GMAT Club Olympics 2025 (Day 1): In a store, 40 items are arranged on

It's letter D because you can know the average of all items knowing the average of the rows or the columns.

1) avg= x1+x2+.......x5/5 = 850/5 =170 sufficient
2) y1+y2+.......+ y8/8 = 1360/8= 170 sufficient
ANS: D both r sufficient

(1)
We can calculate the sum of all the items of each row multiplying the average of that row and the number of items in each row (8).
8X1+8X2+8X3+8X4+8X5=8(X1+X2+X3+X4+X5)=8*850=6800
6800/40=170

Sufficient

(2)
We can calculate the sum of all the items of each column multiplying the average of that column and the number of items in each column (5)
5Y1+5Y2+5Y3+5Y4+5Y5+5Y6+5Y7+5Y8=5(Y1+Y2+Y3+Y4+Y5+Y6+Y7+Y8)=5*1360=6800
6800/40=170

Sufficient

Correct answer is D

We need the total sum of prices to compute the overall average.
Total items = 5 × 8 = 40

(1) Row averages given:

(2) Column averages given:

Both give total sum = 6800 → average = 6800/40=170

(D)

See, lets think a room with 5 row and 8 column which means in one roww we have 8 benches ? and simillalry we can think in 1 column we have 5 benches.

So statement 1 tells us average sum of thse 5 row , and if we try to find total AM, then we can arrange the benches so that it becomes 8 x ( X_1 + X_2 + ... + X_5) /40

Simillarly we can do for 2nd statement and we find that both statement is same so wither one of statement is true for finding us average price of all

Statement 1: Gives the sum of the average prices of the 5 rows.
Each row has 8 items → So total = 8 × (sum of row averages) = total price of all items.
Divide that by 40 → the average!

Statement 2: Gives the sum of the average prices of the 8 columns.
Each column has 5 items → So total = 5 × (sum of column averages) = total price of all items.
Again, divide by 40 → the average!

Answer: Each statement alone is sufficient.

(1): Since each of the 5 rows contains 8 items, the average price of a row multiplied by 8 gives the total price for that row. Summing the averages of all 5 rows and multiplying by 8 gives the total price of all 40 items. Dividing this total by 40 gives the average price of all items. So, this is sufficient.
Row averages × 8 items each → total = 8 × 850 = 6,800. Average = 6,800 ÷ 40 = 170 ✅

(2):Similarly, each of the 8 columns contains 5 items. The average price in each column multiplied by 5 gives the total for that column. Summing the averages of all 8 columns and multiplying by 5 gives the total price of all 40 items. Dividing by 40 gives the overall average. So, this is also sufficient.
Column averages × 5 items each → total = 5 × 1,360 = 6,800. Average = 6,800 ÷ 40 = 170 ✅

Ans: D

(1) X1+X2+...+X5 = 850
Sum of all the items = 8*X1+8*X2+...+8*X5 = 8*(X1+X2+...+X5) = 8*850 = 6800

Average = 6800/40 = 170

Statement is sufficient

(2) Y1+Y2+...+Y8 = 1360
Sum of all the items = 5*Y1+5*Y2+...+5*Y5 = 5*(Y1+Y2+...+Y5) = 5*1360 = 6800

Average = 6800/40 = 170

Statement is sufficient

The right answer is D

	Col 1	Col 2	Col 3	Col 4	Col 5	Col 6	Col 7	Col 8	Row Avg
Row 1	A11	A12	A13	A14	A15	A16	A17	A18	X1
Row 2	A21	A22	A23	A24	A25	A26	A27	A28	X2
Row 3	A31	A32	A33	A34	A35	A36	A37	A38	X3
Row 4	A41	A42	A43	A44	A45	A46	A47	A48	X4
Row 5	A51	A52	A53	A54	A55	A56	A57	A58	X5
Col Avg	Y1	Y2	Y3	Y4	Y5	Y6	Y7	Y8

Each statement is sufficient because it gives us the total price of all 40 items, which is all we need to find the average.

Statement (1) average price = 8×850/40 = 6,800/40 = 170
Statement (2) average price = 5×1,360/40 = 6,800/40 = 170

I will go with Option D

Let

• Xm = average price of the 8 items in row m (m=1,...,5)
• Yn = average price of the 5 items in column n (n=1,...,8)

Statement (1)
X1+X2+⋯+X5=850
Total price=8(850)=6,800
⟹Average=6,800/40=170.
So Statement (1) alone lets us compute the average — sufficient.

Statement (2)
Y1+Y2+⋯+Y8=1,360
Total price=5(1,360)=6,800
⟹Average=6,800/40=170.
Statement (2) alone is also sufficient.

Because each statement independently yields the overall average, the correct data-sufficiency choice is D.

[ltr]
From the given info, we know that 5*(X1+X2+X3+X4+X5)/40 = average of all

and also, 8*(Y1+.....Y8)/40 = average of all

Now, looking at the options:-

(1) X1+X2+...+X5=$850. This can answer the question alone.

(2) Y1+Y2+...+Y8=$1,360. This also answers the question on it's own.

Hence, the right choice here is (D)[/ltr]

Analysing the question stem:

The average price of all items on the rack would be Sum of all prices divided by 40.

(1) \(X_1 + X_2 + ... + X_5 = $850\)

we know that sum of n items = n * average. so each row, will be 8*X1, 8*X2..so on.

sum of all items = 8 * (X1+ X2 + ..... X5) = 8*850. Sufficient.

(2) \(Y_1 + Y_2 + ... + Y_8 = $1,360\)

sum = 5*1360. Sufficient.

Option (D) is the answer.

we know , avg x n = total
hence when we use each statement individually to get the answer. more reasoning: we can multiply the sum of averages x n (n here are the entities in 1 row / 1 column to derive the totals). answer: D

(1)
X1+X2+...+X5=$850

(2)
Y1+Y2+...+Y8=$1,360

From the given info, we know that 5*(X1+X2+X3+X4+X5)/40 = average of all

and also, 8*(Y1+.....Y8)/40 = average of all

Now, looking at the options:-

(1) X1+X2+...+X5=$850. This can answer the question alone.

(2) Y1+Y2+...+Y8=$1,360. This also answers the question on it's own.

Hence, the right choice here is (D)

There are \(5 \times 8 = 40\) items in total.
Let \(S\) be the total price of all 40 items.
The average price is \(S / 40\).
We are told:

• Each row has 8 items ⇒ total price = \(8(X_1 + X_2 + X_3 + X_4 + X_5)\)
• Each column has 5 items ⇒ total price = \(5(Y_1 + Y_2 + \cdots + Y_8)\)

Statement (1): \(X_1 + X_2 + \cdots + X_5 = 850\)
Then,
\(S = 8 \cdot (X_1 + X_2 + \cdots + X_5) = 8 \cdot 850 = 6800\)
Average = \(6800 / 40 = 170\)
Statement (1) is sufficient

Statement (2): \(Y_1 + Y_2 + \cdots + Y_8 = 1360\)
Then,
\(S = 5 \cdot (Y_1 + Y_2 + \cdots + Y_8) = 5 \cdot 1360 = 6800\)
Average = \(6800 / 40 = 170\)
Statement (2) is sufficient

Final Answer: D

Statement (1):
X1 + X2 + X3 + X4 + X5 = 850

So, total of all row sums =
X1 × 8 + X2 × 8 + ... + X5 × 8
= 8 × (X1 + X2 + ... + X5) = 8 × 850 = 6800

This is the total price of all 40 items.
Average price = 6800 / 40 = 170

So, Statement 1 is sufficient

Statement (2):
Y1 + Y2 + ... + Y8 = 1360

Total of all column sums =
5 × (Y1 + Y2 + ... + Y8) = 5 × 1360 = 6800

Average price = 6800 / 40 = 170

So, Statement 2 is also sufficient

Answer: Each statement alone is sufficient

Pankaj Jindal | GMAT Classic 730 | IIM Bangalore | Helping working professionals
Success story: https://gmatclub.com/forum/how-i-scored ... l#p3588949

In a store, 40 items are arranged on a rack in 5 rows and 8 columns. The average (arithmetic mean) of the price of items in each row (m) is Xm [1 ≤ m ≤5]. The average of the price of items in each column (n) is Yn [1 ≤ n ≤ 8]. What is the average price of all items on the rack?
(1) X1+X2+...+X5=$850
(2) Y1+Y2+...+Y8=$1,360

So the average price of all the items on the rack = [8(X1+X2+.....+X5) + 5(Y1+Y2+....+Y8)] / 40
So we need to know the values of X1+X2+...+X5 and Y1+Y2+....+Y8

St1: Insufficient
St2: Insufficient
Together: Sufficient

Answer: (C)