mathewhe/aqua_rat huggingface dataset:
Question: The average (arithmetic mean) of 7, 8, 10 and 11 equals the average of 2, 9, 13, and
(A) 7
(B) 9
(C) 10
(D) 12
(E) 13
Rationale: 7 + 8 + 10 + 11 = 2 + 9 + 13 + x
36 = 24 + x
Or, x = 12
Hence, Answer will be (D) 12
Answer: (D) 12
Question: 34.95 + 240.016 + 23.98 = ?
(A) 298.946
(B) 298.694
(C) 289.496
(D) 289.469
(E) 298.964
Rationale: 34.95
240.016
+ 23.98
--------
298.946
Answer is A.
Answer: (A) 298.946
Question: In 2008, a certain factory produced 20% more widgets than it did in 2007, and its production in 2009 was 120% of its production in 2008. By approximately what percent would its production need to decrease the following year for the factory to produce the same number of widgets it did in 2007?
(A) 31%
(B) 35%
(C) 40%
(D) 44%
(E) 144%
Rationale: Let P be the original level of production in 2007.
Let x be the rate of production in 2010 compared to 2009.
x*1.2*1.2*P = P
x = 1/1.44 = 0.6944 which is a decrease of about 31%.
The answer is A.
Answer: (A) 31%
Question: How long does a train 110 m long running at the speed of 72 km/hr takes to cross a bridge 132 m length?
(A) 12.9 sec
(B) 12.1 sec
(C) 17.9 sec
(D) 16.8 sec
(E) 14.9 sec
Rationale: Speed = 72 * 5/18 = 20 m/sec
Total distance covered = 110 + 132 = 242 m.
Required time = 242/20 = 12.1 sec.
Answer: B
Answer: (B) 12.1 sec
Question: In a mixture of milk and water, the proportion of milk by weight was 80%. If, in a 180 gm mixture, 36 gms of pure milk is added, what would be the percentage of milk in the mixture formed?
(A) 83.83%.
(B) 89.33%.
(C) 89.30%.
(D) 83.98%.
(E) 83.33%.
Rationale: Explanation:
Percentage of milk in the mixture formed = [80/100 (180) + 36] / (180 + 36) * 100% = (144 + 36)/216 * 100% = 5/6 * 100% = 83.33%.
Answer: Option E
Answer: (E) 83.33%.
Question: A network of 20 x 10 squares is given to you.
Can you calculate how many unique squares and rectangles can be formed combining two or more individual squares ?
(A) 11550
(B) 12550
(C) 15550
(D) 13550
(E) 14550
Rationale: Total number of rectangles and squares will be equal to: (Summation of row numbers) * (Summation of column numbers)
= (1 + 2 + 3 +......+ 19 + 20) * (1 + 2 + 3 +......+ 9 + 10)
= 210 * 55
= 11550
correct answer is A)11550
Answer: (A) 11550
Question: If John invested $ 1 at 5 percent interest compounded annually, the total value of the investment, in dollars, at the end of 4 years would be
(A) (1.5)^4
(B) 4(1.5)
(C) (1.05)^4
(D) 1 + (0.05)^4
(E) 1 + 4(0.05)
Rationale: If John invested $ 1 at 5 percent interest compounded annually, the total value of the investment, in dollars, at the end of 4 years would be
1(1.05)^4
1.05^4
C. (1.05)^4
ANSWER:C
Answer: (C) (1.05)^4
Question: In a group of cows and hens, the number of legs are 16 more than twice the number of heads. The number of cows is
(A) 5
(B) 8
(C) 10
(D) 12
(E) 14
Rationale: Explanation:
Let the number of cows be x and the number of hens be y.
Then, 4x + 2y = 2 (x + y) + 16
4x + 2y = 2x + 2y + 16
2x = 16
x = 8.
Answer: B
Answer: (B) 8
Question: Find the perimeter and area of the rectangle of length 11 cm and breadth 7 cm.
(A) 77 cm2
(B) 121 cm2
(C) 141 cm2
(D) 171 cm2
(E) 221 cm2
Rationale: length = 11 cm, breadth = 7 cm
Perimeter of rectangle = 2 (length + breadth)
= 2 (11 + 7) cm
= 2 × 16 cm
= 32 cm
We know that the area of rectangle = length × breadth
= (11 × 7) cm22
= 77 cm2
ANSWER : A
Answer: (A) 77 cm2
Question: Three persons invested Rs.9000 in a joint business. The second person invested Rs.1000 more than the first and the third Rs.1000 more than second. After two years, they gained Rs.7200. How much third person will get?
(A) 2400
(B) 2429
(C) 3200
(D) 2707
(E) 2872
Rationale: First persons investment = x
Second persons investment = x + 1000
Third persons investments = x + 2000
x + x + 1000 + x + 2000 = 9000
3x = 6000
x = 2000
Ratio = 2000 : 3000 : 4000
2:3:4
4/9 * 7200 = 3200
Answer:C
Answer: (C) 3200
Question: A candidate got 33% of the votes polled and he lost to his rival by 833 votes. How many votes were cast?
(A) 2250
(B) 2450
(C) 2650
(D) 2850
(E) 3050
Rationale: Let x be the total number of votes.
0.33x + 833 = 0.67x
0.34x = 833
x = 833/0.34 = 2450
The answer is B.
Answer: (B) 2450
Question: What is the area of the square with the following coordinates: (x, y), (20, 20), (20, 6), (x, 6)?
(A) 64
(B) 81
(C) 125
(D) 196
(E) 225
Rationale: To find the area of a square, knowing the length of one side is sufficient.
From the coordinates given, we can see that one side equals 14.
The area is 14*14 = 196.
The answer is D.
Answer: (D) 196
Question: Mangala completes a piece of work in 5 days, Raju completes the same work in 20 days. If both of them work together, then the number of days required to complete the work is?
(A) 4 days
(B) 12 days
(C) 14 days
(D) 16 days
(E) 18 days
Rationale: If A can complete a work in x days and B can complete the same work in y days, then, both
of them together can complete the work in x y/ x+ y days.
That is, the required No. of days = 5 × 20/25 = 4 days
A)
Answer: (A) 4 days
Question: Cost of 16 mirror and 8 comb is Rs.328 and the cost of 4 mirror and 4 comb is Rs.96. Find the cost of each mirror?
(A) 10
(B) 12
(C) 17
(D) 21
(E) 22
Rationale: Let the cost of each pen and pencil be 'p' and 'q' respectively.
16m + 8c = 328 --- (1)
4m + 4c = 96
8m + 8c = 192 --- (2)
(1) - (2) => 8p = 136
=> m = 17
C
Answer: (C) 17
Question: A bookshop had science and art books in the ratio of 2:5. By the end of the week, 20% of both type of books were sold and 2240 books were unsold. How many science books were there at the starting?
(A) 200
(B) 300
(C) 400
(D) 800
(E) 900
Rationale: science books sold = 2x × 0.2 = 0.4x
science books unsold = 2x – 0.4x = 1.6x
art books sold = 5x × 0.2 = x
art books unsold = 5x – x = 4x
total books unsold = 1.6x + 4x = 5.6x
5.6x = 2240
x = 400
2x science = 800
D
Answer: (D) 800
Question: A Man can row upstream at 95kmph and downward stream at 47 kmph. Find Man's rate of the current
(A) 87km/hr
(B) 20km/hr
(C) 24km/hr
(D) 2.8km/hr
(E) 4.4km/hr
Rationale: Rate of the current=1/2(95-47)km/hr
=24km/hr
correct option is :C
Answer: (C) 24km/hr
Question: A driver would have reduced the time it took to drive from home to the store by 1/3 if the average speed had been increased by 18 miles per hour. What was the actual average speed, in miles per hour, when the driver drove from home to the store?
(A) 36
(B) 40
(C) 44
(D) 48
(E) 52
Rationale: Let R be the original speed and let T be the original time.
Since the distance remains the same (we're just changing the rate and time), any increase in rate or time is met with a decrease in the other term. Decreasing the time by 1/3 would give us:
D = (R)(T) = (2T/3)(x*R)
x = 3/2 since (2T/3)(3R/2) = (R)(T) = D
3R/2 = R + 18
R/2 = 18
R= 36
The answer is A.
Answer: (A) 36
Question: Two unbiased coin are tossed .what is the probability of getting atmost one head?
(A) 3/6
(B) 2/3
(C) 3/4
(D) 1/4
(E) 1/6
Rationale: Here S={HH,HT,TH,TT}
Let Ee=event of getting one head
E={TT,HT,TH}
P(E)=n(E)/n(S)=3/4
Option C
Answer: (C) 3/4
Question: In a group of 6 boys and 4 girls, four children are to be selected. In how many different ways can they be selected such that at least one boy should be there?
(A) 203
(B) 209
(C) 211
(D) 213
(E) 215
Rationale: In a group of 6 boys and 4 girls, four children are to be selected such that at least one boy should be there.
Hence we have 4 options as given below
We can select 4 boys ...(option 1)
Number of ways to this = 6C4
We can select 3 boys and 1 girl ...(option 2)
Number of ways to this = 6C3 × 4C1
We can select 2 boys and 2 girls ...(option 3)
Number of ways to this = 6C2 × 4C2
We can select 1 boy and 3 girls ...(option 4)
Number of ways to this = 6C1 × 4C3
Total number of ways
= 6C4 + 6C3 × 4C1 + 6C2 × 4C2 + 6C1 × 4C3
= 6C2 + 6C3 × 4C1 + 6C2 × 4C2 + 6C1 × 4C1[∵ nCr = nC(n-r)]
=
6
×
5
2
×
1
+
6
×
5
×
4
3
×
2
×
1
×
4
=6×52×1+6×5×43×2×1×4
+
6
×
5
2
×
1
×
4
×
3
2
×
1
+
6
×
4
+6×52×1×4×32×1+6×4
=
15
+
80
+
90
+
24
=
209
B)
Answer: (B) 209
Question: The ratio of the cost price and the selling price is 4 : 5.The profit percent is :
(A) 10%
(B) 20%
(C) 25%
(D) 30%
(E) 35%
Rationale: Solution
Let C.P. = Rs.4x. Then, S.P. = Rs.5x. Gain = Rs.(5x - 4x) = Rs.x.
∴ Gain % =(x/4x X100) % = 25 %
Answer C
Answer: (C) 25%
Question: Shreyas bought an article and sold it for 130% of its cost price. What was the cost price of the article, if Shreyas sold it for Rs.40250/-?
(A) Rs.30962
(B) Rs.35640
(C) Rs.34250/-
(D) Rs.33200
(E) None of these
Rationale: Explanation:
130% of CP = Rs.40250
:. CP = Rs.40250x100/130 = Rs.30962.
Answer: Option A
Answer: (A) Rs.30962
Question: A invested $400 in a business after 6 months B invested $200 in the business. End of the year if they got $100 as profit. Find B's shares?
(A) $100
(B) $75
(C) $20
(D) $120
(E) $50
Rationale: A:B = 400*12:200*6
A:B = 4:1
B's share = 100*1/5 = $20
Answer is C
Answer: (C) $20
Question: Tickets for all but 100 seats in a 10,000-seat stadium were sold. Of the tickets sold, 25% were sold at half price and the remaining tickets were sold at the full price of $2. What was the total revenue from ticket sales?
(A) $15,840
(B) $17,325
(C) $18,000
(D) $19,800
(E) $21,780
Rationale: 10000 seats --> Full Price : Half Price = 7500 : 2500
Price when all seats are filled = 15000 + 2500 = 17500
100 seats are unsold --> Loss due to unfilled seats = 25 + 2*75 = 175
Revenue = 17500 - 175 = 17325
Answer: B
Answer: (B) $17,325
Question: At what rate of compound interest per annum will a sum of Rs. 1200 become Rs. 1348.32 in 2 years?
(A) 6%
(B) 6.5%
(C) 7%
(D) 7.5%
(E) None of these
Rationale: Explanation:
Let the rate be R% p.a.
Then, 1200 x (1 + R/100)2
R = =6%
ANSWER IS A
Answer: (A) 6%
Question: For all real numbers v, an operation is defined by the equation v* = v - v/3. If (v*)* = 20, then v=
(A) 36
(B) 39
(C) 42
(D) 45
(E) 48
Rationale: (v*)* = (v - v/3) - (v - v/3) / 3
20 = 2v/3 - 2v/9 = 4v/9
v = 45
The answer is D.
Answer: (D) 45
Question: An escalator moves towards the top level at the rate of 15 ft.sec and its length is 180 feet. If a person walks on the moving escalator at the rate of 3 feet per second towards the top level, how much time does he take to cover the entire length.
(A) 12sec
(B) 20sec
(C) 15sec
(D) 18sec
(E) 10sec
Rationale: Explanation :
Time taken to cover the entire length = tot.dist/resultant speed = 180/ (15+3) = 10sec
Answer : E
Answer: (E) 10sec
Question: How long does a train 110 m long running at the speed of 72 km/hr takes to cross a bridge 134 m length?
(A) 82.1 sec.
(B) 12.2 sec
(C) 19.1 sec.
(D) 17.1 sec.
(E) 42.1 sec.
Rationale: Speed = 72 * 5/18 = 20 m/sec
Total distance covered = 110 + 134 = 244 m.
Required time = 244/20 = 12.2 sec.
Answer: B
Answer: (B) 12.2 sec
Question: If [Z] denotes the least integer greater than or equal to Z and [Z] = 0, which of the following statements must be true?
(A) Z = 0
(B) 0 <= Z < 1
(C) 0 < Z <= 1
(D) -1 <= Z < 0
(E) -1 < Z <= 0
Rationale: The answer for this is 0 < = Z < = 1
However it is not available in the options. The match to the above is-1 < Z <= 0
Answer = E
Answer: (E) -1 < Z <= 0
Question: The profits of QRS company rose 50% from March to April, then dropped 20% from April to May, then rose 50% from May to June. What was the percent increase for the whole quarter, from March to June?
(A) 15%
(B) 32%
(C) 40%
(D) 62%
(E) 80%
Rationale: Assume 100 in march , then 150 in April as 50% increase , Then 120 in may as 20% decrease from April , and then 180 in june which is 150% of 120 .
So overall increase is from 100 to 180 is 80%
Answer E
Answer: (E) 80%
Question: The average of 15 numbers is calculated as 30. It is discovered later on that while calculating the average, one number namely 36 was wrongly read as 26. The correct average is?
(A) 12
(B) 26
(C) 16
(D) 45
(E) 12
Rationale: 15 * 30 + 36 – 26
= 450/10
= 45
Answer: D
Answer: (D) 45
Question: A rectangular plot measuring 90 metres by 40 metres is to be enclosed by wire fencing. If the poles of the fence are kept 5 metres apart, how many poles will be needed ?
(A) 55
(B) 56
(C) 57
(D) 52
(E) None of these
Rationale: Solution
Perimeter of the plot = 2(90 + 40) = 260 m.
∴ Number of poles = [260/5] =52m
Answer D
Answer: (D) 52
Question: Ashok borrowed some money at the rate of 6% p.a. for the first two years, at the rate of 9% p.a. for the next three years and at the rate of 14% p.a. for the period beyond five years. If he pays a total interest of 11,400/ - at the end of nine years, how much money did he borrow?
(A) 16,060
(B) 14,000
(C) 18,000
(D) 12,000
(E) None of these
Rationale: We have, SI = p×r×t/100
∴ 11400 = p×6×2/100+p×9×3/100+p×14×4/100
or,12p + 27p + 56p = 11400 × 100
or, 95p = 11400 × 100
∴ p = 12000
Answer D
Answer: (D) 12,000
Question: The tax on a commodity is diminished by 14% and its consumption increased by 15%. The effect on revenue is?
(A) 2.1%
(B) 8.1%
(C) 5.1%
(D) 6.1%
(E) 1.1%
Rationale: 100 * 100 = 10000
86 * 115 = 9890
-----------
10000-----------110
100-----------? => 1.1% decrease
Answer: E
Answer: (E) 1.1%
Question: Ten Students take a test. The scores of the test are as follows:
Student A:60
Student B:40
Student C:50
Student D:75
Student E:95
Student F:50
Student G:45
Student H:100
Student I:45
Student J:70
How many scores were greater than the median score but less than the mean score?
(A) None
(B) One
(C) Two
(D) Three
(E) Four
Rationale: List in order: 40,45,45,50,50,60,70,75,95,100
The median = (the average of two middle terms) = (50 + 60)/2 = 55.
The mean = (the sum)/(# of terms) = 630/10 = 63.
Only 60 is between 55 and 63.
Answer: B.
Answer: (B) One
Question: An urn contains 6 red, 5 blue and 2 green marbles. If 2 marbles are picked at random, what is the probability that both are red?
(A) 6/13
(B) 5/26
(C) 6/26
(D) 9/26
(E) 10/27
Rationale: Option(B) is correct
P(Both are red), 6C2/13C2 = 5/26
ANSWER B
Answer: (B) 5/26
Question: A wooden box of dimensions 4 m x 2 m x 4 m is to carry rectangularboxes of dimensions 4 cm x 2 cm x 2 cm. The maximum number ofboxes that can be carried in the wooden box, is
(A) 9800000
(B) 2000000
(C) 7500000
(D) 1200000
(E) None of these
Rationale: Explanation: Number = (400*200*400)/4*2*2 = 2000000 Answer: B
Answer: (B) 2000000
Question: Machine A can finish a job in 4 hours, Machine В can finish the job in 3 hours, and Machine С can finish the job in 6 hours. How many hours will it take for A, B, and С together to finish the job?
(A) 3/2
(B) 4/3
(C) 5/4
(D) 6/5
(E) 8/7
Rationale: The combined rate is 1/4+1/3+1/6 = 9/12 of the job per hour.
The time to complete the job is 12/9 = 4/3 hours.
The answer is B.
Answer: (B) 4/3
Question: P and Q started a business investing Rs. 96,000 and Rs. 28,000 respectively. In what ratio the profit earned after 2 years be divided between P and Q respectively?
(A) 17:6
(B) 24:7
(C) 25:6
(D) 21:3
(E) 17:4
Rationale: P:Q = 96000 : 28000
= 24:7
Answer:B
Answer: (B) 24:7
Question: Harkamal purchased 8kg of grapes at the rate of 80 per kg and 9 kg of mangoes at the rate of 55 per kg. How much amount did he pay to the shopkeeper?
(A) A)1000
(B) B)1055
(C) C)1065
(D) D)1135
(E) E)1080
Rationale: Cost of 8 kg grapes = 80 × 8 = 640.
Cost of 9 kg of mangoes = 55 × 9 = 495.
Total cost he has to pay = 640 + 495 = 1135.
D)
Answer: (D) D)1135
Question: The average weight of 16 girls in a class is 50.25 kg and that of the remaining 8 girls is 45.15 kg. Find the average weights of all the girls in the class.
(A) A)48.55
(B) B)49
(C) C)51
(D) D)61
(E) E)62
Rationale: Required average
= (50.25 x 16 + 45.15 x 8)/(16 + 8)
= (804 + 361.20)/24
= 1165.20/24
= 48.55kg
Answer is A
Answer: (A) A)48.55
Question: A number of 41 marbles is to be divided and contain with boxes. If each box is to contain 3, 4, or 5 marbles, what is the largest possible number of boxes?
(A) 13
(B) 12
(C) 15
(D) 16
(E) 17
Rationale: To maximize # of boxes we should minimize marbles per box: 12*3+1*5=41 --> 12+1=13.
Answer: A.
Answer: (A) 13
Question: On a test, students receive 2 points for each correct answer and are penalized by losing one point for each incorrect answer. There are 6 questions on the test and each question has 4 answer options, A, B, C, and D. It is known that 5 of the questions have option B as the correct answer and one question has option C as the correct answer. If a student marks B for the first 3 questions and C for the last 3 questions, what is the minimum possible score that student can receive?
(A) -2
(B) -1
(C) 0
(D) 1
(E) 2
Rationale: For the minimum possible score, let us take the worst case scenario
Suppose, he gets all of the last 3 qs wrong whose correct answer options are B and one of the first 3 qs wrong whose correct option is C
In that case, he will get only 2 out of the first 3 qs right.
Therefore, minimum possible score=(2*2)-(4*1)=0
Answer C
Answer: (C) 0
Question: When the integer n is divided by 8, the remainder is 3. What is the remainder if 6n is divided by 8?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: When n is divided by 8, the remainder is 3 may be written as
n = 8 k + 3
multiply all terms by 6
6 n = 6(8 k + 3) = 8(6k) + 18
Write 18 as 16 + 2 since 16 = 8 * 2.
= 8(6k) + 16 + 2
Factor 8 out.
= 8(6k + 2) + 2
The above indicates that if 6n is divided by 8, the remainder is 2. The answer is C.
Answer: (C) 2
Question: The banker's gain of a certain sum due 2 years hence at 10% per annum is Rs. 24. The present worth is:
(A) 29
(B) 28
(C) 600
(D) 277
(E) 191
Rationale: T.D. = B.G. x 100 = Rs. 24 x 100 = Rs. 120.
Rate x Time	10 x 2
P.W. =	100 x T.D.	= Rs. 100 x 120 = Rs. 600.
Rate x Time	10 x 2
Answer: C
Answer: (C) 600
Question: In State X, all vehicle license plates have 3 letters from the 26 letters of the alphabet followed by 4 one digit numbers. How many different license plates can State X have if repetition of letters and numbers is allowed?
(A) 23,400
(B) 60,840
(C) 67,600
(D) 608,400
(E) 175,760,000
Rationale: The choices give us the answer without any calculations--
4 one digits places can take 10*10*10*10 ways..
3 letters places can be filled up in 26*26*26 ways
ans= 26*26*26*10*10*10*10=175,760,000
ans E
Answer: (E) 175,760,000
Question: If there are 200 questions in a 3 hr examination. Among these questions are 15 type A problems, which requires twice as much as time be spent than the rest of the type B problems. How many minutes should be spent on type A problems?
(A) 72 min
(B) 25.11628 min
(C) 70 min
(D) 74.11682 min
(E) 76 min
Rationale: x=time for type B prolems
2x=time for type A problem
total time=3hrs=180min
185x+15*2x=180
x=180/215
x=0.837209
time taken for type A problem=15*2*0.837209=25.11628min
ANSWER:B
Answer: (B) 25.11628 min
Question: How many of the following numbers are divisible by 132 ?
264, 396, 462, 792, 968, 2178, 5184, 6336
(A) 1
(B) 4
(C) 5
(D) 7
(E) 3
Rationale: B
By using your calculator you can calculate that the following numbers are divisible by 132 : 264, 396, 792 and 6336.
Required number of number = 4.
Answer: (B) 4
Question: Simplify: 18800+470+20
(A) 4
(B) 1
(C) 5
(D) 2
(E) 3
Rationale: 18800+470+20=(18800/470)+20=40/20=2.
Answer is D.
Answer: (D) 2
Question: In a competitive examination in State A, 6% candidates got selected from the total appeared candidates. State B had an equal number of candidates appeared and 7% candidates got selected with 80 more candidates got selected than A. What was the number of candidates appeared from each State?
(A) 6000
(B) 7000
(C) 8000
(D) 9000
(E) None
Rationale: State A and State B had an equal number of candidates appeared.
In state A, 6% candidates got selected from the total appeared candidates
In state B, 7% candidates got selected from the total appeared candidates
But in State B, 80 more candidates got selected than State A
From these, it is clear that 1% of the total appeared candidates in State B = 80
=> total appeared candidates in State B = 80 x 100 = 8000
=> total appeared candidates in State A = total appeared candidates in State B = 8000
C)
Answer: (C) 8000
Question: A fashion designer sold a pair of jeans to a retail store for 40 percent more than it cost to manufacture the pair of jeans. A customer bought the pair of jeans for 30 percent more than the retailer paid for them. The price the customer paid was what percent greater than the cost of manufacturing the jeans?
(A) 65%
(B) 70%
(C) 75%
(D) 82%
(E) 95%
Rationale: find the product of the two increases: (14/10) * (13/10) which is 1.82 and a 82% increase.
D
Answer: (D) 82%
Question: The length of a train and that of a platform are equal. If with a speed of 54 k/hr, the train crosses the platform in one minute, then the length of the train (in meters) is?
(A) 752
(B) 450
(C) 719
(D) 750
(E) 712
Rationale: Speed = [54 * 5/18] m/sec = 15 m/sec; Time = 1 min. = 60 sec.
Let the length of the train and that of the platform be x meters.
Then, 2x/60 = 15 Ã¨ x = 15 * 60 / 2 = 450
Answer: B
Answer: (B) 450
Question: Sum of the squares of three numbers is 222 and the sum of their products taken two at a time is 131. Find the sum?
(A) 22
(B) 25
(C) 26
(D) 28
(E) 29
Rationale: (a + b + c)2 = a2 + b2 + c2 + 2(ab +bc + ca) = 222 + 2* 131
a + b + c = √484 = 22
A
Answer: (A) 22
Question: The number of new words that can be formed by rearranging the letters of the word 'MACHINE' is ?
(A) 5030
(B) 5039
(C) 5010
(D) 5033
(E) 3000
Rationale: Number of words which can be formed = 7! - 1
= 5040 - 1
= 5039.
Answer:B
Answer: (B) 5039
Question: The expression x#y denotes the product of the consecutive multiples of 3 between x and y, inclusive. What is the sum of the exponents in the prime factorization of 21#36?
(A) 16
(B) 17
(C) 18
(D) 19
(E) 20
Rationale: First, let's translate the expression 21#36, using the definition given:
21#36 = 21×24×27×30×33×36
We need the prime factorization of this product.
Let's factor out 3 from each multiple.
21#36 = 3^6(7×8×9×10×11×12)
Now let's replace each consecutive integer with its prime factorization:
21#36 = 3^6(7×2^3×3^2×(2×5)×11×(2^2×3))
Let's group the prime bases:
21#36 = 2^6×3^9×5×7×11
The sum of the exponents is 6 + 9 + 1 + 1 + 1 = 18
The answer is C.
Answer: (C) 18
Question: The distance between two planets is 3.04 × 10^8 light years. What is the distance between the two planets, in parsecs? (1 parsec = 3.26 light years)
(A)  9.3 × 10^5
(B)  9.9 × 10^6
(C)  9.3 × 10^7
(D)  9.9 × 10^7
(E)  10.1 × 10^8
Rationale: 3.04*10^8 light years = 3.04*10^8/3.26 parsecs.
3.04/3.26 is a little bit less than 1, something like 0.9, thus 3.04*10^8/3.26 = ~0.93*10^8 = 9.3*10^7.
Answer: C.
Answer: (C)  9.3 × 10^7
Question: The distance between a food bank and a church is approximately 8.0 x 10^5 inches. Which of the following is closest to the distance between the food bank and the church, in kilometers? (1 kilometer is approximately 3.9 x 10^4 inches.)
(A) 22.8
(B) 23.4
(C) 19.86
(D) 20.5
(E) 23.9
Rationale: We know that 1 kilometer = 3.9x10^4 inches. Therefore, we now have a ratio of (1 kilometer/3.9x10^4 inches).
We also know that the distance between the food bank and the church is approximately 8.0x10^5 inches. To convert inches to kilometers, we need to multiply 8.0x10^5 inches by the ratio we just found out.
kilometers = 8.0x10^5 inches x (1 kilometer/3.9x10^4 inches) [note: "inches" cancel out, leaving us with just km]
km = 8.0x10^5/3.9x10^4 km
km = 20.51 = 20.5 km
Therefore, we can see that the closest answer is D.
Answer: (D) 20.5
Question: The equation x = 2y^2 + 5y - 18, describes a parabola in the xy coordinate plane. If line l, with slope of 3, intersects the parabola in the upper-left quadrant at x = -5, the equation for l is
(A) 3x + y + 15 = 0
(B) y - 3x - 11 = 0
(C) -2x - y - 7 = 0
(D) -3x + y - 18 = 0
(E) -3x + y + 13.5 = 0
Rationale: The question is made to look difficult though it is pretty simple if you focus on just the line and use process of elimination. (Remember that GMAT does not focus on parabolas so basically, the question should be quite do-able even if someone doesn't know how to handle parabolas.)
We need equation of l. Its slope must be 3.
Slope in option A and C is not 3 so we are left with B, D and E
The line has a point (-5, y) on it where y is positive (since the point lies in upper left quadrant).
In options B and E, if you put x = -5, you get -ve value for y co-ordinate. So ignore them.
Answer must be (D)
Answer: (D) -3x + y - 18 = 0