RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: A thief is spotted by a policeman from a distance of 150 meters. When the policeman starts the chase, the thief also starts running. If the speed of the thief be 8km/hr and that of the policeman 10 km/hr, how far the thief will have run before he is overtaken?
A.350m
B.200m
C.400m
D.600m
Answer: D.600m
Explanation: Relative speed of the policeman = (10-8) km/hr =2 km/hr.
Time taken by police man to cover
(150m/1000) x 1/2 hr = 3/40 hr.
In 3/40 hrs, the thief covers a distance of 8 x 3/40 km = 3/5 km = 600 m
Answer is D
Question: A library has an average of 510 visitors on Sundays and 240 on other days. The average number of visitors per day in a month of 30 days beginning with a Sunday is
A.285
B.337
C.878
D.227
Answer: A.285
Explanation: Explanation:
Since the month begins with a Sunday, so there will be five Sundays in the month,
Required average = (510 * 5 + 240 * 25) / 30 = 8550/30 = 285.
Answer: A
Question: A wheel that has 6 cogs is meshed with a larger wheel of 14 cogs. When the smaller wheel has made 21 revolutions, then the number of revolutions mad by the larger wheel is:
A.4
B.9
C.12
D.49
Answer: B.9
Explanation: Explanation: Let the required number of revolutions made by larger wheel be x.
Then, More cogs, Less revolutions (Indirect Proportion)
14 : 6 :: 21 : x <-> 14 x x = 6 x 21
x = (6 x 21)/14
x = 9
Answer B
Question: The unit digit in the product 1256*6785*4587*9785 is?
A.0
B.1
C.2
D.3
Answer: A.0
Explanation: Unit digit in the given product = unit digit in 6*5*7*5 = 0
Answer is A
Question: 15 people entered a theater before Sujit. 7 people entered the theater between Sujit and Suraj and 20 people entered the theater after Suraj. If Suraj entered the theater before Sujit then how many people are there in the theater?
A.28
B.36
C.44
D.40
Answer: A.28
Explanation: Explanation:
If Suraj entered before Sujit, then the number of people in the theater will be 28.
ANSWER IS A
Question: A man has Rs. 240 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?
A.90
B.70
C.45
D.80
Answer: C.45
Explanation: Let number of notes of each denomination be x.
Then x + 5x + 10x = 240
16x = 240
x = 15.
Hence, total number of notes = 3x = 45.
Answer is C.
Question: The average weight of 19 students is 15kg. by the admission of a new student the average weight is reduced to 14.4 kg. the weight of the new student is ?
A.10.6 kg
B.3 kg
C.11 kg
D.14.9 kg
Answer: B.3 kg
Explanation: Answer
Weight of new student = Total weight of all 20 students - Total weight of initial 19 students
= (20 x 14.4 - 19 x 15) kg
= 3 kg.
Correct Option: B
Question: After decreasing 24% in the price of an article costs Rs.608. Find the actual cost of an article?
A.128
B.277
C.800
D.2688
Answer: C.800
Explanation: CP* (76/100) = 608
CP= 8 * 100 => CP = 800
Answer: C
Question: At what rate percent on simple interest will Rs.750 amount to Rs.900 in 8 years?
A.6%
B.2.5%
C.4%
D.5%
Answer: B.2.5%
Explanation: 150 = (750*8*R)/100
R = 2.5%
Answer: B
Question: 0.9*0.007= ­­­­­­­­­­_________
A.0.063
B.0.0063
C.0.63
D.0.00063
Answer: B.0.0063
Explanation: 9*7=63
Sum of decimal places= 4
So, 0.9*0.007= 0.0063
ANSWER:B
Question: The ratio of males to females in a class is 2:3. The career preferences of the students in the class are represented in a circle graph. If the area of the graph allocated to each career preference is proportional to the number of students who have that career preference, how many degrees of the circle should be used to represent a career that is preferred by one-fourth of the males and one-half of the females in the class?
A.128
B.136
C.144
D.152
Answer: C.144
Explanation: 1/4*2/5 + 1/2*3/5 = 2/20 + 6/20 = 2/5
The number of degrees is 2/5 * 360 = 144 degrees
The answer is C.
Question: Andy solves problems 70 to 125 inclusive in a Math exercise. How many problems does he solve?
A.56
B.52
C.51
D.50
Answer: A.56
Explanation: 125-70+1= 56
'A' is the answer
Question: What sum of money will produce Rs.70 as simple interest in 4 years at 3 1/2 percent?
A.112
B.100
C.882
D.262
Answer: B.100
Explanation: 70 = (P*4*7/2)/100
P = 500.Answer: B
Question: The radius of a wheel is 22.4 cm. What is the distance covered by the wheel in making 400 resolutions.
A.561.68 m
B.562.68 m
C.563.68 m
D.564.68 m
Answer: B.562.68 m
Explanation: In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 400 resolutions.
= 500 * 2 * 22/7 * 22.4
= 56268 cm
= 562.68 m
Answer: B
Question: For an employee to qualify for early retirement at a certain company, the sum of the employee’s age and years of service must be at least 80, If Sue was K years old when she was hired by the company, what is the minimum age at which she could possibly qualify for early retirement?
A.K+40
B.2K+40
C.(80+K)/2
D.(80-K)/2
Answer: C.(80+K)/2
Explanation: Let y be the years of service at the company.
After y years of service, Sue's age will be K + y.
Sue can retire when (K+y) + y = 80
y = (80 - K)/2
Then Sue's age will be K + y = K + (80 - K)/2 = (80+K) / 2
The answer is C.
Question: In a family, there are six members A, B, C, D, E and F.
A and B are a married couple, A being the male member. D is the only son of C, who is the brother of A. E is the sister of D. B is the daughter-in-law of F, whose husband has died. How is E related to C ?
A.Sister
B.Daughter
C.Cousin
D.Mother
Answer: B.Daughter
Explanation: Explanation:
A is a male and married to B. So, A is the husband and B is the wife. C is the brother of A. D is the son of C. E. who is the sister of D will be the daughter of C. B is the daughter-in-law of F whose husband has died means F is the mother of A.
Clearly. E is the daughter of C.
Answer: B)
Question: In how many ways can 5 different toys be packed in 3 identical boxes such that no box is empty, if any of the boxes may hold all of the toys?
A.20
B.30
C.25
D.600
Answer: C.25
Explanation: The toys are different; The boxes are identical.
If none of the boxes is to remain empty, then we can pack the toys in one of the following ways:
Case i. 2, 2, 1
Case ii. 3, 1, 1
Case i:
Number of ways of achieving the first option 2, 2, 1.
Two toys out of the 5 can be selected in 5C2 ways. Another 2 out of the remaining 3 can be selected in 3C2 ways and the last toy can be selected in 1C1 way.
However, as the boxes are identical, the two different ways of selecting which box holds the first two toys and which one holds the second set of two toys will look the same. Hence, we need to divide the result by 2.
Therefore, total number of ways of achieving the 2, 2, 1 option is:C
Question: Four horses are tethered at 4 corners of a square field of side 70 metres so that they just cannot reach one another. The area left ungrazed by the horses is:
A.1050 sq.m
B.3850 sq.m
C.950 sq.m
D.1075 sq.m
Answer: A.1050 sq.m
Explanation: area ungrazed is given by
total area - 4*area grazed by each horse
= 70*70 - 4*(90/360)*pi*(70/2)^2
as the angle made by the horse is 90 degree, so applying the area of the sector,= theta/360*pi*radius^2 above
= 70*70 - pi*(70/2)*(70/2)
= 70*70 { 1- pi/4}
= 70*70{6/(7*4)} , expanding pi = 22/7
= (70*70*6) / (7*4)
= 1050 sq m
ANSWER:A
Question: Set V consists of integers {3, -8, Y, 19, -6} and set B consists of integers {k, -3, 0, 16, -5, 9}. Number L represents the median of set V, number M represents mode of set B and number Z = L^M. If Y is an integer greater than 21, for what value of k will Z be a divisor of 26?
A.-2
B.-1
C.0
D.1
Answer: C.0
Explanation: V = {3,-8,Y,19,-6}
B = {k,-3,0,16,-5,9}
Y > 21
So L = Median of V = 3
M = Mode of Set B
Z = (3)^M
If Z is a divisor of 26, (3)^M = 1 because 26 does not have 3 as a factor
=> M = 0
Hence k = 0, as M is mode and 0 will be the most frequently occuring number in set B.
Answer - C
Question: What is 15 percent of 58?
A.6.9
B.7.4
C.8.7
D.9.3
Answer: C.8.7
Explanation: (15/100) * 58 = 8.7
The answer is C.
Question: Pipes A and B can fill a tank in 3 and 4 hours. Pipe C can empty it in 4 hours. If all pipes are opened together, then the tank will be filled in?
A.3hr
B.1/2hr
C.1hr
D.9/7hr
Answer: A.3hr
Explanation: Net part filled in 1 hour = 1/3 + 1/4 - 1/4 = 1/3
The tank will be full in 3 hr
Answer is A
Question: A company blends two varieties of tea from two different tea gardens, one variety costing 20 per kg and other 25 per kg, in the ratio 5 : 4. He sells the blended tea at 23 per kg. Find his profit percent
A.5% profit
B.3.5% loss
C.3.5% profit
D.No profit, no loss
Answer: C.3.5% profit
Explanation: Let the quantity of two varieties of tea be 5x kg and 4x kg, respectively.
Now, SP = 23 × 9x = 207x
and CP = 20 × 5x + 25 × 4x = 200x
Profit % = 7x/200x×100=3.5%
Answer C
Question: For each positive integer,the quantitySn is defined such thatSn+1=(Sn)^2 -S(n+1).in addition ,S2=1.then which of the following must be true.
A.a)S4 +S3 +1=0
B.b)(S1)^2 +S4 +2=0
C.c) ifS1=-1thenS4 is also equal to-1.
D.d) ifS4 =-7thenS1=-2.
Answer: A.a)S4 +S3 +1=0
Explanation: Since all the answers include S4, let's start from there.
S4=S2^2-S3
S3=S1^2-S2
Substituting S3 into the first equation we get:
S4=S2^2-(S1^2-S2)
Since S2=1
S4=1-(S1^2-1)
S4=2-S1^2
We need S1^2 in order to calculate S4.
E) provides S1 and from there we can calculate S4:
S4=2-(-3)^2
S4=-7
Correct.
As a side note, I would be very careful with answers in the formif S4=x then S1=y(such as option D ), as we are dealing with S1^2 (not S1), S1 can have two different values and it can not be determined for sure which root is the right answer.
For example:
If S4=-7 then S1=3 :
if we substitute S4 with - 7 we get:
-7=2-S1^2
S1^2=9
now S1 can be +/-3 !!
A
Question: A theater is opening and has free seating. There are 15 people who want to watch a movie, and the theater has 10 seats: 1 near the exit, 4 on the first row, 4 in middle row, and 1 in the last row. Only 4 people are claustrophobic and can sit near the exit and they cannot sit anywhere. The other people can sit anywhere. How many different groupings are possible?
A.98340
B.788922
C.138600
D.383848
Answer: C.138600
Explanation: 4C1 select 1 from 4 claustrophobic people;
11C4 select 4 for first row from 11 people (as 4 people can only sit near the exit 15-4=11);
7C4 select 4 for middle row from 7 people (as 4 can only sit near exit and 4 we've already selected for first row 15-4-4=7);
3C1 select 1 last row seat from 3 people (again as 4 can only sit near exit and 4 we've already selected for first row, 4 for second row 15-4-4-4=3)
Total # of selection=4C1*11C4*7C4*3C1=138600
Answer: C.
Question: Last year, for every 100 million vehicles that traveled on a certain highway, 100 vehicles were involved in accidents. If 2 billion vehicles traveled on the highway last year, how many of those vehicles were involved in accidents? (1 billion = 1,000,000,000)
A.500
B.1500
C.2500
D.2000
Answer: D.2000
Explanation: To solve we will set up a proportion. We know that “100 million vehicles is to 100 accidents as 2 billion vehicles is to x accidents”. To express everything in terms of “millions”, we can use 2,000 million rather than 2 billion. Creating a proportion we have:
100/100 = 2,000/x
Cross multiplying gives us:
100x = 2,000 * 100
x = 20 * 100 = 2000
Answer : D
Question: The speed of a train is 90 kmph. What is the distance covered by it in 10 minutes?
A.15
B.87
C.99
D.77
Answer: A.15
Explanation: 90 * 10/60
= 15 kmph
Answer:A
Question: A number increased by 10% gives 550. The number is
A.250
B.500
C.450
D.500
Answer: B.500
Explanation: Formula = TOTAL=100% ,INCRESE = "+" DECREASE= "-"
A number means = 100 %
That same number increased by 10 % = 110 %
110 % -------> 550 (110 ×5 = 550)
100 % -------> 500 (100 × 5= 500)
B)
Question: A shopkeeper fixes the marked price of an item 32% above its cost price. The percentage of discount allowed to gain 7% is
A.18.94%
B.18.93%
C.18.92%
D.18.91%
Answer: B.18.93%
Explanation: Explanation:
Let the cost price = Rs 100
then, Marked price = Rs 132
Required gain = 7%,
So Selling price = Rs 107
Discount = 132 - 107 = 25
Discount% = (25/132)*100 = 18.93%
Option B
Question: The banker's gain on a sum due 6 years hence at 12% per annum is Rs. 540. What is the banker's discount?
A.1240
B.1120
C.1190
D.1290
Answer: D.1290
Explanation: Explanation :
TD = (BG ×100)/TR = (540×100)/(6×12) = (90×100)/12 = (15×100)2/ = Rs. 750
BG = BD – TD
=> 540 = BD - 750
=> BD = 540 + 750 = 1290 Answer : Option D
Question: If the units digit of n^33 is 7, which of the following could be the value of n?
I. n = 41
II. n = 43
III. n = 47
A.Only I
B.Only II
C.Only III
D.I and II
Answer: C.Only III
Explanation: Given n^33 units digit is 7.
If at all we have to get 7 as units digits only 3 and 7 series has 7
3^! = 3 , 3^2 = 9 , 3^3 = 27 , 3^4 = 81
7^1 = 7, 7^2 = 49 , 7^3 = 3 (units ) , 7^4 = 1 (units)
We have n^33 - then divide 33 by 4 = remainder 1.
Then we have for only 7^1 - we have units digit as 7.
Hence 47^33 = 7 (units).
Option C is correct answer
Question: √(49)2
A.7
B.14
C.49
D.21
Answer: C.49
Explanation: explanation
√(49)2 =?
or, ? = 49
Answer C
Question: If the sales tax be reduced from 4 (1/4) % to 1 (1/2) %, then what difference does it make to a person who purchases a bag with marked price of Rs. 4500?
A.Rs. 156.66
B.Rs. 150.23
C.Rs. 123.75
D.Rs. 135.06
Answer: C.Rs. 123.75
Explanation: Explanation:
Required difference = (4 (1/4) of Rs. 4500) - (1(1/2) of Rs.4500)
= (17/4 – 3/2) % of Rs. 4500
= (11/4) x (1/100) x 4500
= Rs. 123.75
ANSWER C
Question: Sixteen percent of the programmers in a startup company weigh 200 pounds or more. Twenty-five percent of the programmers that are under 200 pounds in that same company weigh 100 pounds or less. What percent of the programmers in the startup company weigh between 100 and 200 pounds?
A.15%
B.20%
C.25%
D.63%
Answer: D.63%
Explanation: Initially 84% and 16% split
80% is further divided as 25% and 75%
Q is asking about that 75%
let total be '100' then that 75% is (3/4)∗84
so, the required % is [(3/4)∗84/100]∗100 = 63%
ANSWER:D
Question: If the average (arithmetic mean) of five consecutive negative integers is 12k – 1, what is the difference between the greatest and least of the five integers?
A.4K
B.4k^2 -4k
C.4-4k
D.4
Answer: D.4
Explanation: (n-2 + n - 1 + n + n + 1 + n + 2)/5 = 12k - 1
=> n = 60k - 5
Greatest = n + 2 = 60k - 5 + 2 = 60k - 3
Least = n - 2 = 60k - 5 - 2
=> Difference = 60k - 3 - (60k - 7)
= 4
Answer - D
Question: The maximum length of a pencil that can be kept in a rectangular box of dimensions 8cm×6cm×2cm, is :
A.2√13 cm
B.2√14 cm
C.2√26 cm
D.10√2 cm
Answer: C.2√26 cm
Explanation: Explanation:
Length of pencil = √(8)2+(6)2+(2)2 cm = √104 cm = 2√26 cm
Correct Option: C
Question: In the Hillside summer camp there are 50 children. 85% of the children are boys and the rest are girls. The camp administrator decided to make the number of girls only 5% of the total number of children in the camp. How many more boys must she bring to make that happen?
A.20.
B.45.
C.50.
D.30.
Answer: C.50.
Explanation: Given there are 50 students , 84% of 50 = 42 boys and remaining 8 girls.
Now here 84% are Boys and 16% are Girls.
Now question is asking about how many boys do we need to add, to make the girls percentage to 5 or 8%..
If we add 50 to existing 45 then the count will be 92 and the girls number will be 8 as it.
Now boys are 92% and girls are 8%. ( out of 100 students = 92 boys + 8 girls ).
IMO option C is correct.
Question: At the end of three years what will be the compound interest at the rate of 10% p.a. on an amount of Rs.20000?
A.6620
B.6627
C.6626
D.6622
Answer: A.6620
Explanation: A = 20000(11/10)3
= 26620
= 20000
----------
6620
Answer:A
Question: There are some birds in cage, 1/3rd fly away . Then 2/5th of the remaining left the cage , then 2/3rd of the remaining left the cage . At last 8 were remaining . How many birds were in total ?
A.60
B.27
C.28
D.26
Answer: A.60
Explanation: Sol:
If x birds were there in total , then
x × (1 – 1/3)× (1 – 2/5) ×(1 – 2/3) = 8
x×2/3 × 3/5 × 1/3 = 8
x = 60
Answer:A
Question: The total car population in a Mumbai is 2,94,00 out of which 1,50,00 are made by Honda. Out of every 100 Honda cars, 98 are red in color, but only 53% of the total car population is red. Find the % of non-Honda cars that are red
A.5.24%
B.5.35%
C.6.125%
D.7.45%
Answer: C.6.125%
Explanation: Total Car.29.10 i.e., Honda +non Honda = 29400 Given: Whim. tractor .150W
Now,5346 of 2..00 = Honda +Red Non-Honda 29400 .:4 =15582 Thus...El Mall... 1.0 Now Honda 15582 flow, Non-. Honda =15582 - 15.582-14700=8B2 96 non-Honda =1=1.100 = 6.125%
C
Question: Look at this series: V, VIII, __, XIV, XVII, XX, ... What number should fill the blank?
A.IX
B.XXIII
C.XV
D.XI
Answer: D.XI
Explanation: Explanation: This is a simple addition series; each number is 3 more than the previous number.
Answer: D
Question: An intern wants to label folders with numbers using digit stickers only. If the intern uses 999 stickers, how many folders have been numbered? (The numbers of the folders are consecutive and the number of the first folder is 1).
A.287
B.369
C.370
D.371
Answer: B.369
Explanation: For the first 9 folders we need 9 stickers.
For the next 90 we need 2 stickers each or 180 stickers.
For the next 900 folders we need 3 stickers each.
The first 99 folders correspond to 189 stickers.
Subtract 189 from the total number of stickers (999).
This leaves 810 stickers for folders that use 3 stickers each. So, divide 810 by 3 to get 270 folders.
Add 99 folders to 270 folders to get the total number of folders, 369.
Answer: B
Question: If x is an integer, then x(x - 1)(x - y) must be evenly divisible by three when y is any of the following values EXCEPT
A.-4
B.-2
C.-1
D.2
Answer: B.-2
Explanation: here's another approach
x(x - 1)(x - y)
all three are consecutive, so the product MUST be a multiple of 3
we don't know the value of y just yet ... so let's extend the series ... the extension itself reveals the answers
..(x-5)..(x-2)(x-1)x(x+1)..(x+4)..
we can see the possible values of y too from the series
y = 2 OR 2+3n [25]
y = -1 OR -1+3n [-1-4]
B i.e. -2 does not fit in any value of y
so B it is
Question: A tank contains 10,000 gallons of a solution that is 5 percent sodium chloride by volume. If 2,000 gallons of water evaporate from the tank, the remaining solution will be approximately what percent sodium chloride?
A.1.25%
B.3.75%
C.6.25%
D.6.67%
Answer: C.6.25%
Explanation: The amount of sodium chloride is 0.05*10,000 = 500 gallons
500/8000 = 1/16 = 6.25%
The answer is C.
Question: 6) A marketing firm determined that , of 300 households surveyed, 80 used neither Brand A nor Brand B soap.60 used only Brand A soap and for every household that used both brands of soap, 3 used only brand B soap.how many of the 200 household surveyed used both brands of soap?
A.a) 15
B.b) 20
C.c) 30
D.d) 40
Answer: D.d) 40
Explanation: 220 = At least one of Soap A or B
Both brands = x
Brand B = 3x
=> 60 + x + 3x = 220
=> 4x = 160
=> x = 40
Answer - D
Question: There are 6 red shoes, 4 green shoes. If one draw randomly a shoe what is the probability of getting a red shoe
A.1/9
B.2/9
C.3/5
D.4/9
Answer: C.3/5
Explanation: total 10 from take one.
10c1=10
red 6 from one
6c1=6
6/10= 3/5
ANSWER:C
Question: The cross-section of a cannel is a trapezium in shape. If the cannel is 10 m wide at the top and 6 m wide at the bottom and the area of cross-section is 640 sq m, the depth of cannel is?
A.76
B.28
C.27
D.80
Answer: D.80
Explanation: 1/2 * d (10 + 6) = 640
d = 80
Answer: D
Question: If the a radio is sold for Rs 490 and sold for Rs 465.50.find loss%.
A.4%
B.5%
C.6%
D.3%
Answer: B.5%
Explanation: sol. cp=rs490,sp= 465.50.
loss=rs(490-465.50)=rs 24.50.
loss%=[(24.50/490)*100]%=5%
Answer is B.
Question: Find the value of 72519 x 9999 = m?
A.455465473
B.654676854
C.667676753
D.725117481
Answer: D.725117481
Explanation: 72519 x 9999 = 72519 x (10000 - 1)
= 72519 x 10000 - 72519 x 1
= 725190000 - 72519
= 725117481
D
Question: A cube with its sides numbered 1 through 6 is rolled twice, first landing on a and then landing on b. If any roll of the cube yields an equal chance of landing on any of the numbers 1 through 6, what is the probability Q that a + b is prime?
A. 0
B. 1/12
C. 5/12
D. 7/18
Answer: C. 5/12
Explanation: Total # of outcomes is 6*6=36;
Favorable outcomes:
a-b --> prime
1-1 --> 2;
1-2 --> 3;
2-1 --> 3;
1-4 --> 5;
4-1 --> 5;
2-3 --> 5;
3-2 --> 5;
1-6 --> 7;
6-1 --> 7;
2-5 --> 7;
5-2 --> 7;
3-4 --> 7;
4-3 --> 7;
6-5 --> 11;
5-6 --> 11.
Total of 15 favorable outcomes
Q=15/36.
Answer: C.
Question: A car gets 40 kilometers per gallon of gasoline. How many gallons of gasoline would the car need to travel 180 kilometers?
A.3.5 gallons
B.2.7 gallons
C.5.7 gallons
D.4.5 gallons
Answer: D.4.5 gallons
Explanation: Each 40 kilometers, 1 gallon is needed. We need to know how many 40 kilometers are there in 180 kilometers?
180 ÷ 40 = 4.5 × 1 gallon = 4.5 gallons
correct answer is D) 4.5 gallons
Question: The number of boys in a class is (7/2) times the number of girls. Which one of the following numbers cannot represent the total number of children in the class ?
A.A)48
B.B)54
C.C)42
D.D)40
Answer: B.B)54
Explanation: Explanation:
Let number of girls = x and number of boys = 3.5x.
Then, 3.5x + x = 4.5x = total number of students.
Thus, to find exact value of x, the total number of students must be divisible by 4.5
Answer: B
Question: What is the rate percent when the simple interest on Rs.1500 amount to Rs.250 in 5 Years?
A.3.33%
B.6%
C.2%
D.95%
Answer: A.3.33%
Explanation: Interest for 5yrs = 250
Interest for 1yr = 50
Interest rate = 50/1500 x 100 = 3.33%
Answer : A
Question: If 40% of a number is 16, then the number is
A.number is 60
B.number is 70
C.number is 90
D.number is 40
Answer: D.number is 40
Explanation: Solution:
Let "a" be the number we seek. We get
40% × a = 16
2 × 40% × a = 2 × 16 = 32
80% × a = 32
10% × a = 32 : 8 = 4
100% × a = 4 × 10 = 40
a = 40
Answer D
Question: In how many ways can the letters of the word CAVES be arranged in a row so that the vowels appear in alphabetic order?
A.60
B.30
C.120
D.240
Answer: A.60
Explanation: Two letters can be arranged in 2! ways.
only one combination EIU is required.
5 letters can be arranged in 5! ways.
thus 5!/ 2! * 1 = 60.
A
Question: According to the directions on a packet of smoothie mix, 1 3-ounce packet of smoothie mix is to be combined with 15 ounces of water to make a smoothie. How many 3-ounce packets of smoothie mix are required to prepare 150 12-ounce smoothies?
A. 120
B. 150
C. 180
D. 240
Answer: C. 180
Explanation: This question wasn't particularly grueling, but I think it's the first where I had the opportunity to solve it via theory andinspectionthat many on this board suggest as strategy on the GMAT. It actually came to me by accident. Basically, if we thought that the 3 packets of powder were included in the 12 ounces of water, that would mean we would need 150 packets of smoothie mix (along with 12(150) ounces of water for a total of 150 packets. However, we know, after a more careful reading of the stimulus, that the 3 ounces are NOT included in the 12 ounces. As such, the answer has to be LESS than 150 packets, since 150 would be too much powder considering you already have 150(12) ounces of water and need less packets than water to make a smoothie. As such, the only answer less than 150 is 120, A. Does this make sense? Or am I way off base?
C
Question: A palindrome is a number that reads the same forward and backward, such as 616. How many even, 4-digit numbers are palindromes?
A.40
B.45
C.50
D.90
Answer: A.40
Explanation: First recognize you only need to consider the first two digits (because the second two are just the first two flipped)
There are 90 possibilities for the first two digits of a 4 digit number, 10-99 inclusive. Everything starting with a 2,4,6,8 will be odd, which is 4/9ths of the combinations.
4/9*90 = 40
ANSWER:A