mathewhe/aqua_rat huggingface dataset:
Question: James went on a diet 12 months ago when he weighed 222 pounds. If he now weighs 198 pounds and continues to lose at the same average monthly rate, in approximately how many months will he weigh 190 pounds?
(A)  3
(B)  3.5
(C)  4
(D)  4.5
(E)  5
Rationale: 222 - 198 = 24 pounds lost in 12 months
24/12 = 2, so Joe is losing weight at a rate of 2 pounds per month.
...in approximately how many months will he weigh 190 pounds?
A simple approach is to just list the weights.
Now: 198 lbs
In 1 month: 196 lbs
In 2 months: 194 lbs
In 3 months: 192 lbs
In 4 months: 190 lbs
Answer: C
Answer: (C)  4
Question: You and your friend spent a total of $17 for lunch. Your friend spent $3 more than you. How much did your friend spend on their lunch?
(A) $9
(B) $3
(C) $4
(D) $10
(E) $5
Rationale: My lunch = l, my friends lunch = l+3
(l)+(l+3)=17
l+l+3-3=17-3
2l=14
l=7
My friends lunch l+3 = 7+3=$10, the answer is D
Answer: (D) $10
Question: There are 4 red chips and 2 blue ones. When arranged in a row, they form a certain color pattern, for example RBRRB. How many color patterns?
(A) A)10
(B) B)12
(C) C)24
(D) D)50
(E) E)100
Rationale: Using anagram method:
6_5_4_3_2_1
R_R_R_R_B_B
so..
6!/Number of repeated letters (4!)(2!) = 5
ANS:D
Answer: (D) D)50
Question: If a is a positive integer and a^2 is divisible by 12, then the largest positive integer that must divide a ^3 is
(A)  2^3
(B)  2^6
(C)  3^3
(D)  6^3
(E)  12^2
Rationale: Since a is an integer so a cannot have a 2 and sqrt 3 (because squaring this will give us a 2^2 and 3 (making the product as 12, and making a^2 as a multiple of 12))
a^2 is divisible by 12 (12 = 2*2*3), So, a should have at least one 2 and one 3 so that a^2 has a 2^2 and two 3
So, a will have a 2 and a 3. Or a will be a multiple of 6
So, largest possible integer than should divide a^3 is 6^3
So, Answer will be D
Answer: (D)  6^3
Question: Andy has 20 pairs of matched gloves. If he loses 15 individual gloves, which of the following is NOT a possible number of matched pairs he has left?
(A) 9
(B) 11
(C) 13
(D) 14
(E) 15
Rationale: We can solve this is second. The question isSelect an answer choice where there is no possibility of having a number as a matched pair
Case1: If 15 gloves are gone the maximum probability of losing maximum gloves is 15 pairs of gloves out of 20. This means i m having 5 pairs of gloves. [Minimum number of gloves i can have is 5 pairs]
Case2: If 15 gloves are gone the maximum probability of losing minimum gloves is 15/2 = 7.5 means i can lose 8 glove. in this scenario i will be having 12 gloves.
Hence10 < Available Glove Pair < 13
any given time I cant possess 13 glove pair for the above mentioned scenario. And thats the answer. C.
Answer: (C) 13
Question: By selling 33 metres of cloth , one gains the selling price of 11 metres . Find the gain percent .
(A) 20%
(B) 30%
(C) 40%
(D) 50%
(E) 60%
Rationale: (SP of 33m)-(CP of 33m)=Gain=SP of 11m
SP of 22m = CP of 33m
Let CP of each metre be Re.1 , Then, CP of 22m= Rs.22,SP of 22m=Rs.33.
Gain%=[(11/22)*100]%=50%
ANSWER D
Answer: (D) 50%
Question: Mrs. Rodger got a weekly raise of $149. If she gets paid every other week, write an integer describing how the raise will affect her paycheck.
(A) $140
(B) $141
(C) $142
(D) $149
(E) $145
Rationale: Let the 1st paycheck be x (integer).
Mrs. Rodger got a weekly raise of $ 149.
So after completing the 1st week she will get $ (x+1495).
Similarly after completing the 2nd week she will get $ (x + 149) + $ 149.
= $ (x + 149 + 149)
= $ (x + 298)
So in this way end of every week her salary will increase by $ 149.
correct answer D)$149
Answer: (D) $149
Question: R is the set of positive odd integers less than 200, and S is the set of the squares of the integers in R. How many elements does the intersection of R and S contain ?
(A)  None
(B)  Two
(C)  Four
(D)  Five
(E)  Seven
Rationale: R is the set of positive odd integers less than 200, and S is the set of the squares of the integers in R.
How many elements does the intersection of R and S contain?
R=1,3,5,7,9,11,13,15...
S=1,9,25,49,81...
Numbers: 1, 9, 25, 49, 81, 121, and 169 are odd integers (less than 200) that are in both sets.
Solution: Seven
Answer: E
Answer: (E)  Seven
Question: Find the simple interest on Rs.500 for 9 months at 6 paisa per month?
(A) Rs.345
(B) Rs.270
(C) Rs.275
(D) Rs.324
(E) Rs.325
Rationale: I = (500*9*6)/100 = 270
Answer :B
Answer: (B) Rs.270
Question: The cost price of 13 articles is equal to the selling price of 11 articles. Find the profit percent?
(A) 15 5/15%
(B) 18 2/11%
(C) 16 2/3%
(D) 30%
(E) 40%
Rationale: Explanation:
13 CP = 11 SP
11 --- 2 CP
100 --- ? =>18 2/11%
Answer IS B
Answer: (B) 18 2/11%
Question: If a(a - 6) = 27 and b(b - 6) = 27, where a ≠ b, then a + b =?
(A) 6
(B) −2
(C) −48
(D) 46
(E) 48
Rationale: i.e. if a =-3 then b = 9
or if a = 9 then b =-3
But in each case a+b = -3+9 = 6
Answer: option A
Answer: (A) 6
Question: A train leaves Mumabai at 9 am at a speed of 40 kmph. After one hour, another train leaves Mumbai in the same direction as that of the first train at a speed of 50 kmph. When and at what distance from Mumbai do the two trains meet?
(A) 2:00pm, 206 km
(B) 2:00pm, 220 km
(C) 2:00pm, 200 km
(D) 2:00pm, 208 km
(E) 2:00pm, 230 km
Rationale: When the second train leaves Mumbai the first train covers 40 * 1 = 40 km
So, the distance between first train and second train is 40 km at 10.00am
Time taken by the trains to meet
= Distance / relative speed
= 40 / (50 -40) = 4 hours
So, the two trains meet at 2 p.m. The two trains meet 4 * 50
= 200 km away from Mumbai.
Answer: C
Answer: (C) 2:00pm, 200 km
Question: One day when Ram was walking on the street, one boy requested him to donate for cancer patients welfare fund. He gave him a rupee more than half the money he had. He walked a few more steps. Then came a girl who requested him to donate for poor people's fund for which he gave two rupees more than half the money he had then. After that, again a boy approached him for an orphanage fund. He gave three rupees more than half of what he had. At last he had just one rupee remaining in his hand.How much amount did Ram have in his pocket when he started?
(A) Rs.72
(B) Rs.58
(C) Rs.35
(D) Rs.42
(E) Rs.52
Rationale: Last he had 1 rupee,when he gave to boy 3 rupees more than half so it written as (1+3)*2 similarly remaining
i.e. (((1+3)2+2)2+1)2=42
ANSWER:D
Answer: (D) Rs.42
Question: A positive number x is multiplied by 2, and this product is then divided by 4. If the positive square root of the result of these two operations equals x, what is the value of x ?
(A)  9/4
(B)  3/2
(C)  4/3
(D)  2/3
(E)  1/2
Rationale: We need to produce an equation from the information given in the problem stem. We are first given that x is multiplied by 2 and then the product is divided by 3. This gives us:
2x/3
Next we are given that the positive square root of the result (which is 2x/3) is equal to x. This gives us
√(2x/3) = x
2x/3 = x^2
2x = 3x^2
3x^2 – 2x = 0
x(3x – 2) = 0
x = 0 or
3x – 2 = 0
3x = 2
x = 9/4
Because x is positive, x = 9/4. The answer is A.
Answer: (A)  9/4
Question: Two alloys A and B are composed of two basic elements. The ratios of the compositions of the two basic elements in the two alloys are 5 : 3 and 2 : 1, respectively. A new alloy X is formed by mixing the two alloys A and B in the ratio 4 : 3. What is the ratio of the composition of the two basic elements in alloy X ?
(A) 1 : 1
(B) 2 : 3
(C) 5 : 2
(D) 4 : 3
(E) 9 : 5
Rationale: Mixture A has a total of 5 + 3 = 8 parts. If in the final mixture this represents 4 parts, then the total number of parts in mixture B should be (8/4)*3 = 6.
So, we should take of mixture B a quantity with 4 and 2 parts, respectively.
This will give us in the final mixture (5 + 4) : (3 + 2), which means 9:5
Answer E.
Answer: (E) 9 : 5
Question: A company has 4 directors and 5 managers. How many different committees with 5 people can be chosen having at least 1 director?
(A) 500
(B) 120
(C) 4500
(D) 25
(E) 55
Rationale: atleast one means exactly one and more than one.
different committees with 5 people can be chosen having at least 1 director is
(4c1*5c4) + (4c2*5c3) + (4c3*5c2) = 120;
Hence B.
Answer: (B) 120
Question: A group of five women and three men have tickets for seven adjacent seats in one row of a theatre. If the three men will not sit in three adjacent seats, how many possible different seating arrangements are there for these 8 theatre-goers?
(A)  7! – 2!3!2!
(B)  7! – 4!3!
(C)  8! - 6!3!
(D)  7 × 2!3!2!
(E)  2!3!2!
Rationale: 8 people can sit in 8! different ways. But because 3 men cannot sit together, we take them as a unit.
This unit of men, among themselves can sit in 3! ways.
Hence, 8! - 3!.
This unit of men along with 5 women can sit in 6! different ways which also needs to be eliminated.
Hence 8! - 6!3!
C
Answer: (C)  8! - 6!3!
Question: (2+√3+√5)^2-(√3+√5)^2=?
(A) 1+2√3+2√5
(B) 4+4√3+4√5
(C) 1-√3+√5
(D) 1+√3-√5
(E) √3+√5
Rationale: (2+√3+√5)^2-(√3+√5)^2
(2+√3)^2 + 5 +2 (2+√3) (√5) - ( 3 +5 + 2√3√5)
4+ 3+ 4√3 +5 +4 √5 + 2 √15 - 3-5 -2√15
4+4√3+4√5
B is the answer
Answer: (B) 4+4√3+4√5
Question: On the x-y coordinate plane there is a parabola, y=x(8-x). Which of the following points is in the region that is enclosed by this parabola and the x-axis?
I. (2, 4) II. (3, 6) III. (5, 4)
(A) I only
(B) II only
(C) III only
(D) I and II
(E) I, II, and III
Rationale: Since co-efficient of x^2 is negative, the parabola will be downward facing. So the parabola and the x axis will enclose some points where the y-values of the parabola are positive.
When x = 2, y = 12 lies on the parabola, so (2, 4) will be enclosed by the parabola and x axis.
When x = 3, y = 15 lies on the parabola, so (3, 6) will be enclosed by the parabola and x axis.
When x = 5, y = 15 lies on the parabola, so (5, 4) will be enclosed by the parabola and x axis.
The answer is E.
Answer: (E) I, II, and III
Question: The length of a rectangular landscape is 3times its breadth. There is a playground in it whose area is 1600 square mtr & which is 1/3rd of the total landscape. What is the length of the landscape?
(A) 90
(B) 160
(C) 150
(D) 120
(E) 140
Rationale: Sol. x * 3x = 3 * 2500
x = 50
Length = 3* 50= 150
C
Answer: (C) 150
Question: What annual instalment will discharge a debt of 4,200 due in 5 years at 10% simple interest?
(A) 500 per year
(B) 600 per year
(C) 700 per year
(D) 800 per year
(E) None of these
Rationale: Shortcut method :
If borrowed amount be M and it is to be paid in equal instalments, then
M=na+ra/100×Y×n(n−1)/2
where Y = no. of instalments per annum
a = annual instalment
Here, M = 4200, y = 1, r = 10, n = 5, a = ?
4200 = 5a + 10a⁄100 × 5(5 - 1)⁄2
⇒ 4200 = a[5 + 1] ⇒ 6a = 4200
⇒ a = 700
Answer C
Answer: (C) 700 per year
Question: The average age of 15 students of a class is 15 years. Out of these, the average age of 5 students is 14 years and that of the other 9 students is 16 years, The age of the 15th student is
(A) 11
(B) 66
(C) 18
(D) 16
(E) 12
Rationale: Explanation:
Age of the 15th student = [15 * 15 - (14 * 5 + 16 * 9)] = (225-214) = 11 years.
Answer: A
Answer: (A) 11
Question: If daily wages of a man is double to that of a woman, how many men should work for 20 days to earn Rs.14400? Given that wages for 40 women for 30 days are Rs.21600.
(A) 12
(B) 14
(C) 16
(D) 18
(E) 20
Rationale: Explanation :
Wages of 1 woman for 1 day = 21600/40Ã—30
Wages of 1 man for 1 day = 21600Ã—2/40Ã—30
Wages of 1 man for 20 days = 21600Ã—2Ã—20/40Ã—30
Number of men = 14400/(21600Ã—2Ã—20/40Ã—30)=144/(216Ã—40/40Ã—30)= 20
Answer : Option E
Answer: (E) 20
Question: Ram and Hari invest Rs. 18000 and 24000 respectively. If annual profit is Rs.1400 then Ram will get
(A) 400
(B) 800
(C) 600
(D) 500
(E) 300
Rationale: 18000:24000=3:4
then
3*1400/7=600
ANSWER:C
Answer: (C) 600
Question: Ram's age and Shyam's age are in the ratio 3 : 4. Seven years ago the ratio of their ages was 2: 3. Find the ratio of their ages five years hence?
(A) 26:36
(B) 22:33
(C) 26:38
(D) 26:33
(E) 26:43
Rationale: Let ages of Ramu and Shyamu be x and y respectively.
x/y = 3/4 => x = 3/4 y
Also (x - 7) / (y - 7) = 2/3
=> 3x - 21 = 2y - 14
3x = 2y + 7
But x = 3/4 y
3 * 3/4 y = 2y + 7
9y = 8y + 28 => y = 28 years
Ratio of their ages five years hence
= (21 + 5) / (28 + 5) = 26/33.
Answer:D
Answer: (D) 26:33
Question: When x is even, [x] = x/2 + 1, when x is odd [x] = 2x + 1 then [6]*[3] = ?
(A) [22]
(B) [44]
(C) [45]
(D) [28]
(E) [10]
Rationale: [6]*[3]=(6/2+1)(3*2+1)
=[28].
Ans-D
Answer: (D) [28]
Question: How many different pairs of numbers (s, t) such that s = 2t can be obtained if s and t are selected from the set of number {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: Given s=2t
t can take 0,1,2,3,4
and so s = 0,3,6,9
5 such pairs can be formed.
answer E
Answer: (E) 5
Question: The ratio W , by volume of soap to alcohol to water in a 76 litre solution is 2: 50: 100 . The solution is then altered by adding more soap, alcohol and water.After this alteration the ratio, by volume of soap to water in the solution doubles whereas the ratio, by volume of soap to water remains the same as before. What COULD BE the resulting volume.
(A) 79 litres
(B) 78 litres
(C) 77 litres
(D) 152 liters
(E) 304 litres
Rationale: I guess it should be
the ratio W, by volume ofsoaptowaterin the solutiondoubleswhereas the ratio, by volume ofalocoholtowaterremains thesameas before
2:50: 100 => 1 : 25 : 50. If we add all the parts, we get 76 liters
So we have 1 liters of Soap, 25 liters of Alcohol and 50 liters of Water.
Now as per the Question, Soap : Water doubles but alcohol to water remains the same.
So Soap becomes 2 liters, Alcohol remains 25 liters and Water remains at 50 liters.
Hence 77 liters - Option C)
Answer: (C) 77 litres
Question: In a college, the ratio of the number of boys to girls is 8 : 5. If there are 300 girls, the total number of students in the college is
(A) 420
(B) 520
(C) 620
(D) 780
(E) 820
Rationale: Explanation:
Let the boy are 8x and Girls are 5x
=> 5x = 300
=> x = 60
Total students = 8x+5x = 13x = 13(60) = 780
Option D
Answer: (D) 780
Question: Linda spent 3/4 of her savings on furniture and the rest on a TV. If the TV cost her $220, what were her original savings?
(A) $900
(B) $880
(C) $1000
(D) $700
(E) $1500
Rationale: If Linda spent 3/4 of her savings on furnitute, the rest
4 / 4 - 3 / 4 = 1 / 4 on a TV
But the TV cost her $220. So 1 / 4 of her savings is $220. So her original savings are 4 times $220 = $880
correct answer B
Answer: (B) $880
Question: How many positive integers r less than 30 have no common prime factor with 30?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
Rationale: r=30=2*3*5. So, the number must be less than 30 and not have primes 2, 3, or 5.
This means that the number could be: 1, 7, 11, 13, 17, 19, 23, or 29. Total of 8 numbers.
Answer: D.
Answer: (D) 8
Question: Ayesha’s father was 38 years of age when she was born while her mother was 35 years old when her brother four years younger to her was born. What is the difference between the ages of her parents?
(A) 7 years
(B) 4 years
(C) 6 years
(D) 8 years
(E) None
Rationale: EXPLANATION
Mother’s age when Ayesha’s brother was born = 35 years.
Father’s age when Ayesha’s brother was born = (38 + 4) years = 42 years.
Required difference = (42 – 35) years = 7 years.
Answer A
Answer: (A) 7 years
Question: What amount does Kiran get if he invests Rs.8000 at 10% p.a. compound interest for six years, compounding done annually?
(A) 9688
(B) 9687
(C) 9685
(D) 9682
(E) 14172
Rationale: A= P{1 + R/100}n
=> 8000{1 + 10/100}6 = Rs.14172
Answer:E
Answer: (E) 14172
Question: If x > 1 and y < -2, then which of the following must be true ?
(A) x/y > 1
(B) x/y < -1
(C) x/y < 0
(D) x + y > 0
(E) xy > 0
Rationale: Pick x=3, y = -3
A) x/y > 1 - Incorrect as x/y = -1
B) x/y < -1 - Incorrect as x/y = -1
C) x/y < 0 -Correct. It will hold for all values x > 2 and y < -2 as x/y = -1 < 0
D) x + y > 0 - Incorrect. x + y = 0
E) xy > 0 - Incorrect. XY = -9 which is less than zero.
B should be the answer.
Answer: (B) x/y < -1
Question: John takes 12 hours to complete a certain job, while Bill takes only 6 hours to complete the same job. If Steve is faster than John but slower than Bill at completing the same job, then which of the following could be the time it takes the three men together, working at their constant, individual rates, to complete the job?
(A) 2 hours, 24 minutes
(B) 2 hours, 40 minutes
(C) 3 hours, 20 minutes
(D) 3 hours, 45 minutes
(E) 4 hours, 10 minutes
Rationale: The rate of John plus Bill is 1/12 + 1/6 = 1/4 of the job completed per hour.
If Steve worked at the same rate as John, the rate would be 1/4 + 1/12 = 1/3
The slowest possible time would be 3 hours.
If Steve worked at the same rate as Bill, the rate would be 1/4 + 1/6 = 5/12
The fastest possible time would be 12/5 hours = 2 hours, 24 minutes.
The actual time is somewhere between these two extreme points.
The answer is B.
Answer: (B) 2 hours, 40 minutes
Question: The number 35 is equal to the sum of the cubes of two integers. What is the product of those integers?
(A) 6
(B) 15
(C) 21
(D) 27
(E) 39
Rationale: 2^3 + 3^3 =35 therefore product is 2*3=6
A
Answer: (A) 6
Question: If a and b are positive integers such that a/b = 1.69, which of the following must be a divisor of a
(A) 10
(B) 12
(C) 11
(D) 13
(E) 14
Rationale: a/b = 1.69
a/b = 169/100
a = 169/100*b
We require to find from the available 5 options that must be a divisor of a"
This also means which of the following 5 options can divide 169 evenly
(Ignore b as its value unknown; Ignore 100 as in denominator)
Only option D = 13 best fits in
Answer = 13
ANSWER:D
Answer: (D) 13
Question: If the cost of 8kg of rice is $15. What would be the cost of 10 kg of rice?
(A) 15.4
(B) 18.75
(C) 20.25
(D) 21.56
(E) 22.0
Rationale: The cost of one kg of rice = 15/8=1.875
The cost of 10kg of rice = 1.875x10= $ 18.75
Answer: B
Answer: (B) 18.75
Question: A pipe can fill a cistern in 33 minutes. Find the time in which 1/11 part of the cistern will be filled?
(A) 5min
(B) 2min
(C) 3min
(D) 1min
(E) 10min
Rationale: Full cistern filled in = 33 minutes
1/11 part filled in = 33*1/11 = 3minutes
Answer is C
Answer: (C) 3min
Question: A clothing store purchased a pair of pants for $81 and was selling it at a price that equaled the purchase price of the pants plus a markup that was 25 percent of the selling price. After some time a clothing store owner decided to decrease the selling price by 20 percent. What was the clothing store's gross profit on this sale?
(A) $14
(B) $5.4
(C) $4.4
(D) $1.2
(E) $5.0
Rationale: Sale Price(SP) = 81 + Markup(MP)
--> Mp = SP-81
and given MP=SP/4 ( 25% is 1/4th)
so SP/4= SP-81
3SP/4= 81
SP=108
Now a discount of 20% is given so NEW SP is .8 *108 =86.4
Profit=86.4-81 =5.4$
Answer is B
Answer: (B) $5.4
Question: The edges of cuboid are 4 cm; 5 cm and 6 cm. Find its surface area?
(A) 298
(B) 148
(C) 289
(D) 987
(E) 282
Rationale: 2(4*5 + 5*6 + 4*6)
= 148
Answer:B
Answer: (B) 148
Question: In a cosmetics company , there are 5 engineers out of 20 officers. If 3 officers are picked at random, what is the probability that all are engineers.
(A) 3/114
(B) 1/114
(C) 1/1140
(D) 1/1170
(E) None of these
Rationale: Explanation :
No. of engineer = 5.
No. of total non-engineer = 15.
Total no. of officers = 20 of which 3 officers are picked.
P(all are engineers) =
=> No. of selection with restriction / No. of selection without restriction
=> 5C3 / 20C3 .
=> 10 / 1140.
=> 1 / 114.
Answer : B
Answer: (B) 1/114
Question: Every year Taylor goes to the same carnival, and he attempts to shoot a basketball into a small hoop, hoping that he will win a ten-foot tall teddy bear. If the probability that Taylor does not make a basket is 8/9, what is the probability that Taylor makes exactly one basket in four tries?
(A) 256/729
(B) 170/730
(C) 140/730
(D) 184/730
(E) 160/743
Rationale: Probability of basket = 1/9
Probability of no basket = 8/9
Required probability= 4* (1*8*8*8/9^4)
=256/729
A is the answer
Answer: (A) 256/729
Question: Two cyclist start from the same places in opposite directions. One is going towards north at 18kmph and the other is going towards south 20kmph. What time will they take to be 152km apart?
(A) 1 1/4 hours
(B) 2 1/3 hours
(C) 4hours
(D) 3 3/4 hours
(E) 6hours
Rationale: To be (18+20) km apart, they take 1 hour
To be 152 km apart, they take 1/38 * 152 = 4 hrs
Answer is C
Answer: (C) 4hours
Question: BY HOW MUCH PERCENT IS FOUR-FIFTH OF 70 LESSER THAN FIVE-SEVENTH OF 112?
(A) 24%
(B) 30%
(C) 36%
(D) 42%
(E) None of these
Rationale: 4/5*70=56 AND 5/7*112=80
REQUIRED PERCENTAGE-(80-56/80*100)%=(24/80*100)%=30%
CORRECT OPTIONS:B
Answer: (B) 30%
Question: P, Q and R invested Rs.5500, Rs.9900 and Rs.12100 respectively, in a partnership business. Find the share of Q in profit of Rs.62500 after a year?
(A) 22500
(B) 21500
(C) 20500
(D) 19500
(E) 18500
Rationale: Explanation:
5500:9900:12100
5:9:11
9/25 * 62500 = 22500
A)
Answer: (A) 22500
Question: Jamboree and GMAT Club Contest Starts
QUESTION #11:
How many words (with or without meaning) can be formed using all the letters of the word “SELFIE” so that the two E’s are not together?
(A)  660
(B)  600
(C)  500
(D)  300
(E)  240
Rationale: The question is asking the total number of arrangements possible with the letters of the word “SELFIE” where two E’s are not together.
Arrangements when two E’s are not together = Total arrangements - Arrangements when two E’s are together
In total there are 6 letters but two are identical. so we can arrange in 6! ways. but we divide for those objects that are identical. so divide by 2!. Hence,
Total arrangements = 6!/2!
Now two E's are coupled together. Consider this couple (EE) as one letter. apart from this there are 4 more letters. so we can arrange these 5 different objects in 5! ways.
Two E's can arrange themselves in 2! ways, but we divide for those objects that are identical. so divide by 2!. so arrangement for E's would be 2!/2!.
Hence, Arrangements when two E’s are together = 5! * (2!/2!)
Arrangements when two E’s are not together = 6!/2! - 5! = 5! * ( 6/2 -1 ) = 120 * 2 = 240.
Option D is correct!
Answer: (D)  300
Question: Jane bought 300 packets of chocolate. She was able to sell 1/3 of them at a 10% profit, another 1/3 of them at zero profit and the remainder was sold at a 5% loss. Find the total profit or loss made by Jane after selling those 300 packets. A packet sold at a loss had a price of $9.
Please provide an intuitive answer if possible. Thanks!!
(A) 0
(B) Profit of $20
(C) Loss of $25
(D) Profit of $50
(E) Loss of $35
Rationale: A packet sold at a 10% loss had a price of $9, thus the cost of a packet is $10.
100 packets was sold at a 10% profit --> gives profit of 10*0.1*100 = $100.
100 packets was sold at a 5% loss --> gives loss of 10*0.05*100 = $50.
The overall Profit is $100 - $50 = $50.
Answer: D.
Answer: (D) Profit of $50
Question: A certain restaurant offers 6 different salads, 4 different main courses, and 6 different desserts. If customers choose one salad, one main course, and two different desserts for their meal, how many different meals are possible?
(A) 240
(B) 280
(C) 320
(D) 360
(E) 400
Rationale: The number of possible choices for desserts is 6C2 = 15
The number of possible meals is 6*4*15 = 360
The answer is D.
Answer: (D) 360
Question: When positive integer X is divided by positive integer Y, the remainder is 3. If X/Y = 96.12, what is the value of Y?
(A) 96
(B) 75
(C) 48
(D) 25
(E) 12
Rationale: When positive integer x is divided by positive integer y, the remainder is 3 --> x=qy+3;
x/y=96.12 --> x=96y+0.12y (so q above equals to 96);
0.12y=3 --> y=25.
Answer: D.
Answer: (D) 25
Question: 24 men working at 8 hours a day can finish a work in 10 days. Working at the rate of 10 hours a day, the number of men required to finish the same work in 6 days is?
(A) 30
(B) 32
(C) 34
(D) 36
(E) 38
Rationale: Using Using the chain rule,
M1 x T1 = M2 x T2
Therefore, 24 x 8 x 10 = 10 x X x 6
X= 32
Hence, the number of men required to finish the work = 32.
ANSWER:B
Answer: (B) 32