Solution:

19

Explanation:
77 empty bottles = 15 full bottles + 2 empty bottles
15 full bottles will give him 15 empty bottles more.
15 + 2 = 17
17 empty bottles = 3 full bottles + 2 empty bottles
3 full bottles will give him 2 empty bottles more.
3 + 2 = 5
5 empty bottles = 1 filled bottle

15 + 3 + 1 = 19

Thus we will be able to get 19 full bottles of soft drink.

Solution:

Box A has five balls and Box B has seven balls.

Solution:

The number is 281.

Solution:

18

Explanation:
Number of days with snow in morning and clear afternoon = A
Number of days with clear morning and snow in afternoon = B
Number of days with no snowfall in morning or afternoon = C

Now, number of days with snowfall = A + B = 13
Number of days with clear mornings = B + C = 11
Number of days with clear afternoons = A + C = 12

Adding these three equations, we get

2 * (A + B + C) = 36
Or, A + B + C = 18

Therefore, they spent eighteen days in total at their vacation.

Solution:

Assuming that John has A number of apples and Jacobs has B number of apples.

As per the question,
A + 1 = B - 1
=> B - A = 2 ------ (p)

Also, A - 1 = (B + 1) / 2
=> 2A - B = 3 ------ (q)

Solving (p) and (q)
A = 5 and B = 7

Therefore, A has 5 chocolates and B has 7 chocolates right now.

Solution:

119

Explanation:
Let the minimum number of chocolates = C
When divided by 2, remainder = 1
When divided by 3, remainder = 2
When divided by 4, remainder = 3
When divided by 5, remainder = 4
When divided by 6, remainder = 5
When divided by 7, remainder = 0

Therefore, C is divisible by 7.

Whenever C is divided by any number less than 7, the remainder is 1 less than the divisor.
This implies that, C + 1 is the LCM of 2, 3, 4, 5 and 6.

Now LCM of 2, 3, 4, 5 and 6 = 60
But 60 - 1 = 59 is not divisible by 7

60 * 2 = 120
120 - 1 = 119 which is divisible by 7

Therefore, C + 1 = 120 or C = 119

Number of minimum number of chocolates in the box = 119

Solution:

18

Explanation:
Let us suppose that there were (3 * G) garlic bread sticks originally.

On dividing equally, the number of bread sticks with each of the friend = G

Each one of them ate four. The remaining sticks with each one of them = (G - 4)

Now, the total number of breadsticks left = 3 * (G - 4)
This number is equal to the breadsticks each one of them had after division.

=> 3 * (G - 4) = G
(3 * G) - 12 = G
2 * G = 12
G = 6.

Therefore, the number of breadsticks originally = 3 * G = 3 * 6 = 18.

Solution:

2hr 11min

Explanation:
Now this question cannot be solved unless you know a fact i.e. the hour hand is exactly on the minute mark five times every hour - on the hour, 12 minutes past hour, 24 minutes past hour, 36 minutes past hour and 48 minutes past hour.

Denoting the number of hours with X and the number of minutes as Y, let us begin with the calculation.

When we have the hour hand on the minute mark, the position of hour hand:
5X + Y/12
And the position of the minute hand = Y

When the first observation was taken,
Y = Y = 5X + Y/12 + 6
Or, 60X = 11Y - 72.

With the given facts, we know for sure that Y can only be 0, 12, 24, 36 or 48.
According to which, the possible values for X and Y can be 1 and 12 respectively. Thus the time must be 1:12 when the first observation was taken.

Similarly, in the second observation, let's make the equation:
60X = 11Y - 84
Here, the possible values for X and Y here are 3 and 24 respectively. According to this, the time is 3:24 for sure.

From 1:12 to 3:24, two hours and eleven minutes have passed.

Solution:

6

Explanation:
(2^x)(30^3) = (2^3) (3^3) (4^3) (5^3)

(2^x)(30^3) = (120^3)

(2^x) = (120^3)/ (30^3)

(2^x) = (4^3)

(2^x) = 64

ln(2^x) = ln(64)

x ln(2) = ln(64)

x = ln(64)/ln(2)

x = 6

Thus x = 6.

Solution:

7.5Km

Explanation:
Denoting Ashley with A and Cecelia with C

Speed A = 60 km/hr = 1.2 x Speed C [km/hr] = 1 km/ min

Hence Speed C = 60/1.2 [km/hr] = 50 [km/hr] = 5/6 km/ min

Time C = D [km] /Speed C [km/min] = D/Speed C [min] = D/(5/6) min = 6D/5 min = 1.2 D min

Time A = D [km] /Speed A [km/min] = D/Speed A [min] = D/(1) min = D min

Since Time C – Time A = 1.5 min

Then (1.2 – 1)D min = 0.2D min = 1.5 min



Hence D = 1.5/0.2 km = 1.5*5 = 7.5 km

The total distance as calculated above is 7.5 Km.