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 . The average of the price of items in each column (n) is Y_n . 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

D. Statement (1) alone is sufficient: It provides the sum of the average prices of the rows (X1 + X2 + ... + X5 = $850). Since there are 8 columns in each row, the total price of all items is 8 * (X1 + X2 + ... + X5) = 8 * $850 = $6800. The average price is then $6800 / 40 items = $170. Statement (2) alone is sufficient: It provides the sum of the average prices of the columns (Y1 + Y2 + ... + Y8 = $1,360). Since there are 5 rows in each column, the total price of all items is 5 * (Y1 + Y2 + ... + Y8) = 5 * $1360 = $6800. The average price is then $6800 / 40 items = $170.

average price of all items = total price / number of items We can calculate total price by: average price each row: 8*X1 + 8*X2 +...+ 8*X5 = 8*(X1+X2+...+X5) average price each column: 5*Y1 + 5*Y2 +...+ 5*Y8 = 5*(Y1+Y2+...+Y8) Answer: D

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

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AviNFC

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Reqd average = 8*(X1+X2+X3+X4+X5)/40 OR 5*(Y1+Y2+....Y8)/40

1. X1+X2..+X5= given... Sufficient
2. Y1+Y2..+Y8=given..sufficient

Both are sufficient
Ans D

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Statement (1) alone is sufficient: It provides the sum of the average prices of the rows (X1 + X2 + ... + X5 = $850). Since there are 8 columns in each row, the total price of all items is 8 * (X1 + X2 + ... + X5) = 8 * $850 = $6800. The average price is then $6800 / 40 items = $170.
Statement (2) alone is sufficient: It provides the sum of the average prices of the columns (Y1 + Y2 + ... + Y8 = $1,360). Since there are 5 rows in each column, the total price of all items is 5 * (Y1 + Y2 + ... + Y8) = 5 * $1360 = $6800. The average price is then $6800 / 40 items = $170.

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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for each statment we know the sum of the averages, that divided by 5 for X and 8 for Y will give us the average

Bunuel

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

Using Method 1:
Sum of all prices = 8 × $850 = $6,800
Average price = $6,800/40 = $170
This is sufficient.

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

Using Method 2:
Sum of all prices = 5 × $1,360 = $6,800
Average price = $6,800/40 = $170
This is also sufficient.

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(1) $850 is the sum of the average of the price of items in 5 rows. So the Average of each item is: $850/5 = $170
(2) $1360 is the sum of the average of the price of items on 8 rows. So the Average of each item is: $1360/8 = $170

Therefore, (D) EACH statement ALONE is sufficient!

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To find the average price of all the items on the rack, we would need to find the sum of all items on the rack and then divide the sum by 40.

1. $X_1 + X_2+ X_3 + X_4 + X_5 = 850 $

We know, $X_m = \frac{S_m}{8}$, where $S_m$ is the sum of the prices of all items in row $m$

Then, $X_1 + X_2+ X_3 + X_4 + X_5 = \frac{S_1 + S_2 + S_3 + S_4 + S_5}{8}$
$850*8 = S_1 + S_2 + S_3 + S_4 + S_5$
$S_1 + S_2 + S_3 + S_4 + S_5$ is the sum of the prices of all items on the rack. Dividing this by 40 should get us the average price of all items on the rack

Statement 1 is sufficient.

2. $Y_1+Y_2+...+Y_8 = $1,360$

We know, $Y_n = \frac{S_n}{5}$, where $S_n$ is the sum of the prices of all items in column $n$

Then, $Y_1 + Y_2+......+ Y_8 = \frac{S_1 + S_2 +......+ S_8}{5}$
$1360*5 = S_1 + S_2 +......+ S_8 $
$ S_1 + S_2 +......+ S_8 $ is the sum of the prices of all items on the rack. Dividing this by 40 should get us the average price of all items on the rack

Statement 2 is sufficient.

Answer - D (EACH Statement ALONE is sufficient)

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average price of all items = total price / number of items
We can calculate total price by:

average price each row: 8*X1 + 8*X2 +...+ 8*X5 = 8*(X1+X2+...+X5)
average price each column: 5*Y1 + 5*Y2 +...+ 5*Y8 = 5*(Y1+Y2+...+Y8)

Answer: D

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Total Items 40.
Let's say items are arranged n1, n2 ... n8 in Row 1.
n9, ..n16 in Row 2 and so on till ... n32... n40 in Row 5.

Given X1= Sum(n1, n2, ... n8)/8
similarly X2 = Sum (n9,... ,n16)/8

Avg of all items = Sum( All items prices)/ 40

A. $X_1 + X_2 + ... + X_5 = $850$ = Sum (all items prices)/ 8 -> Sum of all items prices -> Avg Price of all items. SUFFICIENT
B. Similar to A, we can calculate from B. Sequence of Sum of price will be different in Y_1.. Y_2 but overall on sum all items prices will be covered. SUFFICIENT

D is the Answer

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ans C, sum of each row average, then 8(X1 to X5 ), then it will be the sum of all 6800, same as all column average, then 5 ( y1+..to y8) is 6800, then we can easily find avg from each statement.

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S1 - Total sum of all elements = 8(X1) +8(X2)... +8(X5) = 8(X1+X2+...+X5) = 8(850)
total terms = 8 x 5 = 40
Average of all terms = 8(850)/40

Sufficient

S2 - Total sum of all elements = 5(Y1) + 5(Y2) ... +5(Y3) = 5(1360)

Average of all terms = 5(1360)/8

Sufficient

hence answer = D

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D. EACH statement ALONE is sufficient.

The sum of all prices for the products = 8(X1 + X2 +...+ Xn) = 5(Y1 + Y2 +...+ Yn) = S --> A

Total products = 40

Given the formula for mean = S/40, either statement will suffice.

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Since the Avg price for each row/column is given we can calculate the Ag price of all the elemets in both cases independentaly

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Option D
Average price of all items in a row= Xm
=> Total price of all items in a row/8= Xm (there are 8 items in a row)
Average price of all items in a column= Yn
=> Total price of all items in a column/5= Yn (there are 5 items in a column)

S1: X1+X2+X3+X4+X5= $850
=> (total price of items in R1+R2+R3+R4+R5)/8= $850
=> Total price of items in R1+R2+R3+R4+R5= $(850*8)= $6,800
=> Average price of all items on the rack= 6,800/40= $170
SUFF

S2: Y1+Y2+Y3+Y4+Y5+Y6+Y7+Y8=$1,360
=> (total price of items in C1+C2+C3+C4+C5+C6+C6+C7+C8)/5= $1,360
=> Total price of items in C1+C2+C3+C4+C5+C6+C6+C7+C8= $(1,360*5)= $6,800
=> Average price of all items on the rack= 6,800/40= $170
SUFF

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ANS C

(1) X1+X2+...+X5=$850
As they ask for average, we can have the total sum of the elements of each row by multiplying it by the total number of elements in each row. In order to have the sum of all the 40 elements we must add the product of the average of each row by 8 and then divided by 40.
So we multiply all the equation by 8
X1(8)+X2(8)+X3(8)+X4(8)+X5(8)=$850(8)= 6,800
and then that sum divided by 40
SUFFICIENTE

(2) Y1+Y2+...+Y8=$1,360
the same for this case
As they ask for average, we can have the total sum of the elements each column by multiplying it by the total number of elements in each column. In order to have the sum of all the 40 elements we must add the product of the average of each column by 5 and then divided by 40.
So we multiply all the equation by 5
X1(5)+X2(5)+X3(5)+X4(5)+X5(5)=$1360(5)= 6,800
and then that sum divided by 40
SUFFICIENTE

It doesn't matter the value of each average per row of column as the most important thing for an average is the total sum of the elements and the total number of elements, and in both cases we have this information.

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X1+X2+X3+X4+X5
X1=x11+x12+x13+x14+x15+x16+x17+x18
X2=X21+..........x28
.
.
X5=x51+x52+......x58
Thus X1to X5 includes all 40 items

Thus total price = 8*(X1+....X5)= 8*850=6800
Avg Price= 6800/40=170

Option 1 is sufficient

Option 2

Y1+Y2+Y3+Y4+Y5+Y6+Y7+Y8
Y1=y11+y12+y13+y14+y15
Y2=y21+..........y25
.
.
Y8=y81+y82+......y85
Thus Y1to Y5 includes all 40 items

Thus total price = 5*(Y1+....Y8)= 5*1360=6800
Avg Price= 6800/40=170

Option 2 is sufficient

Correct answer is D

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Ans: D (both statement alone are sufficient)

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?

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

Each row has 8 items in it. and average of those items for first row is X1. so total price of those 8 items in first row = 8 * X1
same way for the rest of the 4 rows = 8 * X2, 8 * X3, 8 * X4, and 8 * X5
toal price of 40 items = 8 * ( X1 + X2 + ... + X5) = 8 * 850 = 6800
Average of 40 items = 6800/40 = 170 [Sufficient]

Statement (2): Y1 + Y2 + ... + Y8 = $1,360
same way, total of 40 items = 5 * ( Y1 + Y2 + ... + Y8) = 5 * 1360= 6800
Average = 170 [Sufficient]

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Statement (1): X1+X2+X3+X4+X5=850
Each Xm is the average of 8 items (since there are 8 columns in each row).
So, total price in row m = Xm×8
Therefore:

Total price of all 40 items =
8×(X1+X2+X3+X4+X5)=8×850=6,800

Average price = Total / 40 = 6,800/40=170

So, Statement (1) is sufficient.

Statement (2): Y1+Y2+⋯+Y8=1,360
Each Yn is the average of 5 items (since there are 5 rows in each column).
So, total price in column n= Yn×5

Total price of all items =
5×(Y1+Y2+⋯+Y8)=5×1,360=6,800
So, Average price = 6,800/ 40=170
So, Statement (2) is also sufficient.

Final Answer: D

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Average is calculated as sum of all outcomes/Number of outcomes.

Given:
40 items arranged in 5 rows 8 columns that mean each row will have 8 items or each column will have 5 items.

Avg price in row is Xn
and Avg price in column is Yn

Question:
What is avg price of item on all racks.
we need sum of price of all items.

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

We know,
Xn= sum of price of all items in row n (Sn) / 8

So we can write
(S1/8 +S2/8 +S3/8+ S4/8+ S5/8)=$850

1/8 can be brought out as common factor

so it will look like (1/8)*(S1+S2+S3+S4+S5)=$850
so sum of all items can be concluded to be 850*8, i.e 6800
Avg can be 6800/40

So st1 sufficient.

Statement 2 works on same logic as above.

So Statement 2 is also Sufficent

The answer is D both alone are sufficient.

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There are 40 items in 5 rows and 8 columns. So each row has 8 items and each column has 5 items.
Xm = Average of prices of items in row "m". So, 8Xm = Sum of prices of items in row "m". So, 8X1 + 8X2 + 8X3 + 8X4 + 8X5 = Sum of prices of all the items.
Yn = Average of prices of items in column "n". So, 5Yn = Sum of prices of items in column "n". So, 5Y1 + 5Y2 + ... + 5Y8 = Sum of prices of all the items.

Analyzing Statement 1: X1+X2+...+X5=$850
Since, X1 + X2 + X3 + X4 + X5 is given, sum of prices of all items could be calculated as explained above. Average price of all items = Sum of prices of all products/Total number of items.
So, average = 8*850/40 = $170.

Analyzing Statement 2: Y1+X2+...+Y8=$1,360
Since, Y1 + Y2 + ... + Y8 is given, sum of prices of all items could be calculated as explained above. Average price of all items = Sum of prices of all products/Total number of items.
So, average = 5*1360/40 = $170.

So, each statement alone is sufficient to find the average price of all items on the rack.

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1. 850/5= 170
2. 170
C

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