Question

information about the students at jackson high school is shown in the table.

	tenth grade	eleventh grade	twelfth grade	total
boys		179		511
total	376		306	1,034

which statement must be true?

• out of the 352 eleventh graders at the school, 173 of them are girls.
• out of the 511 boys at the school, 150 of them are tenth graders.
• out of the 523 tenth graders at the school, 173 of them are boys.
• out of the 376 girls at the school, 182 of them are eleventh graders.

Explanation:

To solve this, we analyze each option using the table data:

Step 1: Analyze Option 1

First, find the number of eleventh - grade students. The total number of students in tenth grade is 376, in twelfth grade is 306, and the total number of students in the school is 1034. So the number of eleventh - grade students is \(1034-(376 + 306)=1034 - 682 = 352\).
The number of girls in eleventh grade: Total girls are 523, girls in tenth grade are 194, girls in twelfth grade are 156. So girls in eleventh grade is \(523-(194 + 156)=523 - 350 = 173\).
So out of 352 eleventh - graders, 173 are girls. This statement is true.

Step 2: Analyze Option 2

Number of boys in tenth grade: Total boys are 511, boys in eleventh grade: boys in eleventh grade = total boys-(boys in tenth + boys in twelfth). Boys in twelfth grade is \(511-(179 + \text{boys in tenth})\)? Wait, total in tenth grade is 376, girls in tenth grade is 194, so boys in tenth grade is \(376 - 194 = 182\).
Number of boys in eleventh grade: total boys (511)-boys in tenth (182)-boys in twelfth (let's find boys in twelfth: total in twelfth is 306, girls in twelfth is 156, so boys in twelfth is \(306 - 156 = 150\)). So boys in eleventh grade is \(511-(182 + 150)=511 - 332 = 179\).
The claim is out of 511 boys, 150 are tenth - graders. But we found boys in tenth grade is 182, not 150. So this is false.

Step 3: Analyze Option 3

Total tenth - graders: 376. Girls in tenth grade: 194, so boys in tenth grade: \(376 - 194 = 182\). The claim is out of 523 tenth - graders, 173 are boys. But total tenth - graders are 376, not 523. So this is false.

Step 4: Analyze Option 4

Total girls: 523. Girls in tenth grade: 194, girls in twelfth grade: 156, so girls in eleventh grade: \(523-(194 + 156)=173\). The claim is out of 376 girls, 182 are eleventh - graders. But total girls are 523, not 376. So this is false.

Answer:

Out of the 352 eleventh graders at the school, 173 of them are girls. (The first option)