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30 Jun 2025, 09:18
Kudos
Bookmarks
Average of prices in each row (Xm):
For each row m,
Xm=(Prices of items in 8 columns)/8
So sum of prices in row m=8*Xm
Average of prices in each column (Yn):
For each column n,
Yn=(Prices of items in 5 rows)/5
So sum of prices in row m=5*Yn
Statement (1): X1+X2+⋯+X5=$850
From Statement (1), we are given X1+X2+⋯+X5=850.
So, Total Sum of Prices = 8×850=$6800.
Average Price = (Total number of items)/Total Sum =(6800)/40=$170.
Statement (2): Y1+Y2+⋯+Y8=$1,360
From Statement (2), we are given Y1+Y2+⋯+Y8=1360.
So, Total Sum of Prices = 5×1360=$6800.
Average Price = (Total number of items)/Total Sum =(6800)/40=$170.
Hence,
D) Both statements alone are sufficient to answer the question.
For each row m,
Xm=(Prices of items in 8 columns)/8
So sum of prices in row m=8*Xm
Average of prices in each column (Yn):
For each column n,
Yn=(Prices of items in 5 rows)/5
So sum of prices in row m=5*Yn
Statement (1): X1+X2+⋯+X5=$850
From Statement (1), we are given X1+X2+⋯+X5=850.
So, Total Sum of Prices = 8×850=$6800.
Average Price = (Total number of items)/Total Sum =(6800)/40=$170.
Statement (2): Y1+Y2+⋯+Y8=$1,360
From Statement (2), we are given Y1+Y2+⋯+Y8=1360.
So, Total Sum of Prices = 5×1360=$6800.
Average Price = (Total number of items)/Total Sum =(6800)/40=$170.
Hence,
D) Both statements alone are sufficient to answer the question.
30 Jun 2025, 09:20
Kudos
Bookmarks
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) \(Y_1 + Y_2 + ... + Y_8 = $1,360\)
(1) \(X_1 + X_2 + ... + X_5 = $850\)
(2) \(Y_1 + Y_2 + ... + Y_8 = $1,360\)
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Statement 1
(1) \(X_1 + X_2 + ... + X_5 = $850\)
Total Price of Row 1 = X_1 * 8
Total Price of Row 2 = X_2 * 8
.
.
Total Price of Row 5 = X_5 * 8
Total Price = 8(X_1+X_2 .. + X_5) = 8 * 850 = 6800
Sufficient.
Statement 2
(2) \(Y_1 + Y_2 + ... + Y_8 = $1,360\)
Total Price of Column 1 = Y_1 * 5
Total Price of Column 2 = Y_2 * 5
.
.
Total Price of Column 8 = Y_8 * 5
Total Price = 5* (Y_1+Y_2 .. + Y_8) = 5 * 1360 = 6800
Sufficient.
Option D
30 Jun 2025, 09:20
Kudos
Bookmarks
Statement 1:
Avg of all items = Avg of items in rows/5 = 850̣/5 = 170
Statement 2:
Avg of all items = Avg of items in columns/8 = 1360/8 = 170
So, option D.
Avg of all items = Avg of items in rows/5 = 850̣/5 = 170
Statement 2:
Avg of all items = Avg of items in columns/8 = 1360/8 = 170
So, option D.
