Practice Questions Chat

Critical Reasoning Butler: September 2024
September 13	CR 1	CR 2

Data Sufficiency Butler: September 2024
September 13	DS 1	DS 2

Hi, Can anyone help with this question?

Let’s assume the merchant intends to buy and sell 1 meter (100 cm) of cloth.

### When buying:
- The merchant uses a 120 cm faulty scale instead of 100 cm.
- So, when he buys 1 meter of cloth, he actually gets \( \frac{120}{100} \times 100 = 120 \) cm of cloth.
- Therefore, for every 1 meter he buys, he gets 1.2 meters of cloth.

### When selling:
- The merchant uses an 80 cm faulty scale instead of 100 cm.
- So, when he sells 1 meter of cloth, he actually gives only \( \frac{80}{100} \times 100 = 80 \) cm of cloth.
- Therefore, for every 1 meter he sells, he actually gives 0.8 meters of cloth.

### Profit without discount:
- The merchant buys 1.2 meters of cloth and sells only 0.8 meters as 1 meter.
- The effective amount of cloth sold for 1 meter is \( \frac{1.2}{0.8} = 1.5 \).
- Therefore, his profit is \( 1.5 - 1 = 0.5 \) or 50%.

### Considering the discount:
- After offering a 20% discount, the merchant sells the cloth at 80% of the price.
- So, the selling price becomes 80% of the marked price, which reduces his profit.

### Adjusted profit with the discount:
- The profit with the discount is \( 1.5 \times 0.8 = 1.2 \).
- Therefore, his profit is \( 1.2 - 1 = 0.2 \) or 20%.

Thus, the merchant’s overall profit is **20%**.

Let x, y and z be the number of lawyers with licence in only each of the states respectively.
Let a be the number of lawyers with licence in all 3 states

x + a = 10. (1)
y + a = 11. (2)
Z + a = 13. (3)
x + y + z = 28 (4)


Therefore:
x = 10 - a. (5)
y = 11 - a. (6)
z = 13 - a. (7)

10-a+11-a+13-a =28
34 -2a = 28
2a = 6
a = 3

From eqn 7
z = 13 - 3
z = 10

update to
10-a+11-a+13-a+ a = 28
Same solution, missed writing the “+a” part

Thank you ObyJenny

Logical Way:

28 Lawyers but 10+11+13 = 34 counts.

It means, we have 6 counts extra coming from lawyers who are on a triple duty (double duty is forbidden as it is given that a lawyer either works at 1 firm OR all 3).

Those on triple duty are leaving 2 counts each extra....6/2 = 3
This means, there are 3 lawyers that are on triple duty.

So, each firm’s count minus 3 will give lawyer’s working only for their own firm, which is 13 - 3 = 10 in case of firm Z

Mathematical Way :

Let P be lawyers working for ONLY 1 firm
Let Q be lawyers working for all the 3 firms

Total count = 10+11+13 = 34
Number of lawyers = 28 (given)

So,

P*1 + Q*3 = 34 and,
P + Q = 28

This gives P as 25, and Q as 3.

Lawyers working only at a single firm would be firm size minus Q,
which, for Firm Z, is 13 - 3 = 10

Hello everyone, I have my exam scheduled tomorrow, any quick tips would be appreciated for all 3 sections(especially for verbal).

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66/11*2 ---where P is 2, an prime number, and the odd prime will be 3 which has for least value of X is 66.

X/11p>=3 I.e x>=33p>=66

0.64*50*M + x = 0,7*50 (M+1)

32M + x = 35 (M+1) ->> x=3M+35

Problem Solving Butler: September 2024
September 16	PS 1	PS 2

Critical Reasoning Butler: August 2024
September 16	CR 1	CR 2

Data Sufficiency Butler: September 2024
September 16	DS 1	DS 2

Problem Solving Butler: September 2024
September 17	PS 1	PS 2