationale: x(x+1) is a number that is divisible by both 12 and 9
for x = 27, 71,72, 80 we get number ie divisible by both 12 and 9
so probability would be 4/100 = 1/25
ANSWER:A
Answer: (A) 1/25
Question: The ratio of the present age of Viju to that of Aju is 7:2. Four years from now, the ratio of the ages of Viju to Aju will be 5:2. What was Viju age 3 years ago ? (RBI Assistant 2015)
(A) 24
(B) 20
(C) 12
(D) 15
(E) 18
Rationale: Let the present age of Viju be 7x years and that of Aju be 2x years.
Then, 4 years from now
7x + 4 / 2x + 4 = 5 / 2
or 4x = 12
or x = 3
Viju present age = 7 * 3 = 21 years
Viju age 3 years ago = 21 - 3 = 18 years
answer :E
Answer: (E) 18
Question: If log4 (x) = 12 , then log2 (x/4) is equal to what?
(A) 55
(B) 21
(C) 31
(D) 11
(E) 22
Rationale: Explanation:
log(4) x = 12. We need to find log(2) (x/4)
log(2) (x/4) = log (2) x - log(2) 4
=> log(2) x - log(2) 2^2
use log a^b = a*log b
=> log(2) x - 2 ...(1)
log(4) x = 12
=> x = 4^12
=> x = 2^2^12
=> x = 2^24
take log to base 2 of both the sides
=> log(2) x = 24
Substituting in (1)
log(2) x - 2
=> 24 - 2
=> 22
The required value of log(2)(x/4) = 22
Answer E
Answer: (E) 22
Question: 100 identical coins each with probability 'pp' showingup heads & tossed. If 0
(A) 21/311
(B) 23/321
(C) 51/101
(D) 55/413
(E) 47/321
Rationale: Let aa be the number of coins showing heads
Then, P(A=50)=P(A=51)P(A=50)=P(A=51)
⇒100C50×P50×(1−P)50⇒100C51×P51×(1−P)49⇒100C50×P51×(1−P)50=100C51×P⇒51(1âˆ′P)=50P⇒P=51/101
C
Answer: (C) 51/101
Question: Cricket match is conducted in US. The run rate of a cricket game was only 3.2 in first 10 over. What should be the run rate in the remaining 40 overs to reach the target of 272 runs?
(A) 6
(B) 6.25
(C) 7.25
(D) 7.5
(E) 8
Rationale: Required run rate = 272 - (3.2 x 10) =	240 = 6
40	40
A
Answer: (A) 6
Question: When 15 is subtracted from a number, it reduces to seven-twelve of the number. What is the sum of the digit of the number
(A) 20
(B) 24
(C) 36
(D) 48
(E) 45
Rationale: Explanation:
Let the number be x. Then,
x - 15 = 7x/12 => x - 7x/12 = 15
5x/12 = 15 => x = 36
Answer: Option C
Answer: (C) 36
Question: From the integer n, if n*n*n is odd, then what is true from below options?
(A) n is odd and n*n is even
(B) n*n is even
(C) n is odd
(D) n is even
(E) n*n is odd
Rationale: n is odd and n*n is even
Option A
Answer: (A) n is odd and n*n is even
Question: 860% of 50 + 50% of 860 =?
(A) 430
(B) 516
(C) 660
(D) 860
(E) None
Rationale: Solution
Given expression
= [860 / 100 x 50 + 50 / 100 x 860]
= 430 + 430
= 860.
Answer D
Answer: (D) 860
Question: The sum of first 45 natural numbers is:
(A) 1035
(B) 1038
(C) 1040
(D) 1045
(E) 1050
Rationale: Let Sn =(1 + 2 + 3 + ... + 45). This is an A.P. in which a =1, d =1, n = 45.
Sn = n [2a + (n - 1)d] = 45 x [2 x 1 + (45 - 1) x 1] = 45 x 46 = (45 x 23)
2 2 2
= 45 x (20 + 3)
= 45 x 20 + 45 x 3
= 900 + 135
= 1035.
Shorcut Method:
Sn = n(n + 1) = 45(45 + 1) = 1035.
2 2
A
Answer: (A) 1035
Question: Mira is making telescopes, each consisting of 2 lenses, 1 tube, and 1 eyepiece. Lenses can be purchased only in packs of 50, tubes only in packs of 10, and eyepieces only in packs of 30. However, half of the lenses in each pack are not usable for telescopes. If all parts are used only for the telescopes, what is the minimum number of lenses Mira must purchase to make a set of telescopes with no leftover components other than the unusable lenses?
(A) 60
(B) 150
(C) 1800
(D) 700
(E) 7,500
Rationale: I'd use backsolving for this question.
Check C:
1800 lenses = 900 usable lenses = 450 tubes = 450 eyepieces. We CAN buy 450 tubes and 450 eyepieces, so that not to have leftovers.
Answer: C.
Answer: (C) 1800
Question: The difference between the simple interest received from two different sources on Rs. 1500 for 3 years is Rs. 13.50. The difference between their rates of interest is
(A) A)2.4%
(B) B)2.6%
(C) C)2.0%
(D) D)0.3%
(E) E)1.3%
Rationale: (1500 * R1 * 3)/100 - (1500 * R2 * 3)/100 = 13.50 4500(R1 - R2) = 1350
R1 - R2 = 0.3%
Answer:D
Answer: (D) D)0.3%
Question: A restaurant meal cost $40 and there was no tax. If the tip was more than 12 percent but less than 13 percent of the cost of the meal, then the total amount paid must have been between
(A) $40 and $42
(B) $39 and $41
(C) $38 and $40
(D) $44 and $45
(E) $36 and $37
Rationale: The total amount for the meal was between 40*1.12=44.8 and 40*1.13=~45.2. Only option which covers all possible values of the meal is D.
Answer: D.
Answer: (D) $44 and $45
Question: A meal cost $ 35.50 adn there was no tax. If the tip was more than 15 pc but less than 25pc of the price, then the total amount paid should be:
(A) 41-44
(B) 39-41
(C) 38-40
(D) 37-39
(E) 36-37
Rationale: 15%(35.5) = 5.325
25%(35.5) = 8.875
total amount could have been 35.5+5.325 and 35.5+8.875
=> could have been between 40.825 and 44.375
=> approximately between 41 and 44
Answer is A.
Answer: (A) 41-44
Question: One half of a two digit number exceeds its one third by 4. What is the sum of the digits of the number?
(A) 6
(B) 9
(C) 11
(D) 12
(E) 15
Rationale: Explanation:
x/2 – x/3 = 4 => x =24
2 + 4 =6
A
Answer: (A) 6
Question: It takes 6 beavers 10 hours to build a certain dam, working at a uniform rate. If seven beavers start to build the same dam at noon, and one beaver per hour is added beginning at 6:00 PM, at what time will the dam be complete?
(A) 7:24 PM
(B) 7:48 PM
(C) 8:06 PM
(D) 8:32 PM
(E) 9:12 PM
Rationale: The rate of 1 beaver is 1/60.
The amount of work done by 7 beavers in 6 hours is 7/60 *6 = 42/60
In the next hour, 8 beavers do 8/60 for a total of 50/60.
In the next hour, 9 beavers do 9/60 for a total of 59/60.
In the next 6 minutes, 10 beavers do 10/60 * 6/60 = 1/60 for a total of 60/60.
The dam will be completed at 8:06 pm.
The answer is C.
Answer: (C) 8:06 PM
Question: A train crosses a platform of 160 m in 15 sec, same train crosses another platform of length 250 m in 20 sec. then find the length of the train?
(A) 110
(B) 887
(C) 167
(D) 197
(E) 161
Rationale: Length of the train be ‘X’
X + 160/15 = X + 250/20
20X + 3200 = 15X + 3750
5x=550
X = 110m
Answer: A
Answer: (A) 110
Question: Mahesh marks an article 15% above the cost price of Rs. 540. What must be his discount percentage if he sells it at Rs. 496.80?
(A) 22
(B) 88
(C) 20
(D) 88
(E) 62
Rationale: CP = Rs. 540, MP = 540 + 15% of 540 = Rs. 621
SP = Rs. 496.80, Discount = 621 - 496.80 = 124.20
Discount % = 124.2/621 * 100 = 20%
Answer:C
Answer: (C) 20
Question: A man can swim in still water at 15 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is?
(A) 3.9
(B) 5
(C) 5.3
(D) 1.5
(E) 5.2
Rationale: M = 15
S = x
DS = 15 + x
US = 15 - x
15 + x = (15 - x)2
15 + x = 30 -2x
3x = 15
x = 5
Answer:B
Answer: (B) 5
Question: The total of company C's assets in 1994 was 200% greater than the total in 1993, which in turn was 400% greater than the total in 1992. If the total of company C's assets in in 1992 was N dollars, which one of the following represents company C's assets in 1994:
(A) 7N
(B) 8N
(C) 9N
(D) 15
(E) 20
Rationale: Let's use actual numbers. Starting in 1992, let's say company C had $100 in assets.
In 1993, the total assets were 400% GREATER, which means 1992 PLUS 400% of 1992:
$100 + 4x$100 = $100 + $400 =$500
In 1994, the total assets were 200% GREATER than they were in 1993, which means 1993 PLUS 200% of 1993:
$500 + 2x$500 = $500 + $1000 =$1500
This is 15 times the 1992 number, so the correct answer is 15N.
D
Answer: (D) 15
Question: Four car rental agencies A, B, C and D rented a plot for parking their cars during the night. A parked 15 cars for 12 days, B parked 12 cars for 20 days, C parked 18 cars for 18 days and D parked 16 cars for 15 days. If A paid Rs. 1215 as rent for parking his cars, what is the total rent paid by all the four agencies?
(A) Rs. 4500
(B) Rs. 4800
(C) Rs. 5250
(D) Rs. 6642
(E) None of these
Rationale: The ratio in which the four agencies will be paying the rents = 15 * 12 : 12 * 20 : 18 * 18 : 16 * 15
= 180 : 240 : 324 : 240 = 45 : 60 : 81 : 60
Let us consider the four amounts to be 45k, 60k, 81k and 60k respectively.
The total rent paid by the four agencies = 45k + 60k + 81k + 60k= 246k
It is given that A paid Rs. 1215
45k = 1215 => k = 27
246k = 246(27) = Rs. 6642
Thus the total rent paid by all the four agencies is Rs. 6642.
ANSWER:D
Answer: (D) Rs. 6642
Question: How many 5 digit nos are there if the 2 leftmost digits are odd and the digit 4 can't appear more than once in the number ?
Could someone please provide a solution using a approach other than ( 1-x(none)) approach?
(A) 24300
(B) 25700
(C) 26500
(D) 24400
(E) 26300
Rationale: A. 4 is used once: OO**4 --> (5*5*9*9)*3: 5 choices for the first digit as there are 5 odd numbers, 5 choices for the second digit for the same reason, 9 choices for one of the two * (not-4 digit), 9 choices for another * (not-4 digit), multiplied by 3 as 4 can take the place of any of the three last digits (OO**4, OO*4*, OO4**);
B. 4 is not used: OO*** --> 5*5*9*9*9: the same logic as above.
5*5*9*9*3+5*5*9*9*9=24,300.
ANSWER:A
Answer: (A) 24300
Question: 40!^40! will end in how many zeroes?
(A) 40!
(B) 8 x 40!
(C) 9 x 40!
(D) 8^40!
(E) 9^40!
Rationale: 40/5^1 + 40/5^2 = 8+1 = 9
Ans : 9^40!
ANSWER:E
Answer: (E) 9^40!
Question: At a particular pizza shop, a pizza can be created from any combination of 6 different types of spice, 7 different types of meat, among which are pepperoni and anchovies, and 4 different types of cheese. If a customer at the shop decides to order a pizza with 1 type of spice, 2 types of cheese, and 4 types of meat but without pepperoni and anchovies together, how many possible ways to garnish the pizza are available to the customer?
(A) 6
(B) 35
(C) 120
(D) 450
(E) 900
Rationale: Number of possible ways to select 1 type of spice = 6c1 = 6
Number of possible ways to select 2 types of cheese = 4c2 = 6
Number of possible ways to select 4 types of meat but without pepperoni and anchovies together
= Total number of ways without any restriction - Total number of ways in which pepperoni and anchovies together
= 7c4 - 5c2
=35 - 10
=25
Possible ways to garnish the pizza are available to the customer = 6*6 * 25
=900
Answer E
Answer: (E) 900
Question: You collect baseball cards. Suppose you start out with 19. Maria takes half of one more than the number of baseball cards you have. Since you're nice, you give Peter 1 baseball card. Since his father makes baseball cards, Paul decides to triple your baseball cards. How many baseball cards do you have at the end?
(A) 17
(B) 18
(C) 19
(D) 20
(E) 24
Rationale: Solution
Start with 19 baseball cards.
Maria takes half of one more than the number of baseball cards you have. So Maria takes half of 19 + 1 which is 10,
so you're left with 19 - 10 = 9.
Peter takes 1 baseball card from you: 9 - 1 = 8 baseball cards.
Paul triples the number of baseball cards you have: 8 Ã— 3 = 24 baseball cards.
So you have 24 at the end.
Correct answer : E
Answer: (E) 24
Question: A baseball team won 35 percent of the first 80 games it played. How many of the remaining 82 games will the team have to win in order to have won exactly 50 percent of all the games it played?
(A) 36
(B) 45
(C) 53
(D) 55
(E) 81
Rationale: Games won out of first 80 questions = (35/100)*80 = 28
Total Games = 80+82 = 162
Games to be won = (50/100)*162 = 81
Remaining games to be won = 81-28 = 53
Answer: Option C
Answer: (C) 53
Question: What is the probability that a 4 person committee chosen at random from a group consisting of 6 men, 7 women, and 2 children contains exactly 1 woman?
(A) 77/204
(B) 56/195
(C) 11/77
(D) 308/1411
(E) 22/832
Rationale: Total possible selections = 4 out of 15 group members = 15C4
Favorable selections = 1 out of 7 women and 3 out of 8 (= 6 men + 2 children) = 7C1 * 8C3
Thus the required probability = 7C1*8C3 / 15C4 = 56/195. Thus B is the correct answer.
Answer: (B) 56/195
Question: By selling an article at Rs.800, a shopkeeper makes a profit of 25%. At what price should he sell the article so as to make a loss of 40%?
(A) s.429
(B) s.480
(C) s.429
(D) s.128
(E) s.384
Rationale: SP = 800
Profit = 25%
CP = (SP)*[100/(100+P)]
= 800 * [100/125]
= 640
Loss = 40% = 40% of 640 = Rs.256
SP = CP - Loss = 640 - 256
= Rs.384
Answer:E
Answer: (E) s.384