mathewhe/aqua_rat huggingface dataset:
Question: Rap is working on a set of Data Sufficiency problems for his December GMAT: a geometry problem, an algebra problem, and a data interpretation problem. He has determined that statement 1 of the geometry problem is insufficient on its own, that both statement 1 and 2 of the algebra problem are insufficient on their own, and that statement 2 of the data interpretation problem is insufficient on its own. If the probabilities are expressed as percents T, approximately how much greater is the probability that all three answers are “C” after Rap figures out that statement 1 of the data interpretation problem is also insufficient on its own?
(A) T=2.3%
(B) T=2.8%
(C) T=3.3%
(D) T=5.6%
(E) T=8.3%
Rationale: Step 1: Figure out what we need to know.We have two probabilities T that we need to figure out: the one before Raj figures out that statement 1 of the data interpretation problem is also insufficient, and the one after. The answer is the difference between them, in the form of a percent.
Step 2: The first probability.
If statement 1 of the geometry problem is insufficient, then the only valid answer choices are B, C, and E; the probability that it is C is 1/3.
If both statements of the algebra problem are insufficient on their own, then the only remaining valid answers are C and E; the probability that it is C is 1/2
If statement 2 of the data interpretation problem is insufficient, then the remaining answers are A, C, and E, and the probability that C is correct is 1/3.
The probability of all three occurring is the product of the probability fractions: (1/3)*(1/2)*(1/3) = 1/18.
Step 3: The second probability.
Only the third problem has changed; if Raj now knows that statement 1 is also insufficient, the valid answer choices are only C and E, leaving a 1/2 probability that the answer is C.
The probability of all three occurring is still the product of those fractions, but this time they are (1/3)*(1/2)*(1/2) = 1/12.
Step 4: The answer.Note that here, as will sometimes happen on the GMAT, values that you compute “along the way” appear as wrong answer choices. This problem calls for the difference between our two numbers, (1/12)-(1/18) = 1/36, which is a 2.77777% chance, rounded to 2.8% —the correct answer is Choice B.
Answer: (B) T=2.8%
Question: If the a radio is sold for rs 490 and sold for rs 465.50.find loss value.
(A) 24.5
(B) 12.5
(C) 17.25
(D) 6.5
(E) 13.62
Rationale: cp=rs490,sp= 465.50.
loss=rs(490-465.50)=rs 24.50.
Ans: A
Answer: (A) 24.5
Question: If rupee one produces rupees nine over a period of 40 years, find the rate of simple interest?
(A) 22 1/9 %
(B) 22 2/2 %
(C) 23 1/2 %
(D) 22 1/2 %
(E) 62 1/2 %
Rationale: 9 = (1*40*R)/100
R = 22 1/2 %
Answer:D
Answer: (D) 22 1/2 %
Question: David and Lewis leave Chennai for Tirupati simultaneously at 7 A.M in the morning driving in two cars at speeds of 60 mph and 80 mph respectively. As soon as Lewis reaches Tirupati he returns back to Chennai along the same route and meets David on the way back. If the distance between the two cities is 160 miles, how far from Chennai did David and Lewis meet?
(A) 100 mlies
(B) 120 miles
(C) 90 miles
(D) 95 miles
(E) 110 miles
Rationale: Time taken by Lewis to reach Tirupati = 160/80 = 2 hours
In 2 hours, David travels 60*2 = 120 miles
So distance at which they meet should be greater than 120 miles.
Only B satisfies.
Answer is B.
Answer: (B) 120 miles
Question: In an exam, X scored 30 percent, Y scored 50 percent and Z 40 percent. The maximum score awarded in the exam is 800. Find the average mark scored by all the three candidates?
(A) 270
(B) 280
(C) 290
(D) 300
(E) 320
Rationale: Average mark scored by all the three boys
= [30/100 (800) + 50/100 (800) + 40/100 (800)] / 3
= 320
Answer: E
Answer: (E) 320
Question: In how many ways can 4 boys and 2girls be arranged ata table if 2 girls are never together?
(A) 76
(B) 74
(C) 72
(D) 73
(E) 79
Rationale: Total ways of arranging 6 person in a circle = 5! = 120 ways
If we consider two women as one, then we have 4+1=5 persons. Arranging these five persons in circle will take = 4! = 24 ways
And two women can arrange themselves in 2! ways
Total ways in which two women sit together in circle = 4!*2! = 48 ways
Total ways in which two women doesn’t sit together in circle = 5! - 4!*2! =120 - 48 = 72 ways
C
Answer: (C) 72
Question: If 0 < c< 1 < d, which of the following must be true?
(A) 1 < 1/c< 1/d
(B) 1/c< 1 < 1/d
(C) 1/c< 1/d< 1
(D) 1/d< 1 < 1/c
(E) 1/d< 1/c< 1
Rationale: 0<c<1<d. Let c=1/2 and d=2
Substituting values:
A. 1<2<1/2 ---Wrong
B. 2<1< 1/2 ---Wrong
C. 2<1/2<1 ---Wrong
D. 1/2<1<2 ---Correct
E. 1/2<2<1 ---Wrong
Hence answer is D
Answer: (D) 1/d< 1 < 1/c
Question: a farmer have 10%cow,15%buffalo,25%goat,50% chicken.he has 30 goat.then calculate the no. of cow,buffalo and chicken.
(A) 12,15,45
(B) 12,18,60
(C) 10,18,45
(D) 10,16,60
(E) 14,16,30
Rationale: total no. of livestock is x.
x*25/100=30
x=3000/25=120
no.of cow=120*10/100=12
no. of buffalo=120*15/100=18
no. of chicken=120*50/100=60
answer B
Answer: (B) 12,18,60
Question: The total of a company's assets in 1994 was 200% greater than the total in 1993, which in turn was 300% greater than the total in 1992. If the total of the company's assets in 1992 was N dollars, what were the company's assets in 1994?
(A) 5N
(B) 6N
(C) 9N
(D) 12N
(E) 15N
Rationale: In 1992, the company's assets were N.
In 1993, the company's assets were N + 3N =4N.
In 1994, the company's assets were 4N + 8N = 12N.
The answer is D.
Answer: (D) 12N
Question: A fill pipe can fill 1/6 of cistern in 90 minutes in how many minutes, it can fill 5/6 of the cistern?
(A) 450 min
(B) 360 min
(C) 240 min
(D) 306 min
(E) 500 min
Rationale: 1/6 of the cistern can fill in 90 min
5/6 of the cistern can fill in = 90*6*5/6 = 450 min
Answer is A
Answer: (A) 450 min
Question: If $100,000 is invested at x percent simple annual interest for n years, which of the following represents the total amount of interest, in dollars, that will be earned by this investment in the n years?
(A) 10,000(x^n)
(B) 10,000(x/100)^n
(C) 10,000n(x/100)
(D) 10,000(1+x/100)^n
(E) 100,000n(x/100)
Rationale: I think answer D is for compound interest (which i assumed)
and answer E is for simple interest because it is not compounding.
Answer: (E) 100,000n(x/100)
Question: A farmer grows Broccoli in his farm that is in the shape of a square. Each Broccoli takes 1 square foot of area in his garden. This year, he has increased his output by 101 Broccoli when compared to last year. The shape of the area used for growing the Broccoli has remained a square in both these years. How many Broccoli did he produce this year?
(A) 2400
(B) 2601
(C) 1987
(D) 2000
(E) Cannot be determined
Rationale: Explanatory Answer
The shape of the area used for growing Broccoli has remained a square in both the years.
Let the side of the square area used for growing Broccoli this year be X ft.
Therefore, the area of the ground used for cultivation this year = X2 sq.ft.
Let the side of the square area used for growing Broccoli last year be Y ft.
Therefore, the area of the ground used for cultivation last year = Y2 sq.ft.
As the number of Broccoli grown has increased by 101, the area would have increased by 101 sq ft because each Broccoli takes 1 sq ft space.
Hence, X2 - Y2 = 101
(X + Y)(X - Y) = 101.
101 is a prime number and hence it will have only two factors. i.e., 101and 1.
Therefore, 101 can be expressed as product of 2 numbers in only way = 101 * 1
i.e., (X + Y)(X - Y) = 101* 1
So, (X + Y) should be 101 and (X - Y) should be 1.
Solving the two equations we get X = 51 and Y = 50.
Therefore, number of Broccoli produced this year = X2 = 512 = 2601.
Alternative Approach : Use answer choices
The area in both the years are squares of two numbers.
That rules out choice A,C and D. as 2400,1987 and 2000 are not the square of any number.
Check Choice B: If this year's produce is 2601, last year's produce would have been 2601 - 101 = 2500
2500 is the square of 50.
So, 2601 is the answer.
Choice B
Answer: (B) 2601
Question: 2, 3, 5, 7, 11, ?, 17
(A) 15
(B) 14
(C) 13
(D) 12
(E) 11
Rationale: The series consists of prime numbers starting from 2.
Answer : C.
Answer: (C) 13
Question: Out of 18 students studying in a class, 7 are from Maharashtra, 5 are from Karnataka and 3 are from Goa. Four students are to be selected at random. What are the chances that at least one is from Karnataka?
(A) 12â„13
(B) 11â„13
(C) 10â„15
(D) 59/77
(E) None of these
Rationale: Total possible ways of selecting 4 students out of 18 students = 18C4 =3060
The no. of ways of selecting 4 students in which no student belongs to Karnataka = 13C4=715
âˆ´ Hence no. of ways of selecting at least one student from Karnataka = 18C4 â€“ 13C4 = 2345
âˆ´ Probability = 2345â„3060= 59/77
Answer D
Answer: (D) 59/77
Question: John makes $60 a week from his job. He earns a raise and now makes $100 a week. What is the % increase?
(A) 16%
(B) 66.67%
(C) 17%
(D) 17.61%
(E) 17.56%
Rationale: Increase = (40/60)*100 = (4/6)*100 = 66.67%.
B
Answer: (B) 66.67%
Question: If the sides of a triangle are 30 cm, 28 cm and 10 cm, what is its area?
(A) 120
(B) 110
(C) 130
(D) 140
(E) 150
Rationale: The triangle with sides 30 cm, 28 cm and 10 cm is right angled, where the hypotenuse is 30 cm.
Area of the triangle = 1/2 * 28 * 10 = 140 cm2
Answer: Option D
Answer: (D) 140
Question: Pipe A fills a swimming pool in 4 hours. Pipe B empties the pool in 6 hours. If pipe A was opened at 5:00 am and Pipe B at 6:00 am, at what time will the pool be full?
(A) 13:00
(B) 14:00
(C) 15:00
(D) 17:00
(E) 16:00
Rationale: Pipe A fills the pool in 4 hrs.
1 hour's work : 1/4
Pipe B empties the pool in 6 hrs.
1 hour's work : 1/6
Together if they work, 1 hour's work = 1/4 -1/6 = 1/12
Given : Pipe A started at 5:00 a.m and Pipe B at 6:00 a.m
Pool filled after 1 hour by Pipe A : 1/4 or 3/12
After 6:00 a.m
Pool filled after 1 hour with both the pipes on : 1/12
Pool filled after 9 hours with both pipes on : 9/12
Pool filled in 1 hour + Pool filled in 9 hours = 3/12 +9/12 =1
Therefore, it takes 10 hrs to fill the pool
As Pipe A started at 5:00 a.m, pool is full at 15:00 hrs
Answer : C
Answer: (C) 15:00
Question: we have 7 weights one of 2 kg one of 3 kg one of 5 kg one of 1 kg one of 10 kg one of 15 kg one of 20 kg by using only five weight how many weight u can weight
(A) 19
(B) 18
(C) 24
(D) 21
(E) 32
Rationale: select 5 weight out of 7, 7C5=21
ANSWER:D
Answer: (D) 21
Question: Obra drove 140π meters along a circular track. If the area enclosed by the circular track on which she drove is 57,600π square meters, what percentage of the circular track did Obra drive?
(A) 6.67%
(B) 12.5%
(C) 18.75%
(D) 29.16%
(E) 33.3%
Rationale: area enclosed by the circular track on which she drove is 57,600π square meters
So, π(r^2) = 57,600π ---> (r^2)=57,600 ---> r=240
Circumference of the circular track = 2πr = 480π
Therefore, part of circumference covered = 140π/480π =29.16%
Hence, answer is D.
Answer: (D) 29.16%
Question: A and B go around a circular track of length 600 m on a cycle at speeds of 36 kmph and 54 kmph. After how much time will they meet for the first time at the starting point?
(A) 120
(B) 288
(C) 277
(D) 126
(E) 221
Rationale: Time taken to meet for the first time at the starting point
= LCM { length of the track / speed of A , length of the track / speed of B}
= LCM { 600/ (36 * 5/18) , 600/ (54 * 5 /18) }
= LCM (60, 40) = 120 sec.
Answer: A
Answer: (A) 120
Question: Walking at 5/6th of its usual speed a cab is 8mnts late. Find its usual time to cover the journey?
(A) 25m
(B) 45m
(C) 40m
(D) 50m
(E) 62m
Rationale: New speed = 5/6th of usual speed
New time = 6/5th of usual time
6/5 UT - UT = 8m
UT/5 = 8m
UT = 40m
Answer is C
Answer: (C) 40m
Question: A rectangular grass field is 70 m * 55 m, it has a path of 2.5 m wide all round it on the outside. Find the area of the path and the cost of constructing it at Rs.2 per sq m?
(A) s.1350
(B) s.1300
(C) s.1328
(D) s.1397
(E) s.1927
Rationale: Area = (l + b +2d) 2d
= (70 + 55 +2.5 * 2) 2*2.5 => 650
650 * 2 = Rs.1300
Answer: B
Answer: (B) s.1300
Question: The numerator of a fraction is 1 less than twice the denominator. If the numerator and denominator are both increased by \
1, the fraction becomes 3/5. Find the fraction?
(A) A)5/3
(B) B)3/5
(C) C)4/7
(D) D)5/9
(E) of these
Rationale: Let the numerator and denominator of the fraction be 'n' and 'd' respectively.
n = 2d - 1
(n + 1)/(d + 1) = 3/5
5n + 5 = 3d + 3
5n + 5 = 3(2n - 1) + 3 => n = 5
n = 2d - 1 => d = 3
Hence the fraction is : 5/3
ANSWER:A
Answer: (A) A)5/3
Question: Ravi can do a piece of work in 15 days while Prakash can do it in 30 days. In how many days will they finish it together?
(A) 11 days
(B) 9 days
(C) 8 days
(D) 12 days
(E) 10 days
Rationale: 1/15 + 1/30 = 3/30
10/1 = 10 days
ANSWER:E
Answer: (E) 10 days
Question: The product of three consecutive numbers is 336. Then the sum of the smallest two numbers is ?
(A) 13
(B) 15
(C) 20
(D) 38
(E) 56
Rationale: Product of three numbers = 336
336 = 6*7*8.
So, the three numbers are 6, 7 and 8.
And Sum of smallest of these two = 6+7 = 13.
ANSWER : OPTION A
Answer: (A) 13
Question: The edges of a cuboid are respectively 3cm, 4cm and 12 cm. Find the length of the diagonal of cuboid?
(A) 28 m3
(B) 27 m3
(C) 60 m3
(D) 18 m3
(E) 61 m3
Rationale: lb = 20 ; lh = 15 ; fh
= 12
(lbh)2 = 20 * 15 * 12 => lbh
= 60 m3
Answer: C
Answer: (C) 60 m3
Question: When a student Joe, weighing 44 kg, joins a group of students whose average weight is 30 kg, the average weight goes up by 1 kg. Subsequently, if two students, excluding Joe, leave the group the average weight comes back to 30 kg. What is the difference between the average weight of the two students who left and the weight of Joe?
(A) 5.5 kg
(B) 11 kg
(C) 30 kg
(D) 36.5 kg
(E) 7 kg
Rationale: After two persons leave the group the average remains the same. That means the weight of the two persons = 44+30 = 74
So, the average the two persons = 37
That gives the answer 44-37 = 7
Answer E
Answer: (E) 7 kg
Question: From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there in the committee. In how many ways can it be done?
(A) 1000
(B) 756
(C) 480
(D) 660
(E) 520
Rationale: Total Men = 7
Total Women = 6
Persons in committee = 5
No. of ways to select at least 3 men = 7C5 + 7C4 * 6C1 + 7C3*6C2
= 756
Ans - B
Answer: (B) 756
Question: Consider the sets Tn= {n, n + 1, n + 2, n + 3, n + 4), where n = 1, 2, 3, … , 96. How many of these sets contain 6 or any integral multiple thereof (i.e., any one of the numbers 6, 12, 18, …)?
(A) 80
(B) 81
(C) 82
(D) 83
(E) 84
Rationale: Explanation :
If n = 1, then the set T1 = {1,2,3,4,5}, and it does not have 6 or any multiples.
n = 2 to n = 6 has 6 in the set.
n = 7, has the set T7 = {7,8,9,10,11}, and no 6 or multiples.
So 1 in every 6 members do not have 6 or multiples of 6.
So, till n = 96, there are 16 sets of “6 members” (16*6 = 96) and 16 sets do not have 6 or its multiples, while the remaining 80 sets have.
Answer : A
Answer: (A) 80
Question: On a partly cloudy day, Derek decides to walk back from work. When it is sunny, he walks at a speed of s miles/hr (s is an integer) and when it gets cloudy, he increases his speed to (s + 1) miles/hr. If his average speed for the entire distance is 2.8 miles/hr, what fraction T of the total distance did he cover while the sun was shining on him?
(A) 1/4
(B) 4/5
(C) 1/5
(D) 1/6
(E) 1/7
Rationale: If s is an integer and we know that the average speed is 2.8, s must be = 2. That meanss+1= 3. This implies that the ratio of time for s=2 is 1/4 of the total time. The formula for distance/rate is D=Rt...so the distance travelled when s=2 is 2t. The distance travelled for s+1=3 is 3*4t or 12t. Therefore, total distance covered while the sun was shining over him is T=2/14 = 1/7. Answer: E
Answer: (E) 1/7
Question: A metallic sheet is of rectangular shape with dimensions 48 m x 36 m. From each of its corner, a square is cut off so as to make an open box. If the length of the square is 8 m, the volume of the box (in m3) is
(A) 6420
(B) 8960
(C) 5120
(D) 4830
(E) None
Rationale: Sol.
Clearly, l = (48 - 16) m = 32 m,
b = (36 - 16) m = 20 m,
h= 8 m.
∴ Volume of the box = (32 x 20 x 8) m3 = 5120 m3
Answer C
Answer: (C) 5120
Question: Rajeswari went to the stationers and bought things worth Rs. 100, out of which 50 paise went on sales tax on taxable purchases. If the tax rate was 10%. then what was the cost of the tax free items?
(A) Rs. 90.50
(B) Rs. 89.50
(C) Rs. 94.00
(D) Rs. 99.50
(E) Rs. 94.50
Rationale: Solution
Let the amount of taxable purchases be Rs.x.
Then, 10% of x	= 50/100
x ‹=› (50/100×100/10)
= 5
Cost of tax free items	= Rs.[100 - (5 + 0.50)]
= Rs. 94.50
Answer E
Answer: (E) Rs. 94.50
Question: f(x) is a function such that f(2x + 1) = 2f(x) + 1 for all real numbers x and f(0) = 2. Find the value of f(3).
(A) 10
(B) 11
(C) 12
(D) 13
(E) 14
Rationale: f(2x + 1) = 2f(x) + 1 : given
f(3) = 2f(1) + 1 : x = 1 in A
f(1) = 2f(0) + 1 : x = 0 in A
f(3) = 11 : substitute
correct answer B
Answer: (B) 11
Question: How many triples (a, b, c) of real numbers satisfy the equations
ab = c, ac = b, and bc = a ?
(A) 2
(B) 4
(C) 5
(D) 6
(E) 8
Rationale: Observe that (0, 0, 0) is a triple as in the problem. Now, if one of a, b and c is 0, then the given
equations imply each of them is 0. So we suppose next that each is non-zero. The equations ab = c
and ac = b imply a2bc = bc so that a2 = 1. Hence, a 2 {1,−1}. Similarly, b 2 {1,−1} and
c 2 {1,−1}. One checks that these imply that either (a, b, c) = (1, 1, 1) or exactly one of a, b and
c is 1 and the other two are −1. These observations lead to the total number of tuples being 5.
correct answer C
Answer: (C) 5
Question: An office supply store stocks two sizes of notebooks, each in five colors: blue, green, yellow, red, or pink. The store packs the notebooks in packages that contain either 3 notebooks of the same size and the same color or 3 notebooks of the same size and of 3 different colors. If the order in which the colors are packed is not considered, how many different packages of the types described above are possible?
(A) 15
(B) 20
(C) 24
(D) 30
(E) 36
Rationale: First let's consider the small notebooks.
There are 5 ways to choose 3 notebooks of the same color.
The number of ways to choose 3 notebooks with different colors is 5C3=10.
There are 15 different packages we can make with the small notebooks.
We can use the same process to find 15 different packages with large notebooks.
The total number of different packages is 30.
The answer is D.
Answer: (D) 30
Question: 445, 221, 109, 53,...
(A) 8
(B) 7
(C) 42
(D) 25
(E) 63
Rationale: Explanation :
To obtain next number, subtract 3 from the previous number and divide the result by 2
445
(445-3)/2=221
(221-3)/2=109
(109-3)/2=53
(53-3)/2=25
ANSWER:D
Answer: (D) 25
Question: You have to send 3,000 grapes 1,000 kilometers from grapecity to appleland. Your truck can carry 1,000 grapes at a time. Every time you travel a kilometer towards appleland you must pay a tax of 1 grape but you pay nothing when going in the other direction (towards grapecity).
What is highest number of grapes you can get to appleland?
(A) 833
(B) 765
(C) 665
(D) 679
(E) 874
Rationale: Step one: First you want to make 3 trips of 1,000 grapes 333 kilometers. You will be left with 2,001 grapes and 667 kilometers to go.
Step two: Next you want to take 2 trips of 1,000 grapes 500 kilometers. You will be left with 1,000 grapes and 167 kilometers to go (you have to leave a grape behind).
Step three: Finally, you travel the last 167 kilometers with one load of 1,000 grapes and are left with 833 grapes in appleland.
correct answer is A)833
Answer: (A) 833
Question: A shepherd had n goats in the year 2000. In 2001 the no. of goats increased by 40%. In 2002 the no. of goats declined to 70%. In 2003 the no. of goats grew up 30%. In 2004, he sold 10% goats and then he had only 34,398 goats. The percentage increase of the no. of goats in this duration was :
(A) 16.66%
(B) 14.66%
(C) 11.33%
(D) 20%
(E) None
Rationale: Solution: There is no need of the number of goats given i.e. 34,398.
Initially, let there be 100 goats. Then
100 == 40% ↑==> 140 ==30%↓(declined to 70%)==> 98 ==30%↑ ==> 127.4 ==10%↓(sold)==> 114.66
Hence, % increase = 14.66% [As 100 becomes 114.66].
Answer: Option B
Answer: (B) 14.66%
Question: On a track for remote controlled racing cars, racing car A completes the track in 58 seconds, while racing car B completes it in 35 seconds. If they both start at the same time after how many seconds will they be side by side again.
(A) 275
(B) 325
(C) 2030
(D) 425
(E) None of these
Rationale: Time required in seconds will be LCM ( 35, 58 ) = 2030
Hence, answer will be (C) 2030
Answer: (C) 2030
Question: If f(x) = 5 - 2x, then f -1(-3) = ?
(A) 1
(B) 8
(C) 6
(D) 4
(E) 3
Rationale: Find f -1(x) and then Find f -1(- 3)
y = 5 - 2x , given
x = 5 - 2y , interchange x and y
2y = 5 - x , y = log2(5 - x) , solve for y
f -1(x) = log2(5 - x) , inverse function
f -1(- 3) = log2(5 + 3)
= log2(23) = 3
correct answer E
Answer: (E) 3
Question: A sports retailer ordered white and yellow tennis balls in equal number but the dispatch clerk of the tennis ball company erred and dispatched 20 extra yellow balls and making ratio of white balls to yellow balls 8/13. How many tennis balls did the retailer order originally.
(A) 64
(B) 130
(C) 140
(D) 160
(E) 120
Rationale: White:Yellow = x:(x+20) = 8:13 --> 13x = 8x + 160 --> x = 32.
The total # of balls originally x + x = 32 + 32 = 64.
Answer: A.
Answer: (A) 64
Question: The sum of ages of 5 children born at the intervals of 3 years each is
50 years. Find out the age of the youngest child?
(A) 6 years
(B) 5 years
(C) 4 years
(D) 2 years
(E) 1 year
Rationale: Let the age of the youngest child =x
Then, the ages of 5 children can be written as x,(x+3),(x+6),(x+9) and (x+12)
x+(x+3)+(x+6)+(x+9)x+(x+3)+(x+12)=50
5x+30=50
5x=20
x=20/5=4 Answer: Option C
Answer: (C) 4 years
Question: If w and y are different prime numbers less than ten, what must be true about the sum of w and y?
(A) the sum is even
(B) the sum is odd
(C) the sum is less than ten
(D) the sum is greater than ten
(E) the sum is less than 13
Rationale: This has to be solved by checking for each option:
Prime numbers less that 10 = 2, 3, 5, 7
A. the sum is even
May or may not be true. w = 3, y, = 5 -> True.
w = 2, y = 3 - True
B. the sum is odd
May or may not be true. w = 3, y, = 5 -> False.
w = 2, y = 3 - True
C. the sum is less than ten
May or may not be true w= 5, y = 7, Sum = 12
w = 2, y = 3. Sum = 5
D. the sum is greater than ten
May or may not be true w= 5, y = 7, Sum = 12
w = 2, y = 3. Sum = 5
E. the sum is less than 13
This will always be true.
Maximum sum = 7 + 5 = 12.
This is always less than 13.
Correct Option: E
Answer: (E) the sum is less than 13
Question: Robert is traveling on his cycle and has calculated to reach point A at 2 p.m. if he travels at 10 km/hr; he will reach there at 12 noon if he travels at 15 km/hr. At what speed must he travel to reach A at 1 p.m.?
(A) 22
(B) 88
(C) 12
(D) 77
(E) 99
Rationale: Let the distance traveled be x km.
Then, x/10 - x/15 = 2
3x - 2x = 60 => x = 60 km.
Time taken to travel 60 km at 10 km/hr = 60/10 = 6 hrs.
So, Robert started 6 hours before 2. p.m. i.e., at 8 a.m.
Required speed = 60/5 = 12 kmph.
Answer:C
Answer: (C) 12
Question: Three 6 faced dice are thrown together. The probability that exactly two dice show the same number on them is ?
(A) 5/19
(B) 5/12
(C) 5/29
(D) 5/20
(E) 5/22
Rationale: Using question number 11 and 12, we get the probability as
1 - (1/36 + 5/9)
= 5/12
Answer:B
Answer: (B) 5/12