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(1)
Total price for Row n: 8×Xn (since there are 8 items in the row, each contributing to the average Xn)
The total price for all rows combined is 8X1+8X2+8X3+8X4+8X5=8(X1+X2+X3+X4+X5)=6800

Average price = 6800/40 = 170

Statement (1) alone is sufficient.

(2)
Total price for Column n: 5×Yn (since there are 5 items in the column, each contributing to the average Yn)
The total price for all columns combined is 5Y1+5Y2+5Y3+5Y4+5Y5+5Y6+5Y7+5Y8=5(Y1+Y2+Y3+Y4+Y5+Y6+Y7+Y8)=6800

Average price = 6800/40 = 170

Statement (2) alone is sufficient.

Answer D
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The average price of all items is $170. Statement (1) gives 850/5=170, and statement (2) gives 1360/8=170; each statement alone is sufficient.

Bunuel
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 \(X_m\) [1 ≤ m ≤5]. The average of the price of items in each column (n) is \(Y_n\) [1 ≤ n ≤ 8]. What is the average price of all items on the rack?

(1) \(X_1 + X_2 + ... + X_5 = $850\)
(2) \(Y_1 + Y_2 + ... + Y_8 = $1,360\)


 


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D- each statement is sufficient.

Statement 1- x1+x2+x3+x4+x5= 850
total price = 850*8=6800
Av price =6800/40

Statement 2- Y1 +y2....+y8= 1360
total price =1360*5=6800
Av. price =6800/40
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It's letter D because you can know the average of all items knowing the average of the rows or the columns.
Bunuel
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 \(X_m\) [1 ≤ m ≤5]. The average of the price of items in each column (n) is \(Y_n\) [1 ≤ n ≤ 8]. What is the average price of all items on the rack?

(1) \(X_1 + X_2 + ... + X_5 = $850\)
(2) \(Y_1 + Y_2 + ... + Y_8 = $1,360\)


 


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GMAT Club Olympics 2025 (Day 1): In a store, 40 items are arranged on 30 Jun 2025, 20:19
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1) avg= x1+x2+.......x5/5 = 850/5 =170 sufficient
2) y1+y2+.......+ y8/8 = 1360/8= 170 sufficient
ANS: D both r sufficient
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(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
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GMAT Club Olympics 2025 (Day 1): In a store, 40 items are arranged on 30 Jun 2025, 20:35
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Bunuel
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 \(X_m\) [1 ≤ m ≤5]. The average of the price of items in each column (n) is \(Y_n\) [1 ≤ n ≤ 8]. What is the average price of all items on the rack?

(1) \(X_1 + X_2 + ... + X_5 = $850\)
(2) \(Y_1 + Y_2 + ... + Y_8 = $1,360\)
Show more
We need the total sum of prices to compute the overall average.
Total items = 5 × 8 = 40

(1) Row averages given:

Total sum = (X1+X2+⋯+X5)×8=850×8=6800 Sufficient

(2) Column averages given:

Total sum = (Y1+Y2+⋯+Y8)×5=1360×5=6800 Sufficient

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

(D)
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Bunuel
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 \(X_m\) [1 ≤ m ≤5]. The average of the price of items in each column (n) is \(Y_n\) [1 ≤ n ≤ 8]. What is the average price of all items on the rack?

(1) \(X_1 + X_2 + ... + X_5 = $850\)
(2) \(Y_1 + Y_2 + ... + Y_8 = $1,360\)


 


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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
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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.
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(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
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(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
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Col 1Col 2Col 3Col 4Col 5Col 6Col 7Col 8Row Avg
Row 1A11A12A13A14A15A16A17A18X1
Row 2A21A22A23A24A25A26A27A28X2
Row 3A31A32A33A34A35A36A37A38X3
Row 4A41A42A43A44A45A46A47A48X4
Row 5A51A52A53A54A55A56A57A58X5
Col AvgY1Y2Y3Y4Y5Y6Y7Y8


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
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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.
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GMAT Club Olympics 2025 (Day 1): In a store, 40 items are arranged on 30 Jun 2025, 21:42
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Quote:
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
[ltr]XmXm[/ltr]
[1 ≤ m ≤5]. The average of the price of items in each column (n) is
[ltr]YnYn[/ltr]
[1 ≤ n ≤ 8]. What is the average price of all items on the rack?

(1)
[ltr]X1+X2+...+X5=$850[/ltr]

(2)
[ltr]Y1+Y2+...+Y8=$1,360
[/ltr]
Show more
[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]
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GMAT Club Olympics 2025 (Day 1): In a store, 40 items are arranged on 30 Jun 2025, 21:45
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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.
Bunuel
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 \(X_m\) [1 ≤ m ≤5]. The average of the price of items in each column (n) is \(Y_n\) [1 ≤ n ≤ 8]. What is the average price of all items on the rack?

(1) \(X_1 + X_2 + ... + X_5 = $850\)
(2) \(Y_1 + Y_2 + ... + Y_8 = $1,360\)


 


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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
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Quote:
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
XmXm
[1 ≤ m ≤5]. The average of the price of items in each column (n) is
YnYn
[1 ≤ n ≤ 8]. What is the average price of all items on the rack?
Show more

(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)
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Bunuel
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 \(X_m\) [1 ≤ m ≤5]. The average of the price of items in each column (n) is \(Y_n\) [1 ≤ n ≤ 8]. What is the average price of all items on the rack?

(1) \(X_1 + X_2 + ... + X_5 = $850\)
(2) \(Y_1 + Y_2 + ... + Y_8 = $1,360\)


 


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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
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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

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GMAT Club Olympics 2025 (Day 1): In a store, 40 items are arranged on 30 Jun 2025, 22:38
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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)
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