Test: Quantitative Reasoning (Level 700) - 2 - GMAT MCQ

Now, since 

Answer: B.

Amount of solution after 'k' hours = 100 - ky

100x = 100x+1000-kyx -10ky
k(xy+10y) = 1000

Given that A x B < 10, the possible values of AB are 23, 32, 24 and 42.
It is also given that A * B = C and units digit of (A* A + C * B) = B
Since, A = 4 and B =2 only satisfies above condition, hence AB =42.
Answer: (E)

Total Arrangements of 4 boys and 4 girls can be calculated in these two ways
Case 1: BGBGBGBG i.e. total ways = 4!*4! = 24*24 = 576
Case 2: GBGBGBGB i.e. total ways = 4!*4! = 24*24 = 576
Total ways = 576+576 = 1152
Unfavorable ways = cases in which John and Susan are together = 14*3!*3! = 504 (here number 14 comes as pairs of BG or GB who are John and Susan and remaining 3!*3! are ways in which remaining 3 boys can sit alternately and 3 girls can sit alternately)
Favorable cases = 1152 - 504 = 648
Answer: Option D

This is how I broke it down:
Total Distance = 300 feet
default rate is 3fps (feet per second)
walking rate is 6fps (default + walking)
catch up rate: is walking rate - default rate = 6-3 = 3fps

Part 1: Time for Catch up
As he gets on the walk way he instantly starts "catching up" to the group that is 120 feet ahead of him. How long does this take?
D/R = Time; so 120feet/3fps [ note I'm using the catch up rate here ] = 40 seconds of catch up
After 40 seconds, how much of the 300 feet of the moonwalk has been used? well if he was moving for 40 seconds at 6 feet per second (he was walking) then he covered 240 feet of actual walkway.
300-240 feet = 60 feet.
There are only 60 feet left of walkway.

Part 2: Standing with the crowd
Now bill just idles with the crowd for the last 60 feet. 60ft/3fps [ note this is the default rate ] = 20 seconds.

Part 3: Average rate
6 fps for 40 seconds = 240 feet
3 fps for 20 seconds = 60 feet
X fps for 60 seconds = 300 feet

300/60 = 5fps average rate. Answer is E.

Here we have N1, N2, N3, N4, N5 where the median N3 = 17.

We are given that (N1+N5)/2 = 16 and (N2+N4)/2 = 30. Simplify these to be N1+N5=32 and N2 + N4 = 30.

The difference in the values of N1+N5 and N2+N4 is 2. This means that from the lower and upper bounds, the highest value number and/or the lowest value number has to be at least 2 from the median (N4 cannot be valued below 17 and N2 cannot be above 17 - that would break the rule). We are asked what can be the minimum value of the largest of original five inetegers AKA what is the value of N5? I think we found the answer in the prior sentence (N5 is at least 2 higher than N3), but let's test cases to be sure.
N5 + N1 = 32
19 + N1 = 32 => N1 = 13
Now we must address N2 + N4 = 30
Our bounds are now 13 ≤ N2 ≤ 17 and 17 ≤ N4 ≤ 19 but we have to make the overall value drop by 2. We obviously cannot have N2 < N1 so we must have N2 ≥ N1 and manipulate the upper bound.
13+N4=30 => N4 = 17.
If we were to increase N2 to 14, then N4 would have to equal 16 but we cannot have N4 cross the value of the median so this does not work.
As such you can see 19 is the correct answer for the lowest value for N5. IMO answer is C.

N = 11a+7
i.e. Possible values of N may be 18, 29, 30, 41, 52, 63, 74, 85, 96, 107, 118, 129, 140, 151, 162, 173, 184, 195 and so on
11a may be a 3 digit number such as 121, 242, 363, 979
N = 979+7 = 986
9+8+6 = 23 Satisfied!
986 when divided by 33 leaves remainder = 29
Answer: Option E

{Total} = {Writers} + {Editors} - {Both} + {Neither}.
{Total} = 100;
{Writers} = 45;
{Editors} > 38;
{Both} = x;
{Neither} = 2x;100 = 45 + {Editors} - x + 2x
x = 55 - {Editors}.
We want to maximize x, thus we should minimize {Editors}, minimum possible value of {Editors} is 39, thus:
x = {Both} = 55 - 39 = 16.
Answer: B.

Diana and her two brothers can be assigned to one of the 3 groups, so each has 3 choices, so total # of different assignments of Diana and her 2 brothers to 3 groups is 3∗3∗3 = 3 = 27.
Now, "Diana leaves at the same time as AT LEAST one her brothers" means that Diana is in the same group as at least one her brothers.
Let's find the opposite probability of such event and subtract it from 1. Opposite probability would be the probability that Diana is not in the group with any of her brothers.
In how many ways we can assign Diana and her two brothers to 3 groups so that Diana is not in the group with any of her brothers? If Diana is in the first group, then each of her two brothers will have 2 choices (either the second group or the third) and thus can be assigned in 2 ∗ 2 = 2² = 4 ways to other two groups. As there are 3 groups, then total # of ways to assign Diana and her 2 brothers to these groups so that Diana is not in the group with any her bothers is 3 ∗ 4 = 12 (For each of Diana's choices her brother can be assigned in 4 ways, as Diana has 3 choices: first, second or the third group, then total 3 ∗ 4 = 12). So probability of this event is 12/27.
Probability that Diana is in the same group as at least one her brothers would be 
Answer: E.

Given:

• K = 1 * 2 + 2 * 3 + 3 * 4 + … + 21 * 22

To find:

• The remainder when K is divided by 23

Approach and Working:
If we observe the terms of the series K, we can generalise it as follows:

• 1st term = 1 * 2
• 2nd term = 2 * 3
• 3rd term = 3 * 4
• Hence, nth term = n * (n + 1) = n²+n

Now, sum of all the terms of 

• If n = 21, 

Therefore, it will be always divisible by 23, giving a 0 remainder

Hence, the correct answer is option E.

First of all, clearly 

So, II is bigger than I. Now, what about III? When we take higher order roots, the values move closer to one. If the number starts larger than one, then higher and higher roots make it smaller, closer to one. If the number starts between 0 and 1, then higher and higher roots make it larger, closer to one. Therefore, III is larger than II. From smallest to biggest, I, II, III.
Answer = (A).

From size 8 to size 17, there are 9 increments of .25 each making the size 17 shoe 9*.25 = 2.25 inches more than the size 8 shoe.
This 2.25 accounts for 20% of the length of size 8 shoe so length of size 8 shoe is 2.25*5 = 11.25 inches
Length of size 15 shoe must be 11.25 + .25*7 = 13 inches

Original range of temperatures: 21 degrees Fahrenheit
The thermometer always overstated by 15%
Overstatement of 15% on 21 degrees = 0.15 * 21 = 3.15 degrees
Adjusted range with accurate measurements: 21 - 3.15 = 17.85 degrees
Approximate range after accurate measurements: 18 degrees
Therefore, the approximate range of measurements with accurate readings would be 18 degrees, which corresponds to option C.

We can let the height of both candles be 12 inches. So the first candle burns at a rate of 3 inches per hour and the second candle at a rate of 4 inches per hour. We can let x = the number of hours it takes the first candle to be twice the height of the second candle.
12 - 3x = 2(12 - 4x)
12 - 3x = 24 - 8x
5x = 12
x = 2.4 hours = 2 hours 24 minutes

work rate of men =2x
Work rate of women = 3x
Total work done in 12 days = (40*2x(men's Work) + 20*3x(women's Work))*12
Half work to be done by men in 7 days will be equal to =(140*12x/7)*1/2x(men's Work rate)*1/2(Half work)
gives 60 Men
Answer D.

Should be A. 50mph as the distance comes out to be 55 ft + 137 ft = 192 ft
Rest all go more than 200 ft easily

Number of individuals = C
Amount paid by each individual = n
Total expected amount = Charity's goal = nC = x
n = x/C
Number of individuals who fail to pay = d
Contribution from individuals who would fail to pay = dx/C --> Additional amount
Number of individuals who are paying = C - d
Additional amount has to be divided among the (C - d) individuals --> dx/C(C - d)
Answer: E

From the above table clearly, only for food B, the protein content per dollar is more compared to that of any other foods or combinations.

Given set in ascending order is {n, n+1, n+2, n+4, n+8}.

What is the value of (10⁴ − 10²) ∗ 0.00(12) ? (You can indicate repeated part of the decimal by putting it in brackets) You can solve it as Pinali suggests above, just open the brackets and multiply: (10⁴ − 10²) ∗ 0.00(12) = 10,000∗0.00(12) − 100∗0.00(12) = 12.(12) − 0.(12) = 12, you can see that 0.(12) part is subtracted from 12.(12) which gives 12. But you can do this problem in another way too: 0.00(12) can be written as fraction 12/9,900 (as many 9's as numbers in repeated pattern and as many zeros after as zeros after decimal point). For more on how to convert a recurring decimal to fraction see Number Theory chapter of Math Book (link in my signature).

Answer: E.

8! = 2⁷∗3²∗5∗7
Any factor of 8! can be written as 2^a∗3^b∗5^c∗7^d , where a, b, c and d are integers
a can take 8 values (0 to7)
b can take 3 values (0 to 2)
c can take 2 values (0 to 1)
d can take 2 values (0 to 1)

Number of factors = 8*3*2*2

If the factor of 8! is multiple of 28, in that case-
a can take 6 values (2 to 7)
b can take 3 values (0 to 2)
c can take 2 values (0 to 1)
d can take 1 value (only 1)

Number of multiples of 28 = 6*3*2*1